Date: 2022-03-31T04:48:40+00:00

Actual source code: ts.c

      1: #include <petsc/private/tsimpl.h>
      2: #include <petscdmshell.h>
      3: #include <petscdmda.h>
      4: #include <petscviewer.h>
      5: #include <petscdraw.h>
      6: #include <petscconvest.h>

      8: #define SkipSmallValue(a,b,tol) if (PetscAbsScalar(a)< tol || PetscAbsScalar(b)< tol) continue;

     10: /* Logging support */
     11: PetscClassId  TS_CLASSID, DMTS_CLASSID;
     12: PetscLogEvent TS_Step, TS_PseudoComputeTimeStep, TS_FunctionEval, TS_JacobianEval;

     14: const char *const TSExactFinalTimeOptions[] = {"UNSPECIFIED","STEPOVER","INTERPOLATE","MATCHSTEP","TSExactFinalTimeOption","TS_EXACTFINALTIME_",NULL};

     16: static PetscErrorCode TSAdaptSetDefaultType(TSAdapt adapt,TSAdaptType default_type)
     17: {
     20:   if (!((PetscObject)adapt)->type_name) {
     21:     TSAdaptSetType(adapt,default_type);
     22:   }
     23:   return 0;
     24: }

     26: /*@
     27:    TSSetFromOptions - Sets various TS parameters from user options.

     29:    Collective on TS

     31:    Input Parameter:
     32: .  ts - the TS context obtained from TSCreate()

     34:    Options Database Keys:
     35: +  -ts_type <type> - TSEULER, TSBEULER, TSSUNDIALS, TSPSEUDO, TSCN, TSRK, TSTHETA, TSALPHA, TSGLLE, TSSSP, TSGLEE, TSBSYMP, TSIRK
     36: .  -ts_save_trajectory - checkpoint the solution at each time-step
     37: .  -ts_max_time <time> - maximum time to compute to
     38: .  -ts_max_steps <steps> - maximum number of time-steps to take
     39: .  -ts_init_time <time> - initial time to start computation
     40: .  -ts_final_time <time> - final time to compute to (deprecated: use -ts_max_time)
     41: .  -ts_dt <dt> - initial time step
     42: .  -ts_exact_final_time <stepover,interpolate,matchstep> - whether to stop at the exact given final time and how to compute the solution at that time
     43: .  -ts_max_snes_failures <maxfailures> - Maximum number of nonlinear solve failures allowed
     44: .  -ts_max_reject <maxrejects> - Maximum number of step rejections before step fails
     45: .  -ts_error_if_step_fails <true,false> - Error if no step succeeds
     46: .  -ts_rtol <rtol> - relative tolerance for local truncation error
     47: .  -ts_atol <atol> - Absolute tolerance for local truncation error
     48: .  -ts_rhs_jacobian_test_mult -mat_shell_test_mult_view - test the Jacobian at each iteration against finite difference with RHS function
     49: .  -ts_rhs_jacobian_test_mult_transpose -mat_shell_test_mult_transpose_view - test the Jacobian at each iteration against finite difference with RHS function
     50: .  -ts_adjoint_solve <yes,no> - After solving the ODE/DAE solve the adjoint problem (requires -ts_save_trajectory)
     51: .  -ts_fd_color - Use finite differences with coloring to compute IJacobian
     52: .  -ts_monitor - print information at each timestep
     53: .  -ts_monitor_cancel - Cancel all monitors
     54: .  -ts_monitor_lg_solution - Monitor solution graphically
     55: .  -ts_monitor_lg_error - Monitor error graphically
     56: .  -ts_monitor_error - Monitors norm of error
     57: .  -ts_monitor_lg_timestep - Monitor timestep size graphically
     58: .  -ts_monitor_lg_timestep_log - Monitor log timestep size graphically
     59: .  -ts_monitor_lg_snes_iterations - Monitor number nonlinear iterations for each timestep graphically
     60: .  -ts_monitor_lg_ksp_iterations - Monitor number nonlinear iterations for each timestep graphically
     61: .  -ts_monitor_sp_eig - Monitor eigenvalues of linearized operator graphically
     62: .  -ts_monitor_draw_solution - Monitor solution graphically
     63: .  -ts_monitor_draw_solution_phase  <xleft,yleft,xright,yright> - Monitor solution graphically with phase diagram, requires problem with exactly 2 degrees of freedom
     64: .  -ts_monitor_draw_error - Monitor error graphically, requires use to have provided TSSetSolutionFunction()
     65: .  -ts_monitor_solution [ascii binary draw][:filename][:viewerformat] - monitors the solution at each timestep
     66: .  -ts_monitor_solution_vtk <filename.vts,filename.vtu> - Save each time step to a binary file, use filename-%%03D.vts (filename-%%03D.vtu)
     67: -  -ts_monitor_envelope - determine maximum and minimum value of each component of the solution over the solution time

     69:    Notes:
     70:      See SNESSetFromOptions() and KSPSetFromOptions() for how to control the nonlinear and linear solves used by the time-stepper.

     72:      Certain SNES options get reset for each new nonlinear solver, for example -snes_lag_jacobian <its> and -snes_lag_preconditioner <its>, in order
     73:      to retain them over the multiple nonlinear solves that TS uses you mush also provide -snes_lag_jacobian_persists true and
     74:      -snes_lag_preconditioner_persists true

     76:    Developer Note:
     77:      We should unify all the -ts_monitor options in the way that -xxx_view has been unified

     79:    Level: beginner

     81: .seealso: TSGetType()
     82: @*/
     83: PetscErrorCode  TSSetFromOptions(TS ts)
     84: {
     85:   PetscBool              opt,flg,tflg;
     86:   PetscErrorCode         ierr;
     87:   char                   monfilename[PETSC_MAX_PATH_LEN];
     88:   PetscReal              time_step;
     89:   TSExactFinalTimeOption eftopt;
     90:   char                   dir[16];
     91:   TSIFunction            ifun;
     92:   const char             *defaultType;
     93:   char                   typeName[256];

     97:   TSRegisterAll();
     98:   TSGetIFunction(ts,NULL,&ifun,NULL);

    100:   PetscObjectOptionsBegin((PetscObject)ts);
    101:   if (((PetscObject)ts)->type_name) defaultType = ((PetscObject)ts)->type_name;
    102:   else defaultType = ifun ? TSBEULER : TSEULER;
    103:   PetscOptionsFList("-ts_type","TS method","TSSetType",TSList,defaultType,typeName,256,&opt);
    104:   if (opt) {
    105:     TSSetType(ts,typeName);
    106:   } else {
    107:     TSSetType(ts,defaultType);
    108:   }

    110:   /* Handle generic TS options */
    111:   PetscOptionsDeprecated("-ts_final_time","-ts_max_time","3.10",NULL);
    112:   PetscOptionsReal("-ts_max_time","Maximum time to run to","TSSetMaxTime",ts->max_time,&ts->max_time,NULL);
    113:   PetscOptionsInt("-ts_max_steps","Maximum number of time steps","TSSetMaxSteps",ts->max_steps,&ts->max_steps,NULL);
    114:   PetscOptionsReal("-ts_init_time","Initial time","TSSetTime",ts->ptime,&ts->ptime,NULL);
    115:   PetscOptionsReal("-ts_dt","Initial time step","TSSetTimeStep",ts->time_step,&time_step,&flg);
    116:   if (flg) TSSetTimeStep(ts,time_step);
    117:   PetscOptionsEnum("-ts_exact_final_time","Option for handling of final time step","TSSetExactFinalTime",TSExactFinalTimeOptions,(PetscEnum)ts->exact_final_time,(PetscEnum*)&eftopt,&flg);
    118:   if (flg) TSSetExactFinalTime(ts,eftopt);
    119:   PetscOptionsInt("-ts_max_snes_failures","Maximum number of nonlinear solve failures","TSSetMaxSNESFailures",ts->max_snes_failures,&ts->max_snes_failures,NULL);
    120:   PetscOptionsInt("-ts_max_reject","Maximum number of step rejections before step fails","TSSetMaxStepRejections",ts->max_reject,&ts->max_reject,NULL);
    121:   PetscOptionsBool("-ts_error_if_step_fails","Error if no step succeeds","TSSetErrorIfStepFails",ts->errorifstepfailed,&ts->errorifstepfailed,NULL);
    122:   PetscOptionsReal("-ts_rtol","Relative tolerance for local truncation error","TSSetTolerances",ts->rtol,&ts->rtol,NULL);
    123:   PetscOptionsReal("-ts_atol","Absolute tolerance for local truncation error","TSSetTolerances",ts->atol,&ts->atol,NULL);

    125:   PetscOptionsBool("-ts_rhs_jacobian_test_mult","Test the RHS Jacobian for consistency with RHS at each solve ","None",ts->testjacobian,&ts->testjacobian,NULL);
    126:   PetscOptionsBool("-ts_rhs_jacobian_test_mult_transpose","Test the RHS Jacobian transpose for consistency with RHS at each solve ","None",ts->testjacobiantranspose,&ts->testjacobiantranspose,NULL);
    127:   PetscOptionsBool("-ts_use_splitrhsfunction","Use the split RHS function for multirate solvers ","TSSetUseSplitRHSFunction",ts->use_splitrhsfunction,&ts->use_splitrhsfunction,NULL);
    128: #if defined(PETSC_HAVE_SAWS)
    129:   {
    130:     PetscBool set;
    131:     flg  = PETSC_FALSE;
    132:     PetscOptionsBool("-ts_saws_block","Block for SAWs memory snooper at end of TSSolve","PetscObjectSAWsBlock",((PetscObject)ts)->amspublishblock,&flg,&set);
    133:     if (set) {
    134:       PetscObjectSAWsSetBlock((PetscObject)ts,flg);
    135:     }
    136:   }
    137: #endif

    139:   /* Monitor options */
    140:   PetscOptionsInt("-ts_monitor_frequency", "Number of time steps between monitor output", "TSMonitorSetFrequency", ts->monitorFrequency, &ts->monitorFrequency, NULL);
    141:   TSMonitorSetFromOptions(ts,"-ts_monitor","Monitor time and timestep size","TSMonitorDefault",TSMonitorDefault,NULL);
    142:   TSMonitorSetFromOptions(ts,"-ts_monitor_extreme","Monitor extreme values of the solution","TSMonitorExtreme",TSMonitorExtreme,NULL);
    143:   TSMonitorSetFromOptions(ts,"-ts_monitor_solution","View the solution at each timestep","TSMonitorSolution",TSMonitorSolution,NULL);
    144:   TSMonitorSetFromOptions(ts,"-ts_dmswarm_monitor_moments","Monitor moments of particle distribution","TSDMSwarmMonitorMoments",TSDMSwarmMonitorMoments,NULL);

    146:   PetscOptionsString("-ts_monitor_python","Use Python function","TSMonitorSet",NULL,monfilename,sizeof(monfilename),&flg);
    147:   if (flg) PetscPythonMonitorSet((PetscObject)ts,monfilename);

    149:   PetscOptionsName("-ts_monitor_lg_solution","Monitor solution graphically","TSMonitorLGSolution",&opt);
    150:   if (opt) {
    151:     PetscInt       howoften = 1;
    152:     DM             dm;
    153:     PetscBool      net;

    155:     PetscOptionsInt("-ts_monitor_lg_solution","Monitor solution graphically","TSMonitorLGSolution",howoften,&howoften,NULL);
    156:     TSGetDM(ts,&dm);
    157:     PetscObjectTypeCompare((PetscObject)dm,DMNETWORK,&net);
    158:     if (net) {
    159:       TSMonitorLGCtxNetwork ctx;
    160:       TSMonitorLGCtxNetworkCreate(ts,NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,600,400,howoften,&ctx);
    161:       TSMonitorSet(ts,TSMonitorLGCtxNetworkSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxNetworkDestroy);
    162:       PetscOptionsBool("-ts_monitor_lg_solution_semilogy","Plot the solution with a semi-log axis","",ctx->semilogy,&ctx->semilogy,NULL);
    163:     } else {
    164:       TSMonitorLGCtx ctx;
    165:       TSMonitorLGCtxCreate(PETSC_COMM_SELF,NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);
    166:       TSMonitorSet(ts,TSMonitorLGSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);
    167:     }
    168:   }

    170:   PetscOptionsName("-ts_monitor_lg_error","Monitor error graphically","TSMonitorLGError",&opt);
    171:   if (opt) {
    172:     TSMonitorLGCtx ctx;
    173:     PetscInt       howoften = 1;

    175:     PetscOptionsInt("-ts_monitor_lg_error","Monitor error graphically","TSMonitorLGError",howoften,&howoften,NULL);
    176:     TSMonitorLGCtxCreate(PETSC_COMM_SELF,NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);
    177:     TSMonitorSet(ts,TSMonitorLGError,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);
    178:   }
    179:   TSMonitorSetFromOptions(ts,"-ts_monitor_error","View the error at each timestep","TSMonitorError",TSMonitorError,NULL);

    181:   PetscOptionsName("-ts_monitor_lg_timestep","Monitor timestep size graphically","TSMonitorLGTimeStep",&opt);
    182:   if (opt) {
    183:     TSMonitorLGCtx ctx;
    184:     PetscInt       howoften = 1;

    186:     PetscOptionsInt("-ts_monitor_lg_timestep","Monitor timestep size graphically","TSMonitorLGTimeStep",howoften,&howoften,NULL);
    187:     TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);
    188:     TSMonitorSet(ts,TSMonitorLGTimeStep,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);
    189:   }
    190:   PetscOptionsName("-ts_monitor_lg_timestep_log","Monitor log timestep size graphically","TSMonitorLGTimeStep",&opt);
    191:   if (opt) {
    192:     TSMonitorLGCtx ctx;
    193:     PetscInt       howoften = 1;

    195:     PetscOptionsInt("-ts_monitor_lg_timestep_log","Monitor log timestep size graphically","TSMonitorLGTimeStep",howoften,&howoften,NULL);
    196:     TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);
    197:     TSMonitorSet(ts,TSMonitorLGTimeStep,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);
    198:     ctx->semilogy = PETSC_TRUE;
    199:   }

    201:   PetscOptionsName("-ts_monitor_lg_snes_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGSNESIterations",&opt);
    202:   if (opt) {
    203:     TSMonitorLGCtx ctx;
    204:     PetscInt       howoften = 1;

    206:     PetscOptionsInt("-ts_monitor_lg_snes_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGSNESIterations",howoften,&howoften,NULL);
    207:     TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);
    208:     TSMonitorSet(ts,TSMonitorLGSNESIterations,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);
    209:   }
    210:   PetscOptionsName("-ts_monitor_lg_ksp_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGKSPIterations",&opt);
    211:   if (opt) {
    212:     TSMonitorLGCtx ctx;
    213:     PetscInt       howoften = 1;

    215:     PetscOptionsInt("-ts_monitor_lg_ksp_iterations","Monitor number nonlinear iterations for each timestep graphically","TSMonitorLGKSPIterations",howoften,&howoften,NULL);
    216:     TSMonitorLGCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,400,300,howoften,&ctx);
    217:     TSMonitorSet(ts,TSMonitorLGKSPIterations,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy);
    218:   }
    219:   PetscOptionsName("-ts_monitor_sp_eig","Monitor eigenvalues of linearized operator graphically","TSMonitorSPEig",&opt);
    220:   if (opt) {
    221:     TSMonitorSPEigCtx ctx;
    222:     PetscInt          howoften = 1;

    224:     PetscOptionsInt("-ts_monitor_sp_eig","Monitor eigenvalues of linearized operator graphically","TSMonitorSPEig",howoften,&howoften,NULL);
    225:     TSMonitorSPEigCtxCreate(PETSC_COMM_SELF,NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);
    226:     TSMonitorSet(ts,TSMonitorSPEig,ctx,(PetscErrorCode (*)(void**))TSMonitorSPEigCtxDestroy);
    227:   }
    228:   PetscOptionsName("-ts_monitor_sp_swarm","Display particle phase from the DMSwarm","TSMonitorSPSwarm",&opt);
    229:   if (opt) {
    230:     TSMonitorSPCtx  ctx;
    231:     PetscInt        howoften = 1, retain = 0;
    232:     PetscBool       phase = PETSC_TRUE;

    234:     PetscOptionsInt("-ts_monitor_sp_swarm","Display particles phase from the DMSwarm", "TSMonitorSPSwarm", howoften, &howoften, NULL);
    235:     PetscOptionsInt("-ts_monitor_sp_swarm_retain", "Retain n points plotted to show trajectory, -1 for all points", "TSMonitorSPSwarm", retain, &retain, NULL);
    236:     PetscOptionsBool("-ts_monitor_sp_swarm_phase", "Plot in phase space rather than coordinate space", "TSMonitorSPSwarm", phase, &phase, NULL);
    237:     TSMonitorSPCtxCreate(PetscObjectComm((PetscObject) ts), NULL, NULL, PETSC_DECIDE, PETSC_DECIDE, 300, 300, howoften, retain, phase, &ctx);
    238:     TSMonitorSet(ts, TSMonitorSPSwarmSolution, ctx, (PetscErrorCode (*)(void**))TSMonitorSPCtxDestroy);
    239:   }
    240:   opt  = PETSC_FALSE;
    241:   PetscOptionsName("-ts_monitor_draw_solution","Monitor solution graphically","TSMonitorDrawSolution",&opt);
    242:   if (opt) {
    243:     TSMonitorDrawCtx ctx;
    244:     PetscInt         howoften = 1;

    246:     PetscOptionsInt("-ts_monitor_draw_solution","Monitor solution graphically","TSMonitorDrawSolution",howoften,&howoften,NULL);
    247:     TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),NULL,"Computed Solution",PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);
    248:     TSMonitorSet(ts,TSMonitorDrawSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);
    249:   }
    250:   opt  = PETSC_FALSE;
    251:   PetscOptionsName("-ts_monitor_draw_solution_phase","Monitor solution graphically","TSMonitorDrawSolutionPhase",&opt);
    252:   if (opt) {
    253:     TSMonitorDrawCtx ctx;
    254:     PetscReal        bounds[4];
    255:     PetscInt         n = 4;
    256:     PetscDraw        draw;
    257:     PetscDrawAxis    axis;

    259:     PetscOptionsRealArray("-ts_monitor_draw_solution_phase","Monitor solution graphically","TSMonitorDrawSolutionPhase",bounds,&n,NULL);
    261:     TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,300,300,1,&ctx);
    262:     PetscViewerDrawGetDraw(ctx->viewer,0,&draw);
    263:     PetscViewerDrawGetDrawAxis(ctx->viewer,0,&axis);
    264:     PetscDrawAxisSetLimits(axis,bounds[0],bounds[2],bounds[1],bounds[3]);
    265:     PetscDrawAxisSetLabels(axis,"Phase Diagram","Variable 1","Variable 2");
    266:     TSMonitorSet(ts,TSMonitorDrawSolutionPhase,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);
    267:   }
    268:   opt  = PETSC_FALSE;
    269:   PetscOptionsName("-ts_monitor_draw_error","Monitor error graphically","TSMonitorDrawError",&opt);
    270:   if (opt) {
    271:     TSMonitorDrawCtx ctx;
    272:     PetscInt         howoften = 1;

    274:     PetscOptionsInt("-ts_monitor_draw_error","Monitor error graphically","TSMonitorDrawError",howoften,&howoften,NULL);
    275:     TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),NULL,"Error",PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);
    276:     TSMonitorSet(ts,TSMonitorDrawError,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);
    277:   }
    278:   opt  = PETSC_FALSE;
    279:   PetscOptionsName("-ts_monitor_draw_solution_function","Monitor solution provided by TSMonitorSetSolutionFunction() graphically","TSMonitorDrawSolutionFunction",&opt);
    280:   if (opt) {
    281:     TSMonitorDrawCtx ctx;
    282:     PetscInt         howoften = 1;

    284:     PetscOptionsInt("-ts_monitor_draw_solution_function","Monitor solution provided by TSMonitorSetSolutionFunction() graphically","TSMonitorDrawSolutionFunction",howoften,&howoften,NULL);
    285:     TSMonitorDrawCtxCreate(PetscObjectComm((PetscObject)ts),NULL,"Solution provided by user function",PETSC_DECIDE,PETSC_DECIDE,300,300,howoften,&ctx);
    286:     TSMonitorSet(ts,TSMonitorDrawSolutionFunction,ctx,(PetscErrorCode (*)(void**))TSMonitorDrawCtxDestroy);
    287:   }

    289:   opt  = PETSC_FALSE;
    290:   PetscOptionsString("-ts_monitor_solution_vtk","Save each time step to a binary file, use filename-%%03D.vts","TSMonitorSolutionVTK",NULL,monfilename,sizeof(monfilename),&flg);
    291:   if (flg) {
    292:     const char *ptr,*ptr2;
    293:     char       *filetemplate;
    295:     /* Do some cursory validation of the input. */
    296:     PetscStrstr(monfilename,"%",(char**)&ptr);
    298:     for (ptr++; ptr && *ptr; ptr++) {
    299:       PetscStrchr("DdiouxX",*ptr,(char**)&ptr2);
    301:       if (ptr2) break;
    302:     }
    303:     PetscStrallocpy(monfilename,&filetemplate);
    304:     TSMonitorSet(ts,TSMonitorSolutionVTK,filetemplate,(PetscErrorCode (*)(void**))TSMonitorSolutionVTKDestroy);
    305:   }

    307:   PetscOptionsString("-ts_monitor_dmda_ray","Display a ray of the solution","None","y=0",dir,sizeof(dir),&flg);
    308:   if (flg) {
    309:     TSMonitorDMDARayCtx *rayctx;
    310:     int                  ray = 0;
    311:     DMDirection          ddir;
    312:     DM                   da;
    313:     PetscMPIInt          rank;

    316:     if (dir[0] == 'x') ddir = DM_X;
    317:     else if (dir[0] == 'y') ddir = DM_Y;
    318:     else SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_WRONG,"Unknown ray %s",dir);
    319:     sscanf(dir+2,"%d",&ray);

    321:     PetscInfo(((PetscObject)ts),"Displaying DMDA ray %c = %d\n",dir[0],ray);
    322:     PetscNew(&rayctx);
    323:     TSGetDM(ts,&da);
    324:     DMDAGetRay(da,ddir,ray,&rayctx->ray,&rayctx->scatter);
    325:     MPI_Comm_rank(PetscObjectComm((PetscObject)ts),&rank);
    326:     if (rank == 0) {
    327:       PetscViewerDrawOpen(PETSC_COMM_SELF,NULL,NULL,0,0,600,300,&rayctx->viewer);
    328:     }
    329:     rayctx->lgctx = NULL;
    330:     TSMonitorSet(ts,TSMonitorDMDARay,rayctx,TSMonitorDMDARayDestroy);
    331:   }
    332:   PetscOptionsString("-ts_monitor_lg_dmda_ray","Display a ray of the solution","None","x=0",dir,sizeof(dir),&flg);
    333:   if (flg) {
    334:     TSMonitorDMDARayCtx *rayctx;
    335:     int                 ray = 0;
    336:     DMDirection         ddir;
    337:     DM                  da;
    338:     PetscInt            howoften = 1;

    341:     if      (dir[0] == 'x') ddir = DM_X;
    342:     else if (dir[0] == 'y') ddir = DM_Y;
    343:     else SETERRQ(PetscObjectComm((PetscObject) ts), PETSC_ERR_ARG_WRONG, "Unknown ray direction %s", dir);
    344:     sscanf(dir+2, "%d", &ray);

    346:     PetscInfo(((PetscObject) ts),"Displaying LG DMDA ray %c = %d\n", dir[0], ray);
    347:     PetscNew(&rayctx);
    348:     TSGetDM(ts, &da);
    349:     DMDAGetRay(da, ddir, ray, &rayctx->ray, &rayctx->scatter);
    350:     TSMonitorLGCtxCreate(PETSC_COMM_SELF,NULL,NULL,PETSC_DECIDE,PETSC_DECIDE,600,400,howoften,&rayctx->lgctx);
    351:     TSMonitorSet(ts, TSMonitorLGDMDARay, rayctx, TSMonitorDMDARayDestroy);
    352:   }

    354:   PetscOptionsName("-ts_monitor_envelope","Monitor maximum and minimum value of each component of the solution","TSMonitorEnvelope",&opt);
    355:   if (opt) {
    356:     TSMonitorEnvelopeCtx ctx;

    358:     TSMonitorEnvelopeCtxCreate(ts,&ctx);
    359:     TSMonitorSet(ts,TSMonitorEnvelope,ctx,(PetscErrorCode (*)(void**))TSMonitorEnvelopeCtxDestroy);
    360:   }
    361:   flg  = PETSC_FALSE;
    362:   PetscOptionsBool("-ts_monitor_cancel","Remove all monitors","TSMonitorCancel",flg,&flg,&opt);
    363:   if (opt && flg) TSMonitorCancel(ts);

    365:   flg  = PETSC_FALSE;
    366:   PetscOptionsBool("-ts_fd_color", "Use finite differences with coloring to compute IJacobian", "TSComputeJacobianDefaultColor", flg, &flg, NULL);
    367:   if (flg) {
    368:     DM   dm;
    369:     DMTS tdm;

    371:     TSGetDM(ts, &dm);
    372:     DMGetDMTS(dm, &tdm);
    373:     tdm->ijacobianctx = NULL;
    374:     TSSetIJacobian(ts, NULL, NULL, TSComputeIJacobianDefaultColor, NULL);
    375:     PetscInfo(ts, "Setting default finite difference coloring Jacobian matrix\n");
    376:   }

    378:   /* Handle specific TS options */
    379:   if (ts->ops->setfromoptions) {
    380:     (*ts->ops->setfromoptions)(PetscOptionsObject,ts);
    381:   }

    383:   /* Handle TSAdapt options */
    384:   TSGetAdapt(ts,&ts->adapt);
    385:   TSAdaptSetDefaultType(ts->adapt,ts->default_adapt_type);
    386:   TSAdaptSetFromOptions(PetscOptionsObject,ts->adapt);

    388:   /* TS trajectory must be set after TS, since it may use some TS options above */
    389:   tflg = ts->trajectory ? PETSC_TRUE : PETSC_FALSE;
    390:   PetscOptionsBool("-ts_save_trajectory","Save the solution at each timestep","TSSetSaveTrajectory",tflg,&tflg,NULL);
    391:   if (tflg) {
    392:     TSSetSaveTrajectory(ts);
    393:   }

    395:   TSAdjointSetFromOptions(PetscOptionsObject,ts);

    397:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
    398:   PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject)ts);
    399:   PetscOptionsEnd();

    401:   if (ts->trajectory) {
    402:     TSTrajectorySetFromOptions(ts->trajectory,ts);
    403:   }

    405:   /* why do we have to do this here and not during TSSetUp? */
    406:   TSGetSNES(ts,&ts->snes);
    407:   if (ts->problem_type == TS_LINEAR) {
    408:     PetscObjectTypeCompareAny((PetscObject)ts->snes,&flg,SNESKSPONLY,SNESKSPTRANSPOSEONLY,"");
    409:     if (!flg) SNESSetType(ts->snes,SNESKSPONLY);
    410:   }
    411:   SNESSetFromOptions(ts->snes);
    412:   return 0;
    413: }

    415: /*@
    416:    TSGetTrajectory - Gets the trajectory from a TS if it exists

    418:    Collective on TS

    420:    Input Parameters:
    421: .  ts - the TS context obtained from TSCreate()

    423:    Output Parameters:
    424: .  tr - the TSTrajectory object, if it exists

    426:    Note: This routine should be called after all TS options have been set

    428:    Level: advanced

    430: .seealso: TSGetTrajectory(), TSAdjointSolve(), TSTrajectory, TSTrajectoryCreate()

    432: @*/
    433: PetscErrorCode  TSGetTrajectory(TS ts,TSTrajectory *tr)
    434: {
    436:   *tr = ts->trajectory;
    437:   return 0;
    438: }

    440: /*@
    441:    TSSetSaveTrajectory - Causes the TS to save its solutions as it iterates forward in time in a TSTrajectory object

    443:    Collective on TS

    445:    Input Parameter:
    446: .  ts - the TS context obtained from TSCreate()

    448:    Options Database:
    449: +  -ts_save_trajectory - saves the trajectory to a file
    450: -  -ts_trajectory_type type - set trajectory type

    452: Note: This routine should be called after all TS options have been set

    454:     The TSTRAJECTORYVISUALIZATION files can be loaded into Python with $PETSC_DIR/lib/petsc/bin/PetscBinaryIOTrajectory.py and
    455:    MATLAB with $PETSC_DIR/share/petsc/matlab/PetscReadBinaryTrajectory.m

    457:    Level: intermediate

    459: .seealso: TSGetTrajectory(), TSAdjointSolve()

    461: @*/
    462: PetscErrorCode  TSSetSaveTrajectory(TS ts)
    463: {
    465:   if (!ts->trajectory) {
    466:     TSTrajectoryCreate(PetscObjectComm((PetscObject)ts),&ts->trajectory);
    467:   }
    468:   return 0;
    469: }

    471: /*@
    472:    TSResetTrajectory - Destroys and recreates the internal TSTrajectory object

    474:    Collective on TS

    476:    Input Parameters:
    477: .  ts - the TS context obtained from TSCreate()

    479:    Level: intermediate

    481: .seealso: TSGetTrajectory(), TSAdjointSolve(), TSRemoveTrajectory()

    483: @*/
    484: PetscErrorCode  TSResetTrajectory(TS ts)
    485: {
    487:   if (ts->trajectory) {
    488:     TSTrajectoryDestroy(&ts->trajectory);
    489:     TSTrajectoryCreate(PetscObjectComm((PetscObject)ts),&ts->trajectory);
    490:   }
    491:   return 0;
    492: }

    494: /*@
    495:    TSRemoveTrajectory - Destroys and removes the internal TSTrajectory object from TS

    497:    Collective on TS

    499:    Input Parameters:
    500: .  ts - the TS context obtained from TSCreate()

    502:    Level: intermediate

    504: .seealso: TSResetTrajectory(), TSAdjointSolve()

    506: @*/
    507: PetscErrorCode TSRemoveTrajectory(TS ts)
    508: {
    510:   if (ts->trajectory) {
    511:     TSTrajectoryDestroy(&ts->trajectory);
    512:   }
    513:   return 0;
    514: }

    516: /*@
    517:    TSComputeRHSJacobian - Computes the Jacobian matrix that has been
    518:       set with TSSetRHSJacobian().

    520:    Collective on TS

    522:    Input Parameters:
    523: +  ts - the TS context
    524: .  t - current timestep
    525: -  U - input vector

    527:    Output Parameters:
    528: +  A - Jacobian matrix
    529: -  B - optional preconditioning matrix

    531:    Notes:
    532:    Most users should not need to explicitly call this routine, as it
    533:    is used internally within the nonlinear solvers.

    535:    Level: developer

    537: .seealso:  TSSetRHSJacobian(), KSPSetOperators()
    538: @*/
    539: PetscErrorCode  TSComputeRHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B)
    540: {
    541:   PetscObjectState Ustate;
    542:   PetscObjectId    Uid;
    543:   DM               dm;
    544:   DMTS             tsdm;
    545:   TSRHSJacobian    rhsjacobianfunc;
    546:   void             *ctx;
    547:   TSRHSFunction    rhsfunction;

    552:   TSGetDM(ts,&dm);
    553:   DMGetDMTS(dm,&tsdm);
    554:   DMTSGetRHSFunction(dm,&rhsfunction,NULL);
    555:   DMTSGetRHSJacobian(dm,&rhsjacobianfunc,&ctx);
    556:   PetscObjectStateGet((PetscObject)U,&Ustate);
    557:   PetscObjectGetId((PetscObject)U,&Uid);

    559:   if (ts->rhsjacobian.time == t && (ts->problem_type == TS_LINEAR || (ts->rhsjacobian.Xid == Uid && ts->rhsjacobian.Xstate == Ustate)) && (rhsfunction != TSComputeRHSFunctionLinear)) return 0;

    562:   if (rhsjacobianfunc) {
    563:     PetscLogEventBegin(TS_JacobianEval,ts,U,A,B);
    564:     PetscStackPush("TS user Jacobian function");
    565:     (*rhsjacobianfunc)(ts,t,U,A,B,ctx);
    566:     PetscStackPop;
    567:     ts->rhsjacs++;
    568:     PetscLogEventEnd(TS_JacobianEval,ts,U,A,B);
    569:   } else {
    570:     MatZeroEntries(A);
    571:     if (B && A != B) MatZeroEntries(B);
    572:   }
    573:   ts->rhsjacobian.time  = t;
    574:   ts->rhsjacobian.shift = 0;
    575:   ts->rhsjacobian.scale = 1.;
    576:   PetscObjectGetId((PetscObject)U,&ts->rhsjacobian.Xid);
    577:   PetscObjectStateGet((PetscObject)U,&ts->rhsjacobian.Xstate);
    578:   return 0;
    579: }

    581: /*@
    582:    TSComputeRHSFunction - Evaluates the right-hand-side function.

    584:    Collective on TS

    586:    Input Parameters:
    587: +  ts - the TS context
    588: .  t - current time
    589: -  U - state vector

    591:    Output Parameter:
    592: .  y - right hand side

    594:    Note:
    595:    Most users should not need to explicitly call this routine, as it
    596:    is used internally within the nonlinear solvers.

    598:    Level: developer

    600: .seealso: TSSetRHSFunction(), TSComputeIFunction()
    601: @*/
    602: PetscErrorCode TSComputeRHSFunction(TS ts,PetscReal t,Vec U,Vec y)
    603: {
    604:   TSRHSFunction  rhsfunction;
    605:   TSIFunction    ifunction;
    606:   void           *ctx;
    607:   DM             dm;

    612:   TSGetDM(ts,&dm);
    613:   DMTSGetRHSFunction(dm,&rhsfunction,&ctx);
    614:   DMTSGetIFunction(dm,&ifunction,NULL);

    618:   if (rhsfunction) {
    619:     PetscLogEventBegin(TS_FunctionEval,ts,U,y,0);
    620:     VecLockReadPush(U);
    621:     PetscStackPush("TS user right-hand-side function");
    622:     (*rhsfunction)(ts,t,U,y,ctx);
    623:     PetscStackPop;
    624:     VecLockReadPop(U);
    625:     ts->rhsfuncs++;
    626:     PetscLogEventEnd(TS_FunctionEval,ts,U,y,0);
    627:   } else {
    628:     VecZeroEntries(y);
    629:   }
    630:   return 0;
    631: }

    633: /*@
    634:    TSComputeSolutionFunction - Evaluates the solution function.

    636:    Collective on TS

    638:    Input Parameters:
    639: +  ts - the TS context
    640: -  t - current time

    642:    Output Parameter:
    643: .  U - the solution

    645:    Note:
    646:    Most users should not need to explicitly call this routine, as it
    647:    is used internally within the nonlinear solvers.

    649:    Level: developer

    651: .seealso: TSSetSolutionFunction(), TSSetRHSFunction(), TSComputeIFunction()
    652: @*/
    653: PetscErrorCode TSComputeSolutionFunction(TS ts,PetscReal t,Vec U)
    654: {
    655:   TSSolutionFunction solutionfunction;
    656:   void               *ctx;
    657:   DM                 dm;

    661:   TSGetDM(ts,&dm);
    662:   DMTSGetSolutionFunction(dm,&solutionfunction,&ctx);

    664:   if (solutionfunction) {
    665:     PetscStackPush("TS user solution function");
    666:     (*solutionfunction)(ts,t,U,ctx);
    667:     PetscStackPop;
    668:   }
    669:   return 0;
    670: }
    671: /*@
    672:    TSComputeForcingFunction - Evaluates the forcing function.

    674:    Collective on TS

    676:    Input Parameters:
    677: +  ts - the TS context
    678: -  t - current time

    680:    Output Parameter:
    681: .  U - the function value

    683:    Note:
    684:    Most users should not need to explicitly call this routine, as it
    685:    is used internally within the nonlinear solvers.

    687:    Level: developer

    689: .seealso: TSSetSolutionFunction(), TSSetRHSFunction(), TSComputeIFunction()
    690: @*/
    691: PetscErrorCode TSComputeForcingFunction(TS ts,PetscReal t,Vec U)
    692: {
    693:   void              *ctx;
    694:   DM                 dm;
    695:   TSForcingFunction  forcing;

    699:   TSGetDM(ts,&dm);
    700:   DMTSGetForcingFunction(dm,&forcing,&ctx);

    702:   if (forcing) {
    703:     PetscStackPush("TS user forcing function");
    704:     (*forcing)(ts,t,U,ctx);
    705:     PetscStackPop;
    706:   }
    707:   return 0;
    708: }

    710: static PetscErrorCode TSGetRHSVec_Private(TS ts,Vec *Frhs)
    711: {
    712:   Vec            F;

    714:   *Frhs = NULL;
    715:   TSGetIFunction(ts,&F,NULL,NULL);
    716:   if (!ts->Frhs) {
    717:     VecDuplicate(F,&ts->Frhs);
    718:   }
    719:   *Frhs = ts->Frhs;
    720:   return 0;
    721: }

    723: PetscErrorCode TSGetRHSMats_Private(TS ts,Mat *Arhs,Mat *Brhs)
    724: {
    725:   Mat            A,B;
    726:   TSIJacobian    ijacobian;

    728:   if (Arhs) *Arhs = NULL;
    729:   if (Brhs) *Brhs = NULL;
    730:   TSGetIJacobian(ts,&A,&B,&ijacobian,NULL);
    731:   if (Arhs) {
    732:     if (!ts->Arhs) {
    733:       if (ijacobian) {
    734:         MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&ts->Arhs);
    735:         TSSetMatStructure(ts,SAME_NONZERO_PATTERN);
    736:       } else {
    737:         ts->Arhs = A;
    738:         PetscObjectReference((PetscObject)A);
    739:       }
    740:     } else {
    741:       PetscBool flg;
    742:       SNESGetUseMatrixFree(ts->snes,NULL,&flg);
    743:       /* Handle case where user provided only RHSJacobian and used -snes_mf_operator */
    744:       if (flg && !ijacobian && ts->Arhs == ts->Brhs) {
    745:         PetscObjectDereference((PetscObject)ts->Arhs);
    746:         ts->Arhs = A;
    747:         PetscObjectReference((PetscObject)A);
    748:       }
    749:     }
    750:     *Arhs = ts->Arhs;
    751:   }
    752:   if (Brhs) {
    753:     if (!ts->Brhs) {
    754:       if (A != B) {
    755:         if (ijacobian) {
    756:           MatDuplicate(B,MAT_DO_NOT_COPY_VALUES,&ts->Brhs);
    757:         } else {
    758:           ts->Brhs = B;
    759:           PetscObjectReference((PetscObject)B);
    760:         }
    761:       } else {
    762:         PetscObjectReference((PetscObject)ts->Arhs);
    763:         ts->Brhs = ts->Arhs;
    764:       }
    765:     }
    766:     *Brhs = ts->Brhs;
    767:   }
    768:   return 0;
    769: }

    771: /*@
    772:    TSComputeIFunction - Evaluates the DAE residual written in implicit form F(t,U,Udot)=0

    774:    Collective on TS

    776:    Input Parameters:
    777: +  ts - the TS context
    778: .  t - current time
    779: .  U - state vector
    780: .  Udot - time derivative of state vector
    781: -  imex - flag indicates if the method is IMEX so that the RHSFunction should be kept separate

    783:    Output Parameter:
    784: .  Y - right hand side

    786:    Note:
    787:    Most users should not need to explicitly call this routine, as it
    788:    is used internally within the nonlinear solvers.

    790:    If the user did did not write their equations in implicit form, this
    791:    function recasts them in implicit form.

    793:    Level: developer

    795: .seealso: TSSetIFunction(), TSComputeRHSFunction()
    796: @*/
    797: PetscErrorCode TSComputeIFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec Y,PetscBool imex)
    798: {
    799:   TSIFunction    ifunction;
    800:   TSRHSFunction  rhsfunction;
    801:   void           *ctx;
    802:   DM             dm;

    809:   TSGetDM(ts,&dm);
    810:   DMTSGetIFunction(dm,&ifunction,&ctx);
    811:   DMTSGetRHSFunction(dm,&rhsfunction,NULL);

    815:   PetscLogEventBegin(TS_FunctionEval,ts,U,Udot,Y);
    816:   if (ifunction) {
    817:     PetscStackPush("TS user implicit function");
    818:     (*ifunction)(ts,t,U,Udot,Y,ctx);
    819:     PetscStackPop;
    820:     ts->ifuncs++;
    821:   }
    822:   if (imex) {
    823:     if (!ifunction) {
    824:       VecCopy(Udot,Y);
    825:     }
    826:   } else if (rhsfunction) {
    827:     if (ifunction) {
    828:       Vec Frhs;
    829:       TSGetRHSVec_Private(ts,&Frhs);
    830:       TSComputeRHSFunction(ts,t,U,Frhs);
    831:       VecAXPY(Y,-1,Frhs);
    832:     } else {
    833:       TSComputeRHSFunction(ts,t,U,Y);
    834:       VecAYPX(Y,-1,Udot);
    835:     }
    836:   }
    837:   PetscLogEventEnd(TS_FunctionEval,ts,U,Udot,Y);
    838:   return 0;
    839: }

    841: /*
    842:    TSRecoverRHSJacobian - Recover the Jacobian matrix so that one can call TSComputeRHSJacobian() on it.

    844:    Note:
    845:    This routine is needed when one switches from TSComputeIJacobian() to TSComputeRHSJacobian() because the Jacobian matrix may be shifted or scaled in TSComputeIJacobian().

    847: */
    848: static PetscErrorCode TSRecoverRHSJacobian(TS ts,Mat A,Mat B)
    849: {

    854:   if (ts->rhsjacobian.shift) {
    855:     MatShift(A,-ts->rhsjacobian.shift);
    856:   }
    857:   if (ts->rhsjacobian.scale == -1.) {
    858:     MatScale(A,-1);
    859:   }
    860:   if (B && B == ts->Brhs && A != B) {
    861:     if (ts->rhsjacobian.shift) {
    862:       MatShift(B,-ts->rhsjacobian.shift);
    863:     }
    864:     if (ts->rhsjacobian.scale == -1.) {
    865:       MatScale(B,-1);
    866:     }
    867:   }
    868:   ts->rhsjacobian.shift = 0;
    869:   ts->rhsjacobian.scale = 1.;
    870:   return 0;
    871: }

    873: /*@
    874:    TSComputeIJacobian - Evaluates the Jacobian of the DAE

    876:    Collective on TS

    878:    Input
    879:       Input Parameters:
    880: +  ts - the TS context
    881: .  t - current timestep
    882: .  U - state vector
    883: .  Udot - time derivative of state vector
    884: .  shift - shift to apply, see note below
    885: -  imex - flag indicates if the method is IMEX so that the RHSJacobian should be kept separate

    887:    Output Parameters:
    888: +  A - Jacobian matrix
    889: -  B - matrix from which the preconditioner is constructed; often the same as A

    891:    Notes:
    892:    If F(t,U,Udot)=0 is the DAE, the required Jacobian is

    894:    dF/dU + shift*dF/dUdot

    896:    Most users should not need to explicitly call this routine, as it
    897:    is used internally within the nonlinear solvers.

    899:    Level: developer

    901: .seealso:  TSSetIJacobian()
    902: @*/
    903: PetscErrorCode TSComputeIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat A,Mat B,PetscBool imex)
    904: {
    905:   TSIJacobian    ijacobian;
    906:   TSRHSJacobian  rhsjacobian;
    907:   DM             dm;
    908:   void           *ctx;

    918:   TSGetDM(ts,&dm);
    919:   DMTSGetIJacobian(dm,&ijacobian,&ctx);
    920:   DMTSGetRHSJacobian(dm,&rhsjacobian,NULL);

    924:   PetscLogEventBegin(TS_JacobianEval,ts,U,A,B);
    925:   if (ijacobian) {
    926:     PetscStackPush("TS user implicit Jacobian");
    927:     (*ijacobian)(ts,t,U,Udot,shift,A,B,ctx);
    928:     ts->ijacs++;
    929:     PetscStackPop;
    930:   }
    931:   if (imex) {
    932:     if (!ijacobian) {  /* system was written as Udot = G(t,U) */
    933:       PetscBool assembled;
    934:       if (rhsjacobian) {
    935:         Mat Arhs = NULL;
    936:         TSGetRHSMats_Private(ts,&Arhs,NULL);
    937:         if (A == Arhs) {
    939:           ts->rhsjacobian.time = PETSC_MIN_REAL;
    940:         }
    941:       }
    942:       MatZeroEntries(A);
    943:       MatAssembled(A,&assembled);
    944:       if (!assembled) {
    945:         MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    946:         MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    947:       }
    948:       MatShift(A,shift);
    949:       if (A != B) {
    950:         MatZeroEntries(B);
    951:         MatAssembled(B,&assembled);
    952:         if (!assembled) {
    953:           MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    954:           MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    955:         }
    956:         MatShift(B,shift);
    957:       }
    958:     }
    959:   } else {
    960:     Mat Arhs = NULL,Brhs = NULL;
    961:     if (rhsjacobian) { /* RHSJacobian needs to be converted to part of IJacobian if exists */
    962:       TSGetRHSMats_Private(ts,&Arhs,&Brhs);
    963:     }
    964:     if (Arhs == A) { /* No IJacobian matrix, so we only have the RHS matrix */
    965:       PetscObjectState Ustate;
    966:       PetscObjectId    Uid;
    967:       TSRHSFunction    rhsfunction;

    969:       DMTSGetRHSFunction(dm,&rhsfunction,NULL);
    970:       PetscObjectStateGet((PetscObject)U,&Ustate);
    971:       PetscObjectGetId((PetscObject)U,&Uid);
    972:       if ((rhsjacobian == TSComputeRHSJacobianConstant || (ts->rhsjacobian.time == t && (ts->problem_type == TS_LINEAR || (ts->rhsjacobian.Xid == Uid && ts->rhsjacobian.Xstate == Ustate)) && rhsfunction != TSComputeRHSFunctionLinear)) && ts->rhsjacobian.scale == -1.) { /* No need to recompute RHSJacobian */
    973:         MatShift(A,shift-ts->rhsjacobian.shift); /* revert the old shift and add the new shift with a single call to MatShift */
    974:         if (A != B) {
    975:           MatShift(B,shift-ts->rhsjacobian.shift);
    976:         }
    977:       } else {
    978:         PetscBool flg;

    980:         if (ts->rhsjacobian.reuse) { /* Undo the damage */
    981:           /* MatScale has a short path for this case.
    982:              However, this code path is taken the first time TSComputeRHSJacobian is called
    983:              and the matrices have not been assembled yet */
    984:           TSRecoverRHSJacobian(ts,A,B);
    985:         }
    986:         TSComputeRHSJacobian(ts,t,U,A,B);
    987:         SNESGetUseMatrixFree(ts->snes,NULL,&flg);
    988:         /* since -snes_mf_operator uses the full SNES function it does not need to be shifted or scaled here */
    989:         if (!flg) {
    990:           MatScale(A,-1);
    991:           MatShift(A,shift);
    992:         }
    993:         if (A != B) {
    994:           MatScale(B,-1);
    995:           MatShift(B,shift);
    996:         }
    997:       }
    998:       ts->rhsjacobian.scale = -1;
    999:       ts->rhsjacobian.shift = shift;
    1000:     } else if (Arhs) {          /* Both IJacobian and RHSJacobian */
    1001:       if (!ijacobian) {         /* No IJacobian provided, but we have a separate RHS matrix */
    1002:         MatZeroEntries(A);
    1003:         MatShift(A,shift);
    1004:         if (A != B) {
    1005:           MatZeroEntries(B);
    1006:           MatShift(B,shift);
    1007:         }
    1008:       }
    1009:       TSComputeRHSJacobian(ts,t,U,Arhs,Brhs);
    1010:       MatAXPY(A,-1,Arhs,ts->axpy_pattern);
    1011:       if (A != B) {
    1012:         MatAXPY(B,-1,Brhs,ts->axpy_pattern);
    1013:       }
    1014:     }
    1015:   }
    1016:   PetscLogEventEnd(TS_JacobianEval,ts,U,A,B);
    1017:   return 0;
    1018: }

    1020: /*@C
    1021:     TSSetRHSFunction - Sets the routine for evaluating the function,
    1022:     where U_t = G(t,u).

    1024:     Logically Collective on TS

    1026:     Input Parameters:
    1027: +   ts - the TS context obtained from TSCreate()
    1028: .   r - vector to put the computed right hand side (or NULL to have it created)
    1029: .   f - routine for evaluating the right-hand-side function
    1030: -   ctx - [optional] user-defined context for private data for the
    1031:           function evaluation routine (may be NULL)

    1033:     Calling sequence of f:
    1034: $     PetscErrorCode f(TS ts,PetscReal t,Vec u,Vec F,void *ctx);

    1036: +   ts - timestep context
    1037: .   t - current timestep
    1038: .   u - input vector
    1039: .   F - function vector
    1040: -   ctx - [optional] user-defined function context

    1042:     Level: beginner

    1044:     Notes:
    1045:     You must call this function or TSSetIFunction() to define your ODE. You cannot use this function when solving a DAE.

    1047: .seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSSetIFunction()
    1048: @*/
    1049: PetscErrorCode  TSSetRHSFunction(TS ts,Vec r,PetscErrorCode (*f)(TS,PetscReal,Vec,Vec,void*),void *ctx)
    1050: {
    1051:   SNES           snes;
    1052:   Vec            ralloc = NULL;
    1053:   DM             dm;

    1058:   TSGetDM(ts,&dm);
    1059:   DMTSSetRHSFunction(dm,f,ctx);
    1060:   TSGetSNES(ts,&snes);
    1061:   if (!r && !ts->dm && ts->vec_sol) {
    1062:     VecDuplicate(ts->vec_sol,&ralloc);
    1063:     r = ralloc;
    1064:   }
    1065:   SNESSetFunction(snes,r,SNESTSFormFunction,ts);
    1066:   VecDestroy(&ralloc);
    1067:   return 0;
    1068: }

    1070: /*@C
    1071:     TSSetSolutionFunction - Provide a function that computes the solution of the ODE or DAE

    1073:     Logically Collective on TS

    1075:     Input Parameters:
    1076: +   ts - the TS context obtained from TSCreate()
    1077: .   f - routine for evaluating the solution
    1078: -   ctx - [optional] user-defined context for private data for the
    1079:           function evaluation routine (may be NULL)

    1081:     Calling sequence of f:
    1082: $     PetscErrorCode f(TS ts,PetscReal t,Vec u,void *ctx);

    1084: +   t - current timestep
    1085: .   u - output vector
    1086: -   ctx - [optional] user-defined function context

    1088:     Options Database:
    1089: +  -ts_monitor_lg_error - create a graphical monitor of error history, requires user to have provided TSSetSolutionFunction()
    1090: -  -ts_monitor_draw_error - Monitor error graphically, requires user to have provided TSSetSolutionFunction()

    1092:     Notes:
    1093:     This routine is used for testing accuracy of time integration schemes when you already know the solution.
    1094:     If analytic solutions are not known for your system, consider using the Method of Manufactured Solutions to
    1095:     create closed-form solutions with non-physical forcing terms.

    1097:     For low-dimensional problems solved in serial, such as small discrete systems, TSMonitorLGError() can be used to monitor the error history.

    1099:     Level: beginner

    1101: .seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSComputeSolutionFunction(), TSSetForcingFunction(), TSSetSolution(), TSGetSolution(), TSMonitorLGError(), TSMonitorDrawError()
    1102: @*/
    1103: PetscErrorCode  TSSetSolutionFunction(TS ts,PetscErrorCode (*f)(TS,PetscReal,Vec,void*),void *ctx)
    1104: {
    1105:   DM             dm;

    1108:   TSGetDM(ts,&dm);
    1109:   DMTSSetSolutionFunction(dm,f,ctx);
    1110:   return 0;
    1111: }

    1113: /*@C
    1114:     TSSetForcingFunction - Provide a function that computes a forcing term for a ODE or PDE

    1116:     Logically Collective on TS

    1118:     Input Parameters:
    1119: +   ts - the TS context obtained from TSCreate()
    1120: .   func - routine for evaluating the forcing function
    1121: -   ctx - [optional] user-defined context for private data for the
    1122:           function evaluation routine (may be NULL)

    1124:     Calling sequence of func:
    1125: $     PetscErrorCode func (TS ts,PetscReal t,Vec f,void *ctx);

    1127: +   t - current timestep
    1128: .   f - output vector
    1129: -   ctx - [optional] user-defined function context

    1131:     Notes:
    1132:     This routine is useful for testing accuracy of time integration schemes when using the Method of Manufactured Solutions to
    1133:     create closed-form solutions with a non-physical forcing term. It allows you to use the Method of Manufactored Solution without directly editing the
    1134:     definition of the problem you are solving and hence possibly introducing bugs.

    1136:     This replaces the ODE F(u,u_t,t) = 0 the TS is solving with F(u,u_t,t) - func(t) = 0

    1138:     This forcing function does not depend on the solution to the equations, it can only depend on spatial location, time, and possibly parameters, the
    1139:     parameters can be passed in the ctx variable.

    1141:     For low-dimensional problems solved in serial, such as small discrete systems, TSMonitorLGError() can be used to monitor the error history.

    1143:     Level: beginner

    1145: .seealso: TSSetRHSJacobian(), TSSetIJacobian(), TSComputeSolutionFunction(), TSSetSolutionFunction()
    1146: @*/
    1147: PetscErrorCode  TSSetForcingFunction(TS ts,TSForcingFunction func,void *ctx)
    1148: {
    1149:   DM             dm;

    1152:   TSGetDM(ts,&dm);
    1153:   DMTSSetForcingFunction(dm,func,ctx);
    1154:   return 0;
    1155: }

    1157: /*@C
    1158:    TSSetRHSJacobian - Sets the function to compute the Jacobian of G,
    1159:    where U_t = G(U,t), as well as the location to store the matrix.

    1161:    Logically Collective on TS

    1163:    Input Parameters:
    1164: +  ts  - the TS context obtained from TSCreate()
    1165: .  Amat - (approximate) Jacobian matrix
    1166: .  Pmat - matrix from which preconditioner is to be constructed (usually the same as Amat)
    1167: .  f   - the Jacobian evaluation routine
    1168: -  ctx - [optional] user-defined context for private data for the
    1169:          Jacobian evaluation routine (may be NULL)

    1171:    Calling sequence of f:
    1172: $     PetscErrorCode f(TS ts,PetscReal t,Vec u,Mat A,Mat B,void *ctx);

    1174: +  t - current timestep
    1175: .  u - input vector
    1176: .  Amat - (approximate) Jacobian matrix
    1177: .  Pmat - matrix from which preconditioner is to be constructed (usually the same as Amat)
    1178: -  ctx - [optional] user-defined context for matrix evaluation routine

    1180:    Notes:
    1181:    You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value

    1183:    The TS solver may modify the nonzero structure and the entries of the matrices Amat and Pmat between the calls to f()
    1184:    You should not assume the values are the same in the next call to f() as you set them in the previous call.

    1186:    Level: beginner

    1188: .seealso: SNESComputeJacobianDefaultColor(), TSSetRHSFunction(), TSRHSJacobianSetReuse(), TSSetIJacobian()

    1190: @*/
    1191: PetscErrorCode  TSSetRHSJacobian(TS ts,Mat Amat,Mat Pmat,TSRHSJacobian f,void *ctx)
    1192: {
    1193:   SNES           snes;
    1194:   DM             dm;
    1195:   TSIJacobian    ijacobian;

    1203:   TSGetDM(ts,&dm);
    1204:   DMTSSetRHSJacobian(dm,f,ctx);
    1205:   DMTSGetIJacobian(dm,&ijacobian,NULL);
    1206:   TSGetSNES(ts,&snes);
    1207:   if (!ijacobian) {
    1208:     SNESSetJacobian(snes,Amat,Pmat,SNESTSFormJacobian,ts);
    1209:   }
    1210:   if (Amat) {
    1211:     PetscObjectReference((PetscObject)Amat);
    1212:     MatDestroy(&ts->Arhs);
    1213:     ts->Arhs = Amat;
    1214:   }
    1215:   if (Pmat) {
    1216:     PetscObjectReference((PetscObject)Pmat);
    1217:     MatDestroy(&ts->Brhs);
    1218:     ts->Brhs = Pmat;
    1219:   }
    1220:   return 0;
    1221: }

    1223: /*@C
    1224:    TSSetIFunction - Set the function to compute F(t,U,U_t) where F() = 0 is the DAE to be solved.

    1226:    Logically Collective on TS

    1228:    Input Parameters:
    1229: +  ts  - the TS context obtained from TSCreate()
    1230: .  r   - vector to hold the residual (or NULL to have it created internally)
    1231: .  f   - the function evaluation routine
    1232: -  ctx - user-defined context for private data for the function evaluation routine (may be NULL)

    1234:    Calling sequence of f:
    1235: $     PetscErrorCode f(TS ts,PetscReal t,Vec u,Vec u_t,Vec F,ctx);

    1237: +  t   - time at step/stage being solved
    1238: .  u   - state vector
    1239: .  u_t - time derivative of state vector
    1240: .  F   - function vector
    1241: -  ctx - [optional] user-defined context for matrix evaluation routine

    1243:    Important:
    1244:    The user MUST call either this routine or TSSetRHSFunction() to define the ODE.  When solving DAEs you must use this function.

    1246:    Level: beginner

    1248: .seealso: TSSetRHSJacobian(), TSSetRHSFunction(), TSSetIJacobian()
    1249: @*/
    1250: PetscErrorCode  TSSetIFunction(TS ts,Vec r,TSIFunction f,void *ctx)
    1251: {
    1252:   SNES           snes;
    1253:   Vec            ralloc = NULL;
    1254:   DM             dm;

    1259:   TSGetDM(ts,&dm);
    1260:   DMTSSetIFunction(dm,f,ctx);

    1262:   TSGetSNES(ts,&snes);
    1263:   if (!r && !ts->dm && ts->vec_sol) {
    1264:     VecDuplicate(ts->vec_sol,&ralloc);
    1265:     r  = ralloc;
    1266:   }
    1267:   SNESSetFunction(snes,r,SNESTSFormFunction,ts);
    1268:   VecDestroy(&ralloc);
    1269:   return 0;
    1270: }

    1272: /*@C
    1273:    TSGetIFunction - Returns the vector where the implicit residual is stored and the function/context to compute it.

    1275:    Not Collective

    1277:    Input Parameter:
    1278: .  ts - the TS context

    1280:    Output Parameters:
    1281: +  r - vector to hold residual (or NULL)
    1282: .  func - the function to compute residual (or NULL)
    1283: -  ctx - the function context (or NULL)

    1285:    Level: advanced

    1287: .seealso: TSSetIFunction(), SNESGetFunction()
    1288: @*/
    1289: PetscErrorCode TSGetIFunction(TS ts,Vec *r,TSIFunction *func,void **ctx)
    1290: {
    1291:   SNES           snes;
    1292:   DM             dm;

    1295:   TSGetSNES(ts,&snes);
    1296:   SNESGetFunction(snes,r,NULL,NULL);
    1297:   TSGetDM(ts,&dm);
    1298:   DMTSGetIFunction(dm,func,ctx);
    1299:   return 0;
    1300: }

    1302: /*@C
    1303:    TSGetRHSFunction - Returns the vector where the right hand side is stored and the function/context to compute it.

    1305:    Not Collective

    1307:    Input Parameter:
    1308: .  ts - the TS context

    1310:    Output Parameters:
    1311: +  r - vector to hold computed right hand side (or NULL)
    1312: .  func - the function to compute right hand side (or NULL)
    1313: -  ctx - the function context (or NULL)

    1315:    Level: advanced

    1317: .seealso: TSSetRHSFunction(), SNESGetFunction()
    1318: @*/
    1319: PetscErrorCode TSGetRHSFunction(TS ts,Vec *r,TSRHSFunction *func,void **ctx)
    1320: {
    1321:   SNES           snes;
    1322:   DM             dm;

    1325:   TSGetSNES(ts,&snes);
    1326:   SNESGetFunction(snes,r,NULL,NULL);
    1327:   TSGetDM(ts,&dm);
    1328:   DMTSGetRHSFunction(dm,func,ctx);
    1329:   return 0;
    1330: }

    1332: /*@C
    1333:    TSSetIJacobian - Set the function to compute the matrix dF/dU + a*dF/dU_t where F(t,U,U_t) is the function
    1334:         provided with TSSetIFunction().

    1336:    Logically Collective on TS

    1338:    Input Parameters:
    1339: +  ts  - the TS context obtained from TSCreate()
    1340: .  Amat - (approximate) Jacobian matrix
    1341: .  Pmat - matrix used to compute preconditioner (usually the same as Amat)
    1342: .  f   - the Jacobian evaluation routine
    1343: -  ctx - user-defined context for private data for the Jacobian evaluation routine (may be NULL)

    1345:    Calling sequence of f:
    1346: $    PetscErrorCode f(TS ts,PetscReal t,Vec U,Vec U_t,PetscReal a,Mat Amat,Mat Pmat,void *ctx);

    1348: +  t    - time at step/stage being solved
    1349: .  U    - state vector
    1350: .  U_t  - time derivative of state vector
    1351: .  a    - shift
    1352: .  Amat - (approximate) Jacobian of F(t,U,W+a*U), equivalent to dF/dU + a*dF/dU_t
    1353: .  Pmat - matrix used for constructing preconditioner, usually the same as Amat
    1354: -  ctx  - [optional] user-defined context for matrix evaluation routine

    1356:    Notes:
    1357:    The matrices Amat and Pmat are exactly the matrices that are used by SNES for the nonlinear solve.

    1359:    If you know the operator Amat has a null space you can use MatSetNullSpace() and MatSetTransposeNullSpace() to supply the null
    1360:    space to Amat and the KSP solvers will automatically use that null space as needed during the solution process.

    1362:    The matrix dF/dU + a*dF/dU_t you provide turns out to be
    1363:    the Jacobian of F(t,U,W+a*U) where F(t,U,U_t) = 0 is the DAE to be solved.
    1364:    The time integrator internally approximates U_t by W+a*U where the positive "shift"
    1365:    a and vector W depend on the integration method, step size, and past states. For example with
    1366:    the backward Euler method a = 1/dt and W = -a*U(previous timestep) so
    1367:    W + a*U = a*(U - U(previous timestep)) = (U - U(previous timestep))/dt

    1369:    You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value

    1371:    The TS solver may modify the nonzero structure and the entries of the matrices Amat and Pmat between the calls to f()
    1372:    You should not assume the values are the same in the next call to f() as you set them in the previous call.

    1374:    Level: beginner

    1376: .seealso: TSSetIFunction(), TSSetRHSJacobian(), SNESComputeJacobianDefaultColor(), SNESComputeJacobianDefault(), TSSetRHSFunction()

    1378: @*/
    1379: PetscErrorCode  TSSetIJacobian(TS ts,Mat Amat,Mat Pmat,TSIJacobian f,void *ctx)
    1380: {
    1381:   SNES           snes;
    1382:   DM             dm;

    1390:   TSGetDM(ts,&dm);
    1391:   DMTSSetIJacobian(dm,f,ctx);

    1393:   TSGetSNES(ts,&snes);
    1394:   SNESSetJacobian(snes,Amat,Pmat,SNESTSFormJacobian,ts);
    1395:   return 0;
    1396: }

    1398: /*@
    1399:    TSRHSJacobianSetReuse - restore RHS Jacobian before re-evaluating.  Without this flag, TS will change the sign and
    1400:    shift the RHS Jacobian for a finite-time-step implicit solve, in which case the user function will need to recompute
    1401:    the entire Jacobian.  The reuse flag must be set if the evaluation function will assume that the matrix entries have
    1402:    not been changed by the TS.

    1404:    Logically Collective

    1406:    Input Parameters:
    1407: +  ts - TS context obtained from TSCreate()
    1408: -  reuse - PETSC_TRUE if the RHS Jacobian

    1410:    Level: intermediate

    1412: .seealso: TSSetRHSJacobian(), TSComputeRHSJacobianConstant()
    1413: @*/
    1414: PetscErrorCode TSRHSJacobianSetReuse(TS ts,PetscBool reuse)
    1415: {
    1416:   ts->rhsjacobian.reuse = reuse;
    1417:   return 0;
    1418: }

    1420: /*@C
    1421:    TSSetI2Function - Set the function to compute F(t,U,U_t,U_tt) where F = 0 is the DAE to be solved.

    1423:    Logically Collective on TS

    1425:    Input Parameters:
    1426: +  ts  - the TS context obtained from TSCreate()
    1427: .  F   - vector to hold the residual (or NULL to have it created internally)
    1428: .  fun - the function evaluation routine
    1429: -  ctx - user-defined context for private data for the function evaluation routine (may be NULL)

    1431:    Calling sequence of fun:
    1432: $     PetscErrorCode fun(TS ts,PetscReal t,Vec U,Vec U_t,Vec U_tt,Vec F,ctx);

    1434: +  t    - time at step/stage being solved
    1435: .  U    - state vector
    1436: .  U_t  - time derivative of state vector
    1437: .  U_tt - second time derivative of state vector
    1438: .  F    - function vector
    1439: -  ctx  - [optional] user-defined context for matrix evaluation routine (may be NULL)

    1441:    Level: beginner

    1443: .seealso: TSSetI2Jacobian(), TSSetIFunction(), TSCreate(), TSSetRHSFunction()
    1444: @*/
    1445: PetscErrorCode TSSetI2Function(TS ts,Vec F,TSI2Function fun,void *ctx)
    1446: {
    1447:   DM             dm;

    1451:   TSSetIFunction(ts,F,NULL,NULL);
    1452:   TSGetDM(ts,&dm);
    1453:   DMTSSetI2Function(dm,fun,ctx);
    1454:   return 0;
    1455: }

    1457: /*@C
    1458:   TSGetI2Function - Returns the vector where the implicit residual is stored and the function/context to compute it.

    1460:   Not Collective

    1462:   Input Parameter:
    1463: . ts - the TS context

    1465:   Output Parameters:
    1466: + r - vector to hold residual (or NULL)
    1467: . fun - the function to compute residual (or NULL)
    1468: - ctx - the function context (or NULL)

    1470:   Level: advanced

    1472: .seealso: TSSetIFunction(), SNESGetFunction(), TSCreate()
    1473: @*/
    1474: PetscErrorCode TSGetI2Function(TS ts,Vec *r,TSI2Function *fun,void **ctx)
    1475: {
    1476:   SNES           snes;
    1477:   DM             dm;

    1480:   TSGetSNES(ts,&snes);
    1481:   SNESGetFunction(snes,r,NULL,NULL);
    1482:   TSGetDM(ts,&dm);
    1483:   DMTSGetI2Function(dm,fun,ctx);
    1484:   return 0;
    1485: }

    1487: /*@C
    1488:    TSSetI2Jacobian - Set the function to compute the matrix dF/dU + v*dF/dU_t  + a*dF/dU_tt
    1489:         where F(t,U,U_t,U_tt) is the function you provided with TSSetI2Function().

    1491:    Logically Collective on TS

    1493:    Input Parameters:
    1494: +  ts  - the TS context obtained from TSCreate()
    1495: .  J   - Jacobian matrix
    1496: .  P   - preconditioning matrix for J (may be same as J)
    1497: .  jac - the Jacobian evaluation routine
    1498: -  ctx - user-defined context for private data for the Jacobian evaluation routine (may be NULL)

    1500:    Calling sequence of jac:
    1501: $    PetscErrorCode jac(TS ts,PetscReal t,Vec U,Vec U_t,Vec U_tt,PetscReal v,PetscReal a,Mat J,Mat P,void *ctx);

    1503: +  t    - time at step/stage being solved
    1504: .  U    - state vector
    1505: .  U_t  - time derivative of state vector
    1506: .  U_tt - second time derivative of state vector
    1507: .  v    - shift for U_t
    1508: .  a    - shift for U_tt
    1509: .  J    - Jacobian of G(U) = F(t,U,W+v*U,W'+a*U), equivalent to dF/dU + v*dF/dU_t  + a*dF/dU_tt
    1510: .  P    - preconditioning matrix for J, may be same as J
    1511: -  ctx  - [optional] user-defined context for matrix evaluation routine

    1513:    Notes:
    1514:    The matrices J and P are exactly the matrices that are used by SNES for the nonlinear solve.

    1516:    The matrix dF/dU + v*dF/dU_t + a*dF/dU_tt you provide turns out to be
    1517:    the Jacobian of G(U) = F(t,U,W+v*U,W'+a*U) where F(t,U,U_t,U_tt) = 0 is the DAE to be solved.
    1518:    The time integrator internally approximates U_t by W+v*U and U_tt by W'+a*U  where the positive "shift"
    1519:    parameters 'v' and 'a' and vectors W, W' depend on the integration method, step size, and past states.

    1521:    Level: beginner

    1523: .seealso: TSSetI2Function(), TSGetI2Jacobian()
    1524: @*/
    1525: PetscErrorCode TSSetI2Jacobian(TS ts,Mat J,Mat P,TSI2Jacobian jac,void *ctx)
    1526: {
    1527:   DM             dm;

    1532:   TSSetIJacobian(ts,J,P,NULL,NULL);
    1533:   TSGetDM(ts,&dm);
    1534:   DMTSSetI2Jacobian(dm,jac,ctx);
    1535:   return 0;
    1536: }

    1538: /*@C
    1539:   TSGetI2Jacobian - Returns the implicit Jacobian at the present timestep.

    1541:   Not Collective, but parallel objects are returned if TS is parallel

    1543:   Input Parameter:
    1544: . ts  - The TS context obtained from TSCreate()

    1546:   Output Parameters:
    1547: + J  - The (approximate) Jacobian of F(t,U,U_t,U_tt)
    1548: . P - The matrix from which the preconditioner is constructed, often the same as J
    1549: . jac - The function to compute the Jacobian matrices
    1550: - ctx - User-defined context for Jacobian evaluation routine

    1552:   Notes:
    1553:     You can pass in NULL for any return argument you do not need.

    1555:   Level: advanced

    1557: .seealso: TSGetTimeStep(), TSGetMatrices(), TSGetTime(), TSGetStepNumber(), TSSetI2Jacobian(), TSGetI2Function(), TSCreate()

    1559: @*/
    1560: PetscErrorCode  TSGetI2Jacobian(TS ts,Mat *J,Mat *P,TSI2Jacobian *jac,void **ctx)
    1561: {
    1562:   SNES           snes;
    1563:   DM             dm;

    1565:   TSGetSNES(ts,&snes);
    1566:   SNESSetUpMatrices(snes);
    1567:   SNESGetJacobian(snes,J,P,NULL,NULL);
    1568:   TSGetDM(ts,&dm);
    1569:   DMTSGetI2Jacobian(dm,jac,ctx);
    1570:   return 0;
    1571: }

    1573: /*@
    1574:   TSComputeI2Function - Evaluates the DAE residual written in implicit form F(t,U,U_t,U_tt) = 0

    1576:   Collective on TS

    1578:   Input Parameters:
    1579: + ts - the TS context
    1580: . t - current time
    1581: . U - state vector
    1582: . V - time derivative of state vector (U_t)
    1583: - A - second time derivative of state vector (U_tt)

    1585:   Output Parameter:
    1586: . F - the residual vector

    1588:   Note:
    1589:   Most users should not need to explicitly call this routine, as it
    1590:   is used internally within the nonlinear solvers.

    1592:   Level: developer

    1594: .seealso: TSSetI2Function(), TSGetI2Function()
    1595: @*/
    1596: PetscErrorCode TSComputeI2Function(TS ts,PetscReal t,Vec U,Vec V,Vec A,Vec F)
    1597: {
    1598:   DM             dm;
    1599:   TSI2Function   I2Function;
    1600:   void           *ctx;
    1601:   TSRHSFunction  rhsfunction;

    1609:   TSGetDM(ts,&dm);
    1610:   DMTSGetI2Function(dm,&I2Function,&ctx);
    1611:   DMTSGetRHSFunction(dm,&rhsfunction,NULL);

    1613:   if (!I2Function) {
    1614:     TSComputeIFunction(ts,t,U,A,F,PETSC_FALSE);
    1615:     return 0;
    1616:   }

    1618:   PetscLogEventBegin(TS_FunctionEval,ts,U,V,F);

    1620:   PetscStackPush("TS user implicit function");
    1621:   I2Function(ts,t,U,V,A,F,ctx);
    1622:   PetscStackPop;

    1624:   if (rhsfunction) {
    1625:     Vec Frhs;
    1626:     TSGetRHSVec_Private(ts,&Frhs);
    1627:     TSComputeRHSFunction(ts,t,U,Frhs);
    1628:     VecAXPY(F,-1,Frhs);
    1629:   }

    1631:   PetscLogEventEnd(TS_FunctionEval,ts,U,V,F);
    1632:   return 0;
    1633: }

    1635: /*@
    1636:   TSComputeI2Jacobian - Evaluates the Jacobian of the DAE

    1638:   Collective on TS

    1640:   Input Parameters:
    1641: + ts - the TS context
    1642: . t - current timestep
    1643: . U - state vector
    1644: . V - time derivative of state vector
    1645: . A - second time derivative of state vector
    1646: . shiftV - shift to apply, see note below
    1647: - shiftA - shift to apply, see note below

    1649:   Output Parameters:
    1650: + J - Jacobian matrix
    1651: - P - optional preconditioning matrix

    1653:   Notes:
    1654:   If F(t,U,V,A)=0 is the DAE, the required Jacobian is

    1656:   dF/dU + shiftV*dF/dV + shiftA*dF/dA

    1658:   Most users should not need to explicitly call this routine, as it
    1659:   is used internally within the nonlinear solvers.

    1661:   Level: developer

    1663: .seealso:  TSSetI2Jacobian()
    1664: @*/
    1665: PetscErrorCode TSComputeI2Jacobian(TS ts,PetscReal t,Vec U,Vec V,Vec A,PetscReal shiftV,PetscReal shiftA,Mat J,Mat P)
    1666: {
    1667:   DM             dm;
    1668:   TSI2Jacobian   I2Jacobian;
    1669:   void           *ctx;
    1670:   TSRHSJacobian  rhsjacobian;

    1679:   TSGetDM(ts,&dm);
    1680:   DMTSGetI2Jacobian(dm,&I2Jacobian,&ctx);
    1681:   DMTSGetRHSJacobian(dm,&rhsjacobian,NULL);

    1683:   if (!I2Jacobian) {
    1684:     TSComputeIJacobian(ts,t,U,A,shiftA,J,P,PETSC_FALSE);
    1685:     return 0;
    1686:   }

    1688:   PetscLogEventBegin(TS_JacobianEval,ts,U,J,P);

    1690:   PetscStackPush("TS user implicit Jacobian");
    1691:   I2Jacobian(ts,t,U,V,A,shiftV,shiftA,J,P,ctx);
    1692:   PetscStackPop;

    1694:   if (rhsjacobian) {
    1695:     Mat Jrhs,Prhs;
    1696:     TSGetRHSMats_Private(ts,&Jrhs,&Prhs);
    1697:     TSComputeRHSJacobian(ts,t,U,Jrhs,Prhs);
    1698:     MatAXPY(J,-1,Jrhs,ts->axpy_pattern);
    1699:     if (P != J) MatAXPY(P,-1,Prhs,ts->axpy_pattern);
    1700:   }

    1702:   PetscLogEventEnd(TS_JacobianEval,ts,U,J,P);
    1703:   return 0;
    1704: }

    1706: /*@C
    1707:    TSSetTransientVariable - sets function to transform from state to transient variables

    1709:    Logically Collective

    1711:    Input Parameters:
    1712: +  ts - time stepping context on which to change the transient variable
    1713: .  tvar - a function that transforms to transient variables
    1714: -  ctx - a context for tvar

    1716:     Calling sequence of tvar:
    1717: $     PetscErrorCode tvar(TS ts,Vec p,Vec c,void *ctx);

    1719: +   ts - timestep context
    1720: .   p - input vector (primative form)
    1721: .   c - output vector, transient variables (conservative form)
    1722: -   ctx - [optional] user-defined function context

    1724:    Level: advanced

    1726:    Notes:
    1727:    This is typically used to transform from primitive to conservative variables so that a time integrator (e.g., TSBDF)
    1728:    can be conservative.  In this context, primitive variables P are used to model the state (e.g., because they lead to
    1729:    well-conditioned formulations even in limiting cases such as low-Mach or zero porosity).  The transient variable is
    1730:    C(P), specified by calling this function.  An IFunction thus receives arguments (P, Cdot) and the IJacobian must be
    1731:    evaluated via the chain rule, as in

    1733:      dF/dP + shift * dF/dCdot dC/dP.

    1735: .seealso: DMTSSetTransientVariable(), DMTSGetTransientVariable(), TSSetIFunction(), TSSetIJacobian()
    1736: @*/
    1737: PetscErrorCode TSSetTransientVariable(TS ts,TSTransientVariable tvar,void *ctx)
    1738: {
    1739:   DM             dm;

    1742:   TSGetDM(ts,&dm);
    1743:   DMTSSetTransientVariable(dm,tvar,ctx);
    1744:   return 0;
    1745: }

    1747: /*@
    1748:    TSComputeTransientVariable - transforms state (primitive) variables to transient (conservative) variables

    1750:    Logically Collective

    1752:    Input Parameters:
    1753: +  ts - TS on which to compute
    1754: -  U - state vector to be transformed to transient variables

    1756:    Output Parameters:
    1757: .  C - transient (conservative) variable

    1759:    Developer Notes:
    1760:    If DMTSSetTransientVariable() has not been called, then C is not modified in this routine and C=NULL is allowed.
    1761:    This makes it safe to call without a guard.  One can use TSHasTransientVariable() to check if transient variables are
    1762:    being used.

    1764:    Level: developer

    1766: .seealso: DMTSSetTransientVariable(), TSComputeIFunction(), TSComputeIJacobian()
    1767: @*/
    1768: PetscErrorCode TSComputeTransientVariable(TS ts,Vec U,Vec C)
    1769: {
    1770:   DM             dm;
    1771:   DMTS           dmts;

    1775:   TSGetDM(ts,&dm);
    1776:   DMGetDMTS(dm,&dmts);
    1777:   if (dmts->ops->transientvar) {
    1779:     (*dmts->ops->transientvar)(ts,U,C,dmts->transientvarctx);
    1780:   }
    1781:   return 0;
    1782: }

    1784: /*@
    1785:    TSHasTransientVariable - determine whether transient variables have been set

    1787:    Logically Collective

    1789:    Input Parameters:
    1790: .  ts - TS on which to compute

    1792:    Output Parameters:
    1793: .  has - PETSC_TRUE if transient variables have been set

    1795:    Level: developer

    1797: .seealso: DMTSSetTransientVariable(), TSComputeTransientVariable()
    1798: @*/
    1799: PetscErrorCode TSHasTransientVariable(TS ts,PetscBool *has)
    1800: {
    1801:   DM             dm;
    1802:   DMTS           dmts;

    1805:   TSGetDM(ts,&dm);
    1806:   DMGetDMTS(dm,&dmts);
    1807:   *has = dmts->ops->transientvar ? PETSC_TRUE : PETSC_FALSE;
    1808:   return 0;
    1809: }

    1811: /*@
    1812:    TS2SetSolution - Sets the initial solution and time derivative vectors
    1813:    for use by the TS routines handling second order equations.

    1815:    Logically Collective on TS

    1817:    Input Parameters:
    1818: +  ts - the TS context obtained from TSCreate()
    1819: .  u - the solution vector
    1820: -  v - the time derivative vector

    1822:    Level: beginner

    1824: @*/
    1825: PetscErrorCode  TS2SetSolution(TS ts,Vec u,Vec v)
    1826: {
    1830:   TSSetSolution(ts,u);
    1831:   PetscObjectReference((PetscObject)v);
    1832:   VecDestroy(&ts->vec_dot);
    1833:   ts->vec_dot = v;
    1834:   return 0;
    1835: }

    1837: /*@
    1838:    TS2GetSolution - Returns the solution and time derivative at the present timestep
    1839:    for second order equations. It is valid to call this routine inside the function
    1840:    that you are evaluating in order to move to the new timestep. This vector not
    1841:    changed until the solution at the next timestep has been calculated.

    1843:    Not Collective, but Vec returned is parallel if TS is parallel

    1845:    Input Parameter:
    1846: .  ts - the TS context obtained from TSCreate()

    1848:    Output Parameters:
    1849: +  u - the vector containing the solution
    1850: -  v - the vector containing the time derivative

    1852:    Level: intermediate

    1854: .seealso: TS2SetSolution(), TSGetTimeStep(), TSGetTime()

    1856: @*/
    1857: PetscErrorCode  TS2GetSolution(TS ts,Vec *u,Vec *v)
    1858: {
    1862:   if (u) *u = ts->vec_sol;
    1863:   if (v) *v = ts->vec_dot;
    1864:   return 0;
    1865: }

    1867: /*@C
    1868:   TSLoad - Loads a KSP that has been stored in binary  with KSPView().

    1870:   Collective on PetscViewer

    1872:   Input Parameters:
    1873: + newdm - the newly loaded TS, this needs to have been created with TSCreate() or
    1874:            some related function before a call to TSLoad().
    1875: - viewer - binary file viewer, obtained from PetscViewerBinaryOpen()

    1877:    Level: intermediate

    1879:   Notes:
    1880:    The type is determined by the data in the file, any type set into the TS before this call is ignored.

    1882:   Notes for advanced users:
    1883:   Most users should not need to know the details of the binary storage
    1884:   format, since TSLoad() and TSView() completely hide these details.
    1885:   But for anyone who's interested, the standard binary matrix storage
    1886:   format is
    1887: .vb
    1888:      has not yet been determined
    1889: .ve

    1891: .seealso: PetscViewerBinaryOpen(), TSView(), MatLoad(), VecLoad()
    1892: @*/
    1893: PetscErrorCode  TSLoad(TS ts, PetscViewer viewer)
    1894: {
    1895:   PetscBool      isbinary;
    1896:   PetscInt       classid;
    1897:   char           type[256];
    1898:   DMTS           sdm;
    1899:   DM             dm;

    1903:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);

    1906:   PetscViewerBinaryRead(viewer,&classid,1,NULL,PETSC_INT);
    1908:   PetscViewerBinaryRead(viewer,type,256,NULL,PETSC_CHAR);
    1909:   TSSetType(ts, type);
    1910:   if (ts->ops->load) {
    1911:     (*ts->ops->load)(ts,viewer);
    1912:   }
    1913:   DMCreate(PetscObjectComm((PetscObject)ts),&dm);
    1914:   DMLoad(dm,viewer);
    1915:   TSSetDM(ts,dm);
    1916:   DMCreateGlobalVector(ts->dm,&ts->vec_sol);
    1917:   VecLoad(ts->vec_sol,viewer);
    1918:   DMGetDMTS(ts->dm,&sdm);
    1919:   DMTSLoad(sdm,viewer);
    1920:   return 0;
    1921: }

    1923: #include <petscdraw.h>
    1924: #if defined(PETSC_HAVE_SAWS)
    1925: #include <petscviewersaws.h>
    1926: #endif

    1928: /*@C
    1929:    TSViewFromOptions - View from Options

    1931:    Collective on TS

    1933:    Input Parameters:
    1934: +  A - the application ordering context
    1935: .  obj - Optional object
    1936: -  name - command line option

    1938:    Level: intermediate
    1939: .seealso:  TS, TSView, PetscObjectViewFromOptions(), TSCreate()
    1940: @*/
    1941: PetscErrorCode  TSViewFromOptions(TS A,PetscObject obj,const char name[])
    1942: {
    1944:   PetscObjectViewFromOptions((PetscObject)A,obj,name);
    1945:   return 0;
    1946: }

    1948: /*@C
    1949:     TSView - Prints the TS data structure.

    1951:     Collective on TS

    1953:     Input Parameters:
    1954: +   ts - the TS context obtained from TSCreate()
    1955: -   viewer - visualization context

    1957:     Options Database Key:
    1958: .   -ts_view - calls TSView() at end of TSStep()

    1960:     Notes:
    1961:     The available visualization contexts include
    1962: +     PETSC_VIEWER_STDOUT_SELF - standard output (default)
    1963: -     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
    1964:          output where only the first processor opens
    1965:          the file.  All other processors send their
    1966:          data to the first processor to print.

    1968:     The user can open an alternative visualization context with
    1969:     PetscViewerASCIIOpen() - output to a specified file.

    1971:     In the debugger you can do "call TSView(ts,0)" to display the TS solver. (The same holds for any PETSc object viewer).

    1973:     Level: beginner

    1975: .seealso: PetscViewerASCIIOpen()
    1976: @*/
    1977: PetscErrorCode  TSView(TS ts,PetscViewer viewer)
    1978: {
    1979:   TSType         type;
    1980:   PetscBool      iascii,isstring,isundials,isbinary,isdraw;
    1981:   DMTS           sdm;
    1982: #if defined(PETSC_HAVE_SAWS)
    1983:   PetscBool      issaws;
    1984: #endif

    1987:   if (!viewer) {
    1988:     PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)ts),&viewer);
    1989:   }

    1993:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    1994:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
    1995:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);
    1996:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);
    1997: #if defined(PETSC_HAVE_SAWS)
    1998:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSAWS,&issaws);
    1999: #endif
    2000:   if (iascii) {
    2001:     PetscObjectPrintClassNamePrefixType((PetscObject)ts,viewer);
    2002:     if (ts->ops->view) {
    2003:       PetscViewerASCIIPushTab(viewer);
    2004:       (*ts->ops->view)(ts,viewer);
    2005:       PetscViewerASCIIPopTab(viewer);
    2006:     }
    2007:     if (ts->max_steps < PETSC_MAX_INT) {
    2008:       PetscViewerASCIIPrintf(viewer,"  maximum steps=%D\n",ts->max_steps);
    2009:     }
    2010:     if (ts->max_time < PETSC_MAX_REAL) {
    2011:       PetscViewerASCIIPrintf(viewer,"  maximum time=%g\n",(double)ts->max_time);
    2012:     }
    2013:     if (ts->ifuncs) {
    2014:       PetscViewerASCIIPrintf(viewer,"  total number of I function evaluations=%D\n",ts->ifuncs);
    2015:     }
    2016:     if (ts->ijacs) {
    2017:       PetscViewerASCIIPrintf(viewer,"  total number of I Jacobian evaluations=%D\n",ts->ijacs);
    2018:     }
    2019:     if (ts->rhsfuncs) {
    2020:       PetscViewerASCIIPrintf(viewer,"  total number of RHS function evaluations=%D\n",ts->rhsfuncs);
    2021:     }
    2022:     if (ts->rhsjacs) {
    2023:       PetscViewerASCIIPrintf(viewer,"  total number of RHS Jacobian evaluations=%D\n",ts->rhsjacs);
    2024:     }
    2025:     if (ts->usessnes) {
    2026:       PetscBool lin;
    2027:       if (ts->problem_type == TS_NONLINEAR) {
    2028:         PetscViewerASCIIPrintf(viewer,"  total number of nonlinear solver iterations=%D\n",ts->snes_its);
    2029:       }
    2030:       PetscViewerASCIIPrintf(viewer,"  total number of linear solver iterations=%D\n",ts->ksp_its);
    2031:       PetscObjectTypeCompareAny((PetscObject)ts->snes,&lin,SNESKSPONLY,SNESKSPTRANSPOSEONLY,"");
    2032:       PetscViewerASCIIPrintf(viewer,"  total number of %slinear solve failures=%D\n",lin ? "" : "non",ts->num_snes_failures);
    2033:     }
    2034:     PetscViewerASCIIPrintf(viewer,"  total number of rejected steps=%D\n",ts->reject);
    2035:     if (ts->vrtol) {
    2036:       PetscViewerASCIIPrintf(viewer,"  using vector of relative error tolerances, ");
    2037:     } else {
    2038:       PetscViewerASCIIPrintf(viewer,"  using relative error tolerance of %g, ",(double)ts->rtol);
    2039:     }
    2040:     if (ts->vatol) {
    2041:       PetscViewerASCIIPrintf(viewer,"  using vector of absolute error tolerances\n");
    2042:     } else {
    2043:       PetscViewerASCIIPrintf(viewer,"  using absolute error tolerance of %g\n",(double)ts->atol);
    2044:     }
    2045:     PetscViewerASCIIPushTab(viewer);
    2046:     TSAdaptView(ts->adapt,viewer);
    2047:     PetscViewerASCIIPopTab(viewer);
    2048:   } else if (isstring) {
    2049:     TSGetType(ts,&type);
    2050:     PetscViewerStringSPrintf(viewer," TSType: %-7.7s",type);
    2051:     if (ts->ops->view) (*ts->ops->view)(ts,viewer);
    2052:   } else if (isbinary) {
    2053:     PetscInt    classid = TS_FILE_CLASSID;
    2054:     MPI_Comm    comm;
    2055:     PetscMPIInt rank;
    2056:     char        type[256];

    2058:     PetscObjectGetComm((PetscObject)ts,&comm);
    2059:     MPI_Comm_rank(comm,&rank);
    2060:     if (rank == 0) {
    2061:       PetscViewerBinaryWrite(viewer,&classid,1,PETSC_INT);
    2062:       PetscStrncpy(type,((PetscObject)ts)->type_name,256);
    2063:       PetscViewerBinaryWrite(viewer,type,256,PETSC_CHAR);
    2064:     }
    2065:     if (ts->ops->view) {
    2066:       (*ts->ops->view)(ts,viewer);
    2067:     }
    2068:     if (ts->adapt) TSAdaptView(ts->adapt,viewer);
    2069:     DMView(ts->dm,viewer);
    2070:     VecView(ts->vec_sol,viewer);
    2071:     DMGetDMTS(ts->dm,&sdm);
    2072:     DMTSView(sdm,viewer);
    2073:   } else if (isdraw) {
    2074:     PetscDraw draw;
    2075:     char      str[36];
    2076:     PetscReal x,y,bottom,h;

    2078:     PetscViewerDrawGetDraw(viewer,0,&draw);
    2079:     PetscDrawGetCurrentPoint(draw,&x,&y);
    2080:     PetscStrcpy(str,"TS: ");
    2081:     PetscStrcat(str,((PetscObject)ts)->type_name);
    2082:     PetscDrawStringBoxed(draw,x,y,PETSC_DRAW_BLACK,PETSC_DRAW_BLACK,str,NULL,&h);
    2083:     bottom = y - h;
    2084:     PetscDrawPushCurrentPoint(draw,x,bottom);
    2085:     if (ts->ops->view) {
    2086:       (*ts->ops->view)(ts,viewer);
    2087:     }
    2088:     if (ts->adapt) TSAdaptView(ts->adapt,viewer);
    2089:     if (ts->snes)  SNESView(ts->snes,viewer);
    2090:     PetscDrawPopCurrentPoint(draw);
    2091: #if defined(PETSC_HAVE_SAWS)
    2092:   } else if (issaws) {
    2093:     PetscMPIInt rank;
    2094:     const char  *name;

    2096:     PetscObjectGetName((PetscObject)ts,&name);
    2097:     MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
    2098:     if (!((PetscObject)ts)->amsmem && rank == 0) {
    2099:       char       dir[1024];

    2101:       PetscObjectViewSAWs((PetscObject)ts,viewer);
    2102:       PetscSNPrintf(dir,1024,"/PETSc/Objects/%s/time_step",name);
    2103:       PetscStackCallSAWs(SAWs_Register,(dir,&ts->steps,1,SAWs_READ,SAWs_INT));
    2104:       PetscSNPrintf(dir,1024,"/PETSc/Objects/%s/time",name);
    2105:       PetscStackCallSAWs(SAWs_Register,(dir,&ts->ptime,1,SAWs_READ,SAWs_DOUBLE));
    2106:     }
    2107:     if (ts->ops->view) {
    2108:       (*ts->ops->view)(ts,viewer);
    2109:     }
    2110: #endif
    2111:   }
    2112:   if (ts->snes && ts->usessnes)  {
    2113:     PetscViewerASCIIPushTab(viewer);
    2114:     SNESView(ts->snes,viewer);
    2115:     PetscViewerASCIIPopTab(viewer);
    2116:   }
    2117:   DMGetDMTS(ts->dm,&sdm);
    2118:   DMTSView(sdm,viewer);

    2120:   PetscViewerASCIIPushTab(viewer);
    2121:   PetscObjectTypeCompare((PetscObject)ts,TSSUNDIALS,&isundials);
    2122:   PetscViewerASCIIPopTab(viewer);
    2123:   return 0;
    2124: }

    2126: /*@
    2127:    TSSetApplicationContext - Sets an optional user-defined context for
    2128:    the timesteppers.

    2130:    Logically Collective on TS

    2132:    Input Parameters:
    2133: +  ts - the TS context obtained from TSCreate()
    2134: -  usrP - optional user context

    2136:    Fortran Notes:
    2137:     To use this from Fortran you must write a Fortran interface definition for this
    2138:     function that tells Fortran the Fortran derived data type that you are passing in as the ctx argument.

    2140:    Level: intermediate

    2142: .seealso: TSGetApplicationContext()
    2143: @*/
    2144: PetscErrorCode  TSSetApplicationContext(TS ts,void *usrP)
    2145: {
    2147:   ts->user = usrP;
    2148:   return 0;
    2149: }

    2151: /*@
    2152:     TSGetApplicationContext - Gets the user-defined context for the
    2153:     timestepper.

    2155:     Not Collective

    2157:     Input Parameter:
    2158: .   ts - the TS context obtained from TSCreate()

    2160:     Output Parameter:
    2161: .   usrP - user context

    2163:    Fortran Notes:
    2164:     To use this from Fortran you must write a Fortran interface definition for this
    2165:     function that tells Fortran the Fortran derived data type that you are passing in as the ctx argument.

    2167:     Level: intermediate

    2169: .seealso: TSSetApplicationContext()
    2170: @*/
    2171: PetscErrorCode  TSGetApplicationContext(TS ts,void *usrP)
    2172: {
    2174:   *(void**)usrP = ts->user;
    2175:   return 0;
    2176: }

    2178: /*@
    2179:    TSGetStepNumber - Gets the number of steps completed.

    2181:    Not Collective

    2183:    Input Parameter:
    2184: .  ts - the TS context obtained from TSCreate()

    2186:    Output Parameter:
    2187: .  steps - number of steps completed so far

    2189:    Level: intermediate

    2191: .seealso: TSGetTime(), TSGetTimeStep(), TSSetPreStep(), TSSetPreStage(), TSSetPostStage(), TSSetPostStep()
    2192: @*/
    2193: PetscErrorCode TSGetStepNumber(TS ts,PetscInt *steps)
    2194: {
    2197:   *steps = ts->steps;
    2198:   return 0;
    2199: }

    2201: /*@
    2202:    TSSetStepNumber - Sets the number of steps completed.

    2204:    Logically Collective on TS

    2206:    Input Parameters:
    2207: +  ts - the TS context
    2208: -  steps - number of steps completed so far

    2210:    Notes:
    2211:    For most uses of the TS solvers the user need not explicitly call
    2212:    TSSetStepNumber(), as the step counter is appropriately updated in
    2213:    TSSolve()/TSStep()/TSRollBack(). Power users may call this routine to
    2214:    reinitialize timestepping by setting the step counter to zero (and time
    2215:    to the initial time) to solve a similar problem with different initial
    2216:    conditions or parameters. Other possible use case is to continue
    2217:    timestepping from a previously interrupted run in such a way that TS
    2218:    monitors will be called with a initial nonzero step counter.

    2220:    Level: advanced

    2222: .seealso: TSGetStepNumber(), TSSetTime(), TSSetTimeStep(), TSSetSolution()
    2223: @*/
    2224: PetscErrorCode TSSetStepNumber(TS ts,PetscInt steps)
    2225: {
    2229:   ts->steps = steps;
    2230:   return 0;
    2231: }

    2233: /*@
    2234:    TSSetTimeStep - Allows one to reset the timestep at any time,
    2235:    useful for simple pseudo-timestepping codes.

    2237:    Logically Collective on TS

    2239:    Input Parameters:
    2240: +  ts - the TS context obtained from TSCreate()
    2241: -  time_step - the size of the timestep

    2243:    Level: intermediate

    2245: .seealso: TSGetTimeStep(), TSSetTime()

    2247: @*/
    2248: PetscErrorCode  TSSetTimeStep(TS ts,PetscReal time_step)
    2249: {
    2252:   ts->time_step = time_step;
    2253:   return 0;
    2254: }

    2256: /*@
    2257:    TSSetExactFinalTime - Determines whether to adapt the final time step to
    2258:      match the exact final time, interpolate solution to the exact final time,
    2259:      or just return at the final time TS computed.

    2261:   Logically Collective on TS

    2263:    Input Parameters:
    2264: +   ts - the time-step context
    2265: -   eftopt - exact final time option

    2267: $  TS_EXACTFINALTIME_STEPOVER    - Don't do anything if final time is exceeded
    2268: $  TS_EXACTFINALTIME_INTERPOLATE - Interpolate back to final time
    2269: $  TS_EXACTFINALTIME_MATCHSTEP - Adapt final time step to match the final time

    2271:    Options Database:
    2272: .   -ts_exact_final_time <stepover,interpolate,matchstep> - select the final step at runtime

    2274:    Warning: If you use the option TS_EXACTFINALTIME_STEPOVER the solution may be at a very different time
    2275:     then the final time you selected.

    2277:    Level: beginner

    2279: .seealso: TSExactFinalTimeOption, TSGetExactFinalTime()
    2280: @*/
    2281: PetscErrorCode TSSetExactFinalTime(TS ts,TSExactFinalTimeOption eftopt)
    2282: {
    2285:   ts->exact_final_time = eftopt;
    2286:   return 0;
    2287: }

    2289: /*@
    2290:    TSGetExactFinalTime - Gets the exact final time option.

    2292:    Not Collective

    2294:    Input Parameter:
    2295: .  ts - the TS context

    2297:    Output Parameter:
    2298: .  eftopt - exact final time option

    2300:    Level: beginner

    2302: .seealso: TSExactFinalTimeOption, TSSetExactFinalTime()
    2303: @*/
    2304: PetscErrorCode TSGetExactFinalTime(TS ts,TSExactFinalTimeOption *eftopt)
    2305: {
    2308:   *eftopt = ts->exact_final_time;
    2309:   return 0;
    2310: }

    2312: /*@
    2313:    TSGetTimeStep - Gets the current timestep size.

    2315:    Not Collective

    2317:    Input Parameter:
    2318: .  ts - the TS context obtained from TSCreate()

    2320:    Output Parameter:
    2321: .  dt - the current timestep size

    2323:    Level: intermediate

    2325: .seealso: TSSetTimeStep(), TSGetTime()

    2327: @*/
    2328: PetscErrorCode  TSGetTimeStep(TS ts,PetscReal *dt)
    2329: {
    2332:   *dt = ts->time_step;
    2333:   return 0;
    2334: }

    2336: /*@
    2337:    TSGetSolution - Returns the solution at the present timestep. It
    2338:    is valid to call this routine inside the function that you are evaluating
    2339:    in order to move to the new timestep. This vector not changed until
    2340:    the solution at the next timestep has been calculated.

    2342:    Not Collective, but Vec returned is parallel if TS is parallel

    2344:    Input Parameter:
    2345: .  ts - the TS context obtained from TSCreate()

    2347:    Output Parameter:
    2348: .  v - the vector containing the solution

    2350:    Note: If you used TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP); this does not return the solution at the requested
    2351:    final time. It returns the solution at the next timestep.

    2353:    Level: intermediate

    2355: .seealso: TSGetTimeStep(), TSGetTime(), TSGetSolveTime(), TSGetSolutionComponents(), TSSetSolutionFunction()

    2357: @*/
    2358: PetscErrorCode  TSGetSolution(TS ts,Vec *v)
    2359: {
    2362:   *v = ts->vec_sol;
    2363:   return 0;
    2364: }

    2366: /*@
    2367:    TSGetSolutionComponents - Returns any solution components at the present
    2368:    timestep, if available for the time integration method being used.
    2369:    Solution components are quantities that share the same size and
    2370:    structure as the solution vector.

    2372:    Not Collective, but Vec returned is parallel if TS is parallel

    2374:    Parameters :
    2375: +  ts - the TS context obtained from TSCreate() (input parameter).
    2376: .  n - If v is PETSC_NULL, then the number of solution components is
    2377:        returned through n, else the n-th solution component is
    2378:        returned in v.
    2379: -  v - the vector containing the n-th solution component
    2380:        (may be PETSC_NULL to use this function to find out
    2381:         the number of solutions components).

    2383:    Level: advanced

    2385: .seealso: TSGetSolution()

    2387: @*/
    2388: PetscErrorCode  TSGetSolutionComponents(TS ts,PetscInt *n,Vec *v)
    2389: {
    2391:   if (!ts->ops->getsolutioncomponents) *n = 0;
    2392:   else {
    2393:     (*ts->ops->getsolutioncomponents)(ts,n,v);
    2394:   }
    2395:   return 0;
    2396: }

    2398: /*@
    2399:    TSGetAuxSolution - Returns an auxiliary solution at the present
    2400:    timestep, if available for the time integration method being used.

    2402:    Not Collective, but Vec returned is parallel if TS is parallel

    2404:    Parameters :
    2405: +  ts - the TS context obtained from TSCreate() (input parameter).
    2406: -  v - the vector containing the auxiliary solution

    2408:    Level: intermediate

    2410: .seealso: TSGetSolution()

    2412: @*/
    2413: PetscErrorCode  TSGetAuxSolution(TS ts,Vec *v)
    2414: {
    2416:   if (ts->ops->getauxsolution) {
    2417:     (*ts->ops->getauxsolution)(ts,v);
    2418:   } else {
    2419:     VecZeroEntries(*v);
    2420:   }
    2421:   return 0;
    2422: }

    2424: /*@
    2425:    TSGetTimeError - Returns the estimated error vector, if the chosen
    2426:    TSType has an error estimation functionality.

    2428:    Not Collective, but Vec returned is parallel if TS is parallel

    2430:    Note: MUST call after TSSetUp()

    2432:    Parameters :
    2433: +  ts - the TS context obtained from TSCreate() (input parameter).
    2434: .  n - current estimate (n=0) or previous one (n=-1)
    2435: -  v - the vector containing the error (same size as the solution).

    2437:    Level: intermediate

    2439: .seealso: TSGetSolution(), TSSetTimeError()

    2441: @*/
    2442: PetscErrorCode  TSGetTimeError(TS ts,PetscInt n,Vec *v)
    2443: {
    2445:   if (ts->ops->gettimeerror) {
    2446:     (*ts->ops->gettimeerror)(ts,n,v);
    2447:   } else {
    2448:     VecZeroEntries(*v);
    2449:   }
    2450:   return 0;
    2451: }

    2453: /*@
    2454:    TSSetTimeError - Sets the estimated error vector, if the chosen
    2455:    TSType has an error estimation functionality. This can be used
    2456:    to restart such a time integrator with a given error vector.

    2458:    Not Collective, but Vec returned is parallel if TS is parallel

    2460:    Parameters :
    2461: +  ts - the TS context obtained from TSCreate() (input parameter).
    2462: -  v - the vector containing the error (same size as the solution).

    2464:    Level: intermediate

    2466: .seealso: TSSetSolution(), TSGetTimeError)

    2468: @*/
    2469: PetscErrorCode  TSSetTimeError(TS ts,Vec v)
    2470: {
    2473:   if (ts->ops->settimeerror) {
    2474:     (*ts->ops->settimeerror)(ts,v);
    2475:   }
    2476:   return 0;
    2477: }

    2479: /* ----- Routines to initialize and destroy a timestepper ---- */
    2480: /*@
    2481:   TSSetProblemType - Sets the type of problem to be solved.

    2483:   Not collective

    2485:   Input Parameters:
    2486: + ts   - The TS
    2487: - type - One of TS_LINEAR, TS_NONLINEAR where these types refer to problems of the forms
    2488: .vb
    2489:          U_t - A U = 0      (linear)
    2490:          U_t - A(t) U = 0   (linear)
    2491:          F(t,U,U_t) = 0     (nonlinear)
    2492: .ve

    2494:    Level: beginner

    2496: .seealso: TSSetUp(), TSProblemType, TS
    2497: @*/
    2498: PetscErrorCode  TSSetProblemType(TS ts, TSProblemType type)
    2499: {
    2501:   ts->problem_type = type;
    2502:   if (type == TS_LINEAR) {
    2503:     SNES snes;
    2504:     TSGetSNES(ts,&snes);
    2505:     SNESSetType(snes,SNESKSPONLY);
    2506:   }
    2507:   return 0;
    2508: }

    2510: /*@C
    2511:   TSGetProblemType - Gets the type of problem to be solved.

    2513:   Not collective

    2515:   Input Parameter:
    2516: . ts   - The TS

    2518:   Output Parameter:
    2519: . type - One of TS_LINEAR, TS_NONLINEAR where these types refer to problems of the forms
    2520: .vb
    2521:          M U_t = A U
    2522:          M(t) U_t = A(t) U
    2523:          F(t,U,U_t)
    2524: .ve

    2526:    Level: beginner

    2528: .seealso: TSSetUp(), TSProblemType, TS
    2529: @*/
    2530: PetscErrorCode  TSGetProblemType(TS ts, TSProblemType *type)
    2531: {
    2534:   *type = ts->problem_type;
    2535:   return 0;
    2536: }

    2538: /*
    2539:     Attempt to check/preset a default value for the exact final time option. This is needed at the beginning of TSSolve() and in TSSetUp()
    2540: */
    2541: static PetscErrorCode TSSetExactFinalTimeDefault(TS ts)
    2542: {
    2543:   PetscBool      isnone;

    2545:   TSGetAdapt(ts,&ts->adapt);
    2546:   TSAdaptSetDefaultType(ts->adapt,ts->default_adapt_type);

    2548:   PetscObjectTypeCompare((PetscObject)ts->adapt,TSADAPTNONE,&isnone);
    2549:   if (!isnone && ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED) {
    2550:     ts->exact_final_time = TS_EXACTFINALTIME_MATCHSTEP;
    2551:   } else if (ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED) {
    2552:     ts->exact_final_time = TS_EXACTFINALTIME_INTERPOLATE;
    2553:   }
    2554:   return 0;
    2555: }

    2557: /*@
    2558:    TSSetUp - Sets up the internal data structures for the later use of a timestepper.

    2560:    Collective on TS

    2562:    Input Parameter:
    2563: .  ts - the TS context obtained from TSCreate()

    2565:    Notes:
    2566:    For basic use of the TS solvers the user need not explicitly call
    2567:    TSSetUp(), since these actions will automatically occur during
    2568:    the call to TSStep() or TSSolve().  However, if one wishes to control this
    2569:    phase separately, TSSetUp() should be called after TSCreate()
    2570:    and optional routines of the form TSSetXXX(), but before TSStep() and TSSolve().

    2572:    Level: advanced

    2574: .seealso: TSCreate(), TSStep(), TSDestroy(), TSSolve()
    2575: @*/
    2576: PetscErrorCode  TSSetUp(TS ts)
    2577: {
    2578:   DM             dm;
    2579:   PetscErrorCode (*func)(SNES,Vec,Vec,void*);
    2580:   PetscErrorCode (*jac)(SNES,Vec,Mat,Mat,void*);
    2581:   TSIFunction    ifun;
    2582:   TSIJacobian    ijac;
    2583:   TSI2Jacobian   i2jac;
    2584:   TSRHSJacobian  rhsjac;

    2587:   if (ts->setupcalled) return 0;

    2589:   if (!((PetscObject)ts)->type_name) {
    2590:     TSGetIFunction(ts,NULL,&ifun,NULL);
    2591:     TSSetType(ts,ifun ? TSBEULER : TSEULER);
    2592:   }

    2594:   if (!ts->vec_sol) {
    2595:     if (ts->dm) {
    2596:       DMCreateGlobalVector(ts->dm,&ts->vec_sol);
    2597:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call TSSetSolution() first");
    2598:   }

    2600:   if (!ts->Jacp && ts->Jacprhs) { /* IJacobianP shares the same matrix with RHSJacobianP if only RHSJacobianP is provided */
    2601:     PetscObjectReference((PetscObject)ts->Jacprhs);
    2602:     ts->Jacp = ts->Jacprhs;
    2603:   }

    2605:   if (ts->quadraturets) {
    2606:     TSSetUp(ts->quadraturets);
    2607:     VecDestroy(&ts->vec_costintegrand);
    2608:     VecDuplicate(ts->quadraturets->vec_sol,&ts->vec_costintegrand);
    2609:   }

    2611:   TSGetRHSJacobian(ts,NULL,NULL,&rhsjac,NULL);
    2612:   if (rhsjac == TSComputeRHSJacobianConstant) {
    2613:     Mat Amat,Pmat;
    2614:     SNES snes;
    2615:     TSGetSNES(ts,&snes);
    2616:     SNESGetJacobian(snes,&Amat,&Pmat,NULL,NULL);
    2617:     /* Matching matrices implies that an IJacobian is NOT set, because if it had been set, the IJacobian's matrix would
    2618:      * have displaced the RHS matrix */
    2619:     if (Amat && Amat == ts->Arhs) {
    2620:       /* we need to copy the values of the matrix because for the constant Jacobian case the user will never set the numerical values in this new location */
    2621:       MatDuplicate(ts->Arhs,MAT_COPY_VALUES,&Amat);
    2622:       SNESSetJacobian(snes,Amat,NULL,NULL,NULL);
    2623:       MatDestroy(&Amat);
    2624:     }
    2625:     if (Pmat && Pmat == ts->Brhs) {
    2626:       MatDuplicate(ts->Brhs,MAT_COPY_VALUES,&Pmat);
    2627:       SNESSetJacobian(snes,NULL,Pmat,NULL,NULL);
    2628:       MatDestroy(&Pmat);
    2629:     }
    2630:   }

    2632:   TSGetAdapt(ts,&ts->adapt);
    2633:   TSAdaptSetDefaultType(ts->adapt,ts->default_adapt_type);

    2635:   if (ts->ops->setup) {
    2636:     (*ts->ops->setup)(ts);
    2637:   }

    2639:   TSSetExactFinalTimeDefault(ts);

    2641:   /* In the case where we've set a DMTSFunction or what have you, we need the default SNESFunction
    2642:      to be set right but can't do it elsewhere due to the overreliance on ctx=ts.
    2643:    */
    2644:   TSGetDM(ts,&dm);
    2645:   DMSNESGetFunction(dm,&func,NULL);
    2646:   if (!func) {
    2647:     DMSNESSetFunction(dm,SNESTSFormFunction,ts);
    2648:   }
    2649:   /* If the SNES doesn't have a jacobian set and the TS has an ijacobian or rhsjacobian set, set the SNES to use it.
    2650:      Otherwise, the SNES will use coloring internally to form the Jacobian.
    2651:    */
    2652:   DMSNESGetJacobian(dm,&jac,NULL);
    2653:   DMTSGetIJacobian(dm,&ijac,NULL);
    2654:   DMTSGetI2Jacobian(dm,&i2jac,NULL);
    2655:   DMTSGetRHSJacobian(dm,&rhsjac,NULL);
    2656:   if (!jac && (ijac || i2jac || rhsjac)) {
    2657:     DMSNESSetJacobian(dm,SNESTSFormJacobian,ts);
    2658:   }

    2660:   /* if time integration scheme has a starting method, call it */
    2661:   if (ts->ops->startingmethod) {
    2662:     (*ts->ops->startingmethod)(ts);
    2663:   }

    2665:   ts->setupcalled = PETSC_TRUE;
    2666:   return 0;
    2667: }

    2669: /*@
    2670:    TSReset - Resets a TS context and removes any allocated Vecs and Mats.

    2672:    Collective on TS

    2674:    Input Parameter:
    2675: .  ts - the TS context obtained from TSCreate()

    2677:    Level: beginner

    2679: .seealso: TSCreate(), TSSetup(), TSDestroy()
    2680: @*/
    2681: PetscErrorCode  TSReset(TS ts)
    2682: {
    2683:   TS_RHSSplitLink ilink = ts->tsrhssplit,next;

    2687:   if (ts->ops->reset) {
    2688:     (*ts->ops->reset)(ts);
    2689:   }
    2690:   if (ts->snes) SNESReset(ts->snes);
    2691:   if (ts->adapt) TSAdaptReset(ts->adapt);

    2693:   MatDestroy(&ts->Arhs);
    2694:   MatDestroy(&ts->Brhs);
    2695:   VecDestroy(&ts->Frhs);
    2696:   VecDestroy(&ts->vec_sol);
    2697:   VecDestroy(&ts->vec_dot);
    2698:   VecDestroy(&ts->vatol);
    2699:   VecDestroy(&ts->vrtol);
    2700:   VecDestroyVecs(ts->nwork,&ts->work);

    2702:   MatDestroy(&ts->Jacprhs);
    2703:   MatDestroy(&ts->Jacp);
    2704:   if (ts->forward_solve) {
    2705:     TSForwardReset(ts);
    2706:   }
    2707:   if (ts->quadraturets) {
    2708:     TSReset(ts->quadraturets);
    2709:     VecDestroy(&ts->vec_costintegrand);
    2710:   }
    2711:   while (ilink) {
    2712:     next = ilink->next;
    2713:     TSDestroy(&ilink->ts);
    2714:     PetscFree(ilink->splitname);
    2715:     ISDestroy(&ilink->is);
    2716:     PetscFree(ilink);
    2717:     ilink = next;
    2718:   }
    2719:   ts->tsrhssplit = NULL;
    2720:   ts->num_rhs_splits = 0;
    2721:   ts->setupcalled = PETSC_FALSE;
    2722:   return 0;
    2723: }

    2725: /*@C
    2726:    TSDestroy - Destroys the timestepper context that was created
    2727:    with TSCreate().

    2729:    Collective on TS

    2731:    Input Parameter:
    2732: .  ts - the TS context obtained from TSCreate()

    2734:    Level: beginner

    2736: .seealso: TSCreate(), TSSetUp(), TSSolve()
    2737: @*/
    2738: PetscErrorCode  TSDestroy(TS *ts)
    2739: {
    2740:   if (!*ts) return 0;
    2742:   if (--((PetscObject)(*ts))->refct > 0) {*ts = NULL; return 0;}

    2744:   TSReset(*ts);
    2745:   TSAdjointReset(*ts);
    2746:   if ((*ts)->forward_solve) {
    2747:     TSForwardReset(*ts);
    2748:   }
    2749:   /* if memory was published with SAWs then destroy it */
    2750:   PetscObjectSAWsViewOff((PetscObject)*ts);
    2751:   if ((*ts)->ops->destroy) (*(*ts)->ops->destroy)((*ts));

    2753:   TSTrajectoryDestroy(&(*ts)->trajectory);

    2755:   TSAdaptDestroy(&(*ts)->adapt);
    2756:   TSEventDestroy(&(*ts)->event);

    2758:   SNESDestroy(&(*ts)->snes);
    2759:   DMDestroy(&(*ts)->dm);
    2760:   TSMonitorCancel((*ts));
    2761:   TSAdjointMonitorCancel((*ts));

    2763:   TSDestroy(&(*ts)->quadraturets);
    2764:   PetscHeaderDestroy(ts);
    2765:   return 0;
    2766: }

    2768: /*@
    2769:    TSGetSNES - Returns the SNES (nonlinear solver) associated with
    2770:    a TS (timestepper) context. Valid only for nonlinear problems.

    2772:    Not Collective, but SNES is parallel if TS is parallel

    2774:    Input Parameter:
    2775: .  ts - the TS context obtained from TSCreate()

    2777:    Output Parameter:
    2778: .  snes - the nonlinear solver context

    2780:    Notes:
    2781:    The user can then directly manipulate the SNES context to set various
    2782:    options, etc.  Likewise, the user can then extract and manipulate the
    2783:    KSP, KSP, and PC contexts as well.

    2785:    TSGetSNES() does not work for integrators that do not use SNES; in
    2786:    this case TSGetSNES() returns NULL in snes.

    2788:    Level: beginner

    2790: @*/
    2791: PetscErrorCode  TSGetSNES(TS ts,SNES *snes)
    2792: {
    2795:   if (!ts->snes) {
    2796:     SNESCreate(PetscObjectComm((PetscObject)ts),&ts->snes);
    2797:     PetscObjectSetOptions((PetscObject)ts->snes,((PetscObject)ts)->options);
    2798:     SNESSetFunction(ts->snes,NULL,SNESTSFormFunction,ts);
    2799:     PetscLogObjectParent((PetscObject)ts,(PetscObject)ts->snes);
    2800:     PetscObjectIncrementTabLevel((PetscObject)ts->snes,(PetscObject)ts,1);
    2801:     if (ts->dm) SNESSetDM(ts->snes,ts->dm);
    2802:     if (ts->problem_type == TS_LINEAR) {
    2803:       SNESSetType(ts->snes,SNESKSPONLY);
    2804:     }
    2805:   }
    2806:   *snes = ts->snes;
    2807:   return 0;
    2808: }

    2810: /*@
    2811:    TSSetSNES - Set the SNES (nonlinear solver) to be used by the timestepping context

    2813:    Collective

    2815:    Input Parameters:
    2816: +  ts - the TS context obtained from TSCreate()
    2817: -  snes - the nonlinear solver context

    2819:    Notes:
    2820:    Most users should have the TS created by calling TSGetSNES()

    2822:    Level: developer

    2824: @*/
    2825: PetscErrorCode TSSetSNES(TS ts,SNES snes)
    2826: {
    2827:   PetscErrorCode (*func)(SNES,Vec,Mat,Mat,void*);

    2831:   PetscObjectReference((PetscObject)snes);
    2832:   SNESDestroy(&ts->snes);

    2834:   ts->snes = snes;

    2836:   SNESSetFunction(ts->snes,NULL,SNESTSFormFunction,ts);
    2837:   SNESGetJacobian(ts->snes,NULL,NULL,&func,NULL);
    2838:   if (func == SNESTSFormJacobian) {
    2839:     SNESSetJacobian(ts->snes,NULL,NULL,SNESTSFormJacobian,ts);
    2840:   }
    2841:   return 0;
    2842: }

    2844: /*@
    2845:    TSGetKSP - Returns the KSP (linear solver) associated with
    2846:    a TS (timestepper) context.

    2848:    Not Collective, but KSP is parallel if TS is parallel

    2850:    Input Parameter:
    2851: .  ts - the TS context obtained from TSCreate()

    2853:    Output Parameter:
    2854: .  ksp - the nonlinear solver context

    2856:    Notes:
    2857:    The user can then directly manipulate the KSP context to set various
    2858:    options, etc.  Likewise, the user can then extract and manipulate the
    2859:    KSP and PC contexts as well.

    2861:    TSGetKSP() does not work for integrators that do not use KSP;
    2862:    in this case TSGetKSP() returns NULL in ksp.

    2864:    Level: beginner

    2866: @*/
    2867: PetscErrorCode  TSGetKSP(TS ts,KSP *ksp)
    2868: {
    2869:   SNES           snes;

    2875:   TSGetSNES(ts,&snes);
    2876:   SNESGetKSP(snes,ksp);
    2877:   return 0;
    2878: }

    2880: /* ----------- Routines to set solver parameters ---------- */

    2882: /*@
    2883:    TSSetMaxSteps - Sets the maximum number of steps to use.

    2885:    Logically Collective on TS

    2887:    Input Parameters:
    2888: +  ts - the TS context obtained from TSCreate()
    2889: -  maxsteps - maximum number of steps to use

    2891:    Options Database Keys:
    2892: .  -ts_max_steps <maxsteps> - Sets maxsteps

    2894:    Notes:
    2895:    The default maximum number of steps is 5000

    2897:    Level: intermediate

    2899: .seealso: TSGetMaxSteps(), TSSetMaxTime(), TSSetExactFinalTime()
    2900: @*/
    2901: PetscErrorCode TSSetMaxSteps(TS ts,PetscInt maxsteps)
    2902: {
    2906:   ts->max_steps = maxsteps;
    2907:   return 0;
    2908: }

    2910: /*@
    2911:    TSGetMaxSteps - Gets the maximum number of steps to use.

    2913:    Not Collective

    2915:    Input Parameters:
    2916: .  ts - the TS context obtained from TSCreate()

    2918:    Output Parameter:
    2919: .  maxsteps - maximum number of steps to use

    2921:    Level: advanced

    2923: .seealso: TSSetMaxSteps(), TSGetMaxTime(), TSSetMaxTime()
    2924: @*/
    2925: PetscErrorCode TSGetMaxSteps(TS ts,PetscInt *maxsteps)
    2926: {
    2929:   *maxsteps = ts->max_steps;
    2930:   return 0;
    2931: }

    2933: /*@
    2934:    TSSetMaxTime - Sets the maximum (or final) time for timestepping.

    2936:    Logically Collective on TS

    2938:    Input Parameters:
    2939: +  ts - the TS context obtained from TSCreate()
    2940: -  maxtime - final time to step to

    2942:    Options Database Keys:
    2943: .  -ts_max_time <maxtime> - Sets maxtime

    2945:    Notes:
    2946:    The default maximum time is 5.0

    2948:    Level: intermediate

    2950: .seealso: TSGetMaxTime(), TSSetMaxSteps(), TSSetExactFinalTime()
    2951: @*/
    2952: PetscErrorCode TSSetMaxTime(TS ts,PetscReal maxtime)
    2953: {
    2956:   ts->max_time = maxtime;
    2957:   return 0;
    2958: }

    2960: /*@
    2961:    TSGetMaxTime - Gets the maximum (or final) time for timestepping.

    2963:    Not Collective

    2965:    Input Parameters:
    2966: .  ts - the TS context obtained from TSCreate()

    2968:    Output Parameter:
    2969: .  maxtime - final time to step to

    2971:    Level: advanced

    2973: .seealso: TSSetMaxTime(), TSGetMaxSteps(), TSSetMaxSteps()
    2974: @*/
    2975: PetscErrorCode TSGetMaxTime(TS ts,PetscReal *maxtime)
    2976: {
    2979:   *maxtime = ts->max_time;
    2980:   return 0;
    2981: }

    2983: /*@
    2984:    TSSetInitialTimeStep - Deprecated, use TSSetTime() and TSSetTimeStep().

    2986:    Level: deprecated

    2988: @*/
    2989: PetscErrorCode  TSSetInitialTimeStep(TS ts,PetscReal initial_time,PetscReal time_step)
    2990: {
    2992:   TSSetTime(ts,initial_time);
    2993:   TSSetTimeStep(ts,time_step);
    2994:   return 0;
    2995: }

    2997: /*@
    2998:    TSGetDuration - Deprecated, use TSGetMaxSteps() and TSGetMaxTime().

    3000:    Level: deprecated

    3002: @*/
    3003: PetscErrorCode TSGetDuration(TS ts, PetscInt *maxsteps, PetscReal *maxtime)
    3004: {
    3006:   if (maxsteps) {
    3008:     *maxsteps = ts->max_steps;
    3009:   }
    3010:   if (maxtime) {
    3012:     *maxtime = ts->max_time;
    3013:   }
    3014:   return 0;
    3015: }

    3017: /*@
    3018:    TSSetDuration - Deprecated, use TSSetMaxSteps() and TSSetMaxTime().

    3020:    Level: deprecated

    3022: @*/
    3023: PetscErrorCode TSSetDuration(TS ts,PetscInt maxsteps,PetscReal maxtime)
    3024: {
    3028:   if (maxsteps >= 0) ts->max_steps = maxsteps;
    3029:   if (maxtime != PETSC_DEFAULT) ts->max_time = maxtime;
    3030:   return 0;
    3031: }

    3033: /*@
    3034:    TSGetTimeStepNumber - Deprecated, use TSGetStepNumber().

    3036:    Level: deprecated

    3038: @*/
    3039: PetscErrorCode TSGetTimeStepNumber(TS ts,PetscInt *steps) { return TSGetStepNumber(ts,steps); }

    3041: /*@
    3042:    TSGetTotalSteps - Deprecated, use TSGetStepNumber().

    3044:    Level: deprecated

    3046: @*/
    3047: PetscErrorCode TSGetTotalSteps(TS ts,PetscInt *steps) { return TSGetStepNumber(ts,steps); }

    3049: /*@
    3050:    TSSetSolution - Sets the initial solution vector
    3051:    for use by the TS routines.

    3053:    Logically Collective on TS

    3055:    Input Parameters:
    3056: +  ts - the TS context obtained from TSCreate()
    3057: -  u - the solution vector

    3059:    Level: beginner

    3061: .seealso: TSSetSolutionFunction(), TSGetSolution(), TSCreate()
    3062: @*/
    3063: PetscErrorCode  TSSetSolution(TS ts,Vec u)
    3064: {
    3065:   DM             dm;

    3069:   PetscObjectReference((PetscObject)u);
    3070:   VecDestroy(&ts->vec_sol);
    3071:   ts->vec_sol = u;

    3073:   TSGetDM(ts,&dm);
    3074:   DMShellSetGlobalVector(dm,u);
    3075:   return 0;
    3076: }

    3078: /*@C
    3079:   TSSetPreStep - Sets the general-purpose function
    3080:   called once at the beginning of each time step.

    3082:   Logically Collective on TS

    3084:   Input Parameters:
    3085: + ts   - The TS context obtained from TSCreate()
    3086: - func - The function

    3088:   Calling sequence of func:
    3089: .vb
    3090:   PetscErrorCode func (TS ts);
    3091: .ve

    3093:   Level: intermediate

    3095: .seealso: TSSetPreStage(), TSSetPostStage(), TSSetPostStep(), TSStep(), TSRestartStep()
    3096: @*/
    3097: PetscErrorCode  TSSetPreStep(TS ts, PetscErrorCode (*func)(TS))
    3098: {
    3100:   ts->prestep = func;
    3101:   return 0;
    3102: }

    3104: /*@
    3105:   TSPreStep - Runs the user-defined pre-step function.

    3107:   Collective on TS

    3109:   Input Parameters:
    3110: . ts   - The TS context obtained from TSCreate()

    3112:   Notes:
    3113:   TSPreStep() is typically used within time stepping implementations,
    3114:   so most users would not generally call this routine themselves.

    3116:   Level: developer

    3118: .seealso: TSSetPreStep(), TSPreStage(), TSPostStage(), TSPostStep()
    3119: @*/
    3120: PetscErrorCode  TSPreStep(TS ts)
    3121: {
    3123:   if (ts->prestep) {
    3124:     Vec              U;
    3125:     PetscObjectId    idprev;
    3126:     PetscBool        sameObject;
    3127:     PetscObjectState sprev,spost;

    3129:     TSGetSolution(ts,&U);
    3130:     PetscObjectGetId((PetscObject)U,&idprev);
    3131:     PetscObjectStateGet((PetscObject)U,&sprev);
    3132:     PetscStackCallStandard((*ts->prestep),ts);
    3133:     TSGetSolution(ts,&U);
    3134:     PetscObjectCompareId((PetscObject)U,idprev,&sameObject);
    3135:     PetscObjectStateGet((PetscObject)U,&spost);
    3136:     if (!sameObject || sprev != spost) TSRestartStep(ts);
    3137:   }
    3138:   return 0;
    3139: }

    3141: /*@C
    3142:   TSSetPreStage - Sets the general-purpose function
    3143:   called once at the beginning of each stage.

    3145:   Logically Collective on TS

    3147:   Input Parameters:
    3148: + ts   - The TS context obtained from TSCreate()
    3149: - func - The function

    3151:   Calling sequence of func:
    3152: .vb
    3153:   PetscErrorCode func(TS ts, PetscReal stagetime);
    3154: .ve

    3156:   Level: intermediate

    3158:   Note:
    3159:   There may be several stages per time step. If the solve for a given stage fails, the step may be rejected and retried.
    3160:   The time step number being computed can be queried using TSGetStepNumber() and the total size of the step being
    3161:   attempted can be obtained using TSGetTimeStep(). The time at the start of the step is available via TSGetTime().

    3163: .seealso: TSSetPostStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
    3164: @*/
    3165: PetscErrorCode  TSSetPreStage(TS ts, PetscErrorCode (*func)(TS,PetscReal))
    3166: {
    3168:   ts->prestage = func;
    3169:   return 0;
    3170: }

    3172: /*@C
    3173:   TSSetPostStage - Sets the general-purpose function
    3174:   called once at the end of each stage.

    3176:   Logically Collective on TS

    3178:   Input Parameters:
    3179: + ts   - The TS context obtained from TSCreate()
    3180: - func - The function

    3182:   Calling sequence of func:
    3183: .vb
    3184:   PetscErrorCode func(TS ts, PetscReal stagetime, PetscInt stageindex, Vec* Y);
    3185: .ve

    3187:   Level: intermediate

    3189:   Note:
    3190:   There may be several stages per time step. If the solve for a given stage fails, the step may be rejected and retried.
    3191:   The time step number being computed can be queried using TSGetStepNumber() and the total size of the step being
    3192:   attempted can be obtained using TSGetTimeStep(). The time at the start of the step is available via TSGetTime().

    3194: .seealso: TSSetPreStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
    3195: @*/
    3196: PetscErrorCode  TSSetPostStage(TS ts, PetscErrorCode (*func)(TS,PetscReal,PetscInt,Vec*))
    3197: {
    3199:   ts->poststage = func;
    3200:   return 0;
    3201: }

    3203: /*@C
    3204:   TSSetPostEvaluate - Sets the general-purpose function
    3205:   called once at the end of each step evaluation.

    3207:   Logically Collective on TS

    3209:   Input Parameters:
    3210: + ts   - The TS context obtained from TSCreate()
    3211: - func - The function

    3213:   Calling sequence of func:
    3214: .vb
    3215:   PetscErrorCode func(TS ts);
    3216: .ve

    3218:   Level: intermediate

    3220:   Note:
    3221:   Semantically, TSSetPostEvaluate() differs from TSSetPostStep() since the function it sets is called before event-handling
    3222:   thus guaranteeing the same solution (computed by the time-stepper) will be passed to it. On the other hand, TSPostStep()
    3223:   may be passed a different solution, possibly changed by the event handler. TSPostEvaluate() is called after the next step
    3224:   solution is evaluated allowing to modify it, if need be. The solution can be obtained with TSGetSolution(), the time step
    3225:   with TSGetTimeStep(), and the time at the start of the step is available via TSGetTime()

    3227: .seealso: TSSetPreStage(), TSSetPreStep(), TSSetPostStep(), TSGetApplicationContext()
    3228: @*/
    3229: PetscErrorCode  TSSetPostEvaluate(TS ts, PetscErrorCode (*func)(TS))
    3230: {
    3232:   ts->postevaluate = func;
    3233:   return 0;
    3234: }

    3236: /*@
    3237:   TSPreStage - Runs the user-defined pre-stage function set using TSSetPreStage()

    3239:   Collective on TS

    3241:   Input Parameters:
    3242: . ts          - The TS context obtained from TSCreate()
    3243:   stagetime   - The absolute time of the current stage

    3245:   Notes:
    3246:   TSPreStage() is typically used within time stepping implementations,
    3247:   most users would not generally call this routine themselves.

    3249:   Level: developer

    3251: .seealso: TSPostStage(), TSSetPreStep(), TSPreStep(), TSPostStep()
    3252: @*/
    3253: PetscErrorCode  TSPreStage(TS ts, PetscReal stagetime)
    3254: {
    3256:   if (ts->prestage) {
    3257:     PetscStackCallStandard((*ts->prestage),ts,stagetime);
    3258:   }
    3259:   return 0;
    3260: }

    3262: /*@
    3263:   TSPostStage - Runs the user-defined post-stage function set using TSSetPostStage()

    3265:   Collective on TS

    3267:   Input Parameters:
    3268: . ts          - The TS context obtained from TSCreate()
    3269:   stagetime   - The absolute time of the current stage
    3270:   stageindex  - Stage number
    3271:   Y           - Array of vectors (of size = total number
    3272:                 of stages) with the stage solutions

    3274:   Notes:
    3275:   TSPostStage() is typically used within time stepping implementations,
    3276:   most users would not generally call this routine themselves.

    3278:   Level: developer

    3280: .seealso: TSPreStage(), TSSetPreStep(), TSPreStep(), TSPostStep()
    3281: @*/
    3282: PetscErrorCode  TSPostStage(TS ts, PetscReal stagetime, PetscInt stageindex, Vec *Y)
    3283: {
    3285:   if (ts->poststage) {
    3286:     PetscStackCallStandard((*ts->poststage),ts,stagetime,stageindex,Y);
    3287:   }
    3288:   return 0;
    3289: }

    3291: /*@
    3292:   TSPostEvaluate - Runs the user-defined post-evaluate function set using TSSetPostEvaluate()

    3294:   Collective on TS

    3296:   Input Parameters:
    3297: . ts          - The TS context obtained from TSCreate()

    3299:   Notes:
    3300:   TSPostEvaluate() is typically used within time stepping implementations,
    3301:   most users would not generally call this routine themselves.

    3303:   Level: developer

    3305: .seealso: TSSetPostEvaluate(), TSSetPreStep(), TSPreStep(), TSPostStep()
    3306: @*/
    3307: PetscErrorCode  TSPostEvaluate(TS ts)
    3308: {
    3310:   if (ts->postevaluate) {
    3311:     Vec              U;
    3312:     PetscObjectState sprev,spost;

    3314:     TSGetSolution(ts,&U);
    3315:     PetscObjectStateGet((PetscObject)U,&sprev);
    3316:     PetscStackCallStandard((*ts->postevaluate),ts);
    3317:     PetscObjectStateGet((PetscObject)U,&spost);
    3318:     if (sprev != spost) TSRestartStep(ts);
    3319:   }
    3320:   return 0;
    3321: }

    3323: /*@C
    3324:   TSSetPostStep - Sets the general-purpose function
    3325:   called once at the end of each time step.

    3327:   Logically Collective on TS

    3329:   Input Parameters:
    3330: + ts   - The TS context obtained from TSCreate()
    3331: - func - The function

    3333:   Calling sequence of func:
    3334: $ func (TS ts);

    3336:   Notes:
    3337:   The function set by TSSetPostStep() is called after each successful step. The solution vector X
    3338:   obtained by TSGetSolution() may be different than that computed at the step end if the event handler
    3339:   locates an event and TSPostEvent() modifies it. Use TSSetPostEvaluate() if an unmodified solution is needed instead.

    3341:   Level: intermediate

    3343: .seealso: TSSetPreStep(), TSSetPreStage(), TSSetPostEvaluate(), TSGetTimeStep(), TSGetStepNumber(), TSGetTime(), TSRestartStep()
    3344: @*/
    3345: PetscErrorCode  TSSetPostStep(TS ts, PetscErrorCode (*func)(TS))
    3346: {
    3348:   ts->poststep = func;
    3349:   return 0;
    3350: }

    3352: /*@
    3353:   TSPostStep - Runs the user-defined post-step function.

    3355:   Collective on TS

    3357:   Input Parameters:
    3358: . ts   - The TS context obtained from TSCreate()

    3360:   Notes:
    3361:   TSPostStep() is typically used within time stepping implementations,
    3362:   so most users would not generally call this routine themselves.

    3364:   Level: developer

    3366: @*/
    3367: PetscErrorCode  TSPostStep(TS ts)
    3368: {
    3370:   if (ts->poststep) {
    3371:     Vec              U;
    3372:     PetscObjectId    idprev;
    3373:     PetscBool        sameObject;
    3374:     PetscObjectState sprev,spost;

    3376:     TSGetSolution(ts,&U);
    3377:     PetscObjectGetId((PetscObject)U,&idprev);
    3378:     PetscObjectStateGet((PetscObject)U,&sprev);
    3379:     PetscStackCallStandard((*ts->poststep),ts);
    3380:     TSGetSolution(ts,&U);
    3381:     PetscObjectCompareId((PetscObject)U,idprev,&sameObject);
    3382:     PetscObjectStateGet((PetscObject)U,&spost);
    3383:     if (!sameObject || sprev != spost) TSRestartStep(ts);
    3384:   }
    3385:   return 0;
    3386: }

    3388: /*@
    3389:    TSInterpolate - Interpolate the solution computed during the previous step to an arbitrary location in the interval

    3391:    Collective on TS

    3393:    Input Parameters:
    3394: +  ts - time stepping context
    3395: -  t - time to interpolate to

    3397:    Output Parameter:
    3398: .  U - state at given time

    3400:    Level: intermediate

    3402:    Developer Notes:
    3403:    TSInterpolate() and the storing of previous steps/stages should be generalized to support delay differential equations and continuous adjoints.

    3405: .seealso: TSSetExactFinalTime(), TSSolve()
    3406: @*/
    3407: PetscErrorCode TSInterpolate(TS ts,PetscReal t,Vec U)
    3408: {
    3413:   (*ts->ops->interpolate)(ts,t,U);
    3414:   return 0;
    3415: }

    3417: /*@
    3418:    TSStep - Steps one time step

    3420:    Collective on TS

    3422:    Input Parameter:
    3423: .  ts - the TS context obtained from TSCreate()

    3425:    Level: developer

    3427:    Notes:
    3428:    The public interface for the ODE/DAE solvers is TSSolve(), you should almost for sure be using that routine and not this routine.

    3430:    The hook set using TSSetPreStep() is called before each attempt to take the step. In general, the time step size may
    3431:    be changed due to adaptive error controller or solve failures. Note that steps may contain multiple stages.

    3433:    This may over-step the final time provided in TSSetMaxTime() depending on the time-step used. TSSolve() interpolates to exactly the
    3434:    time provided in TSSetMaxTime(). One can use TSInterpolate() to determine an interpolated solution within the final timestep.

    3436: .seealso: TSCreate(), TSSetUp(), TSDestroy(), TSSolve(), TSSetPreStep(), TSSetPreStage(), TSSetPostStage(), TSInterpolate()
    3437: @*/
    3438: PetscErrorCode  TSStep(TS ts)
    3439: {
    3440:   PetscErrorCode   ierr;
    3441:   static PetscBool cite = PETSC_FALSE;
    3442:   PetscReal        ptime;

    3445:   PetscCitationsRegister("@article{tspaper,\n"
    3446:                                 "  title         = {{PETSc/TS}: A Modern Scalable {DAE/ODE} Solver Library},\n"
    3447:                                 "  author        = {Abhyankar, Shrirang and Brown, Jed and Constantinescu, Emil and Ghosh, Debojyoti and Smith, Barry F. and Zhang, Hong},\n"
    3448:                                 "  journal       = {arXiv e-preprints},\n"
    3449:                                 "  eprint        = {1806.01437},\n"
    3450:                                 "  archivePrefix = {arXiv},\n"
    3451:                                 "  year          = {2018}\n}\n",&cite);

    3453:   TSSetUp(ts);
    3454:   TSTrajectorySetUp(ts->trajectory,ts);

    3461:   if (!ts->steps) ts->ptime_prev = ts->ptime;
    3462:   ptime = ts->ptime; ts->ptime_prev_rollback = ts->ptime_prev;
    3463:   ts->reason = TS_CONVERGED_ITERATING;

    3465:   PetscLogEventBegin(TS_Step,ts,0,0,0);
    3466:   (*ts->ops->step)(ts);
    3467:   PetscLogEventEnd(TS_Step,ts,0,0,0);

    3469:   if (ts->reason >= 0) {
    3470:     ts->ptime_prev = ptime;
    3471:     ts->steps++;
    3472:     ts->steprollback = PETSC_FALSE;
    3473:     ts->steprestart  = PETSC_FALSE;
    3474:   }

    3476:   if (!ts->reason) {
    3477:     if (ts->steps >= ts->max_steps) ts->reason = TS_CONVERGED_ITS;
    3478:     else if (ts->ptime >= ts->max_time) ts->reason = TS_CONVERGED_TIME;
    3479:   }

    3483:   return 0;
    3484: }

    3486: /*@
    3487:    TSEvaluateWLTE - Evaluate the weighted local truncation error norm
    3488:    at the end of a time step with a given order of accuracy.

    3490:    Collective on TS

    3492:    Input Parameters:
    3493: +  ts - time stepping context
    3494: -  wnormtype - norm type, either NORM_2 or NORM_INFINITY

    3496:    Input/Output Parameter:
    3497: .  order - optional, desired order for the error evaluation or PETSC_DECIDE;
    3498:            on output, the actual order of the error evaluation

    3500:    Output Parameter:
    3501: .  wlte - the weighted local truncation error norm

    3503:    Level: advanced

    3505:    Notes:
    3506:    If the timestepper cannot evaluate the error in a particular step
    3507:    (eg. in the first step or restart steps after event handling),
    3508:    this routine returns wlte=-1.0 .

    3510: .seealso: TSStep(), TSAdapt, TSErrorWeightedNorm()
    3511: @*/
    3512: PetscErrorCode TSEvaluateWLTE(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
    3513: {
    3522:   (*ts->ops->evaluatewlte)(ts,wnormtype,order,wlte);
    3523:   return 0;
    3524: }

    3526: /*@
    3527:    TSEvaluateStep - Evaluate the solution at the end of a time step with a given order of accuracy.

    3529:    Collective on TS

    3531:    Input Parameters:
    3532: +  ts - time stepping context
    3533: .  order - desired order of accuracy
    3534: -  done - whether the step was evaluated at this order (pass NULL to generate an error if not available)

    3536:    Output Parameter:
    3537: .  U - state at the end of the current step

    3539:    Level: advanced

    3541:    Notes:
    3542:    This function cannot be called until all stages have been evaluated.
    3543:    It is normally called by adaptive controllers before a step has been accepted and may also be called by the user after TSStep() has returned.

    3545: .seealso: TSStep(), TSAdapt
    3546: @*/
    3547: PetscErrorCode TSEvaluateStep(TS ts,PetscInt order,Vec U,PetscBool *done)
    3548: {
    3553:   (*ts->ops->evaluatestep)(ts,order,U,done);
    3554:   return 0;
    3555: }

    3557: /*@C
    3558:   TSGetComputeInitialCondition - Get the function used to automatically compute an initial condition for the timestepping.

    3560:   Not collective

    3562:   Input Parameter:
    3563: . ts        - time stepping context

    3565:   Output Parameter:
    3566: . initConditions - The function which computes an initial condition

    3568:    Level: advanced

    3570:    Notes:
    3571:    The calling sequence for the function is
    3572: $ initCondition(TS ts, Vec u)
    3573: $ ts - The timestepping context
    3574: $ u  - The input vector in which the initial condition is stored

    3576: .seealso: TSSetComputeInitialCondition(), TSComputeInitialCondition()
    3577: @*/
    3578: PetscErrorCode TSGetComputeInitialCondition(TS ts, PetscErrorCode (**initCondition)(TS, Vec))
    3579: {
    3582:   *initCondition = ts->ops->initcondition;
    3583:   return 0;
    3584: }

    3586: /*@C
    3587:   TSSetComputeInitialCondition - Set the function used to automatically compute an initial condition for the timestepping.

    3589:   Logically collective on ts

    3591:   Input Parameters:
    3592: + ts        - time stepping context
    3593: - initCondition - The function which computes an initial condition

    3595:   Level: advanced

    3597:   Calling sequence for initCondition:
    3598: $ PetscErrorCode initCondition(TS ts, Vec u)

    3600: + ts - The timestepping context
    3601: - u  - The input vector in which the initial condition is to be stored

    3603: .seealso: TSGetComputeInitialCondition(), TSComputeInitialCondition()
    3604: @*/
    3605: PetscErrorCode TSSetComputeInitialCondition(TS ts, PetscErrorCode (*initCondition)(TS, Vec))
    3606: {
    3609:   ts->ops->initcondition = initCondition;
    3610:   return 0;
    3611: }

    3613: /*@
    3614:   TSComputeInitialCondition - Compute an initial condition for the timestepping using the function previously set.

    3616:   Collective on ts

    3618:   Input Parameters:
    3619: + ts - time stepping context
    3620: - u  - The Vec to store the condition in which will be used in TSSolve()

    3622:   Level: advanced

    3624: .seealso: TSGetComputeInitialCondition(), TSSetComputeInitialCondition(), TSSolve()
    3625: @*/
    3626: PetscErrorCode TSComputeInitialCondition(TS ts, Vec u)
    3627: {
    3630:   if (ts->ops->initcondition) (*ts->ops->initcondition)(ts, u);
    3631:   return 0;
    3632: }

    3634: /*@C
    3635:   TSGetComputeExactError - Get the function used to automatically compute the exact error for the timestepping.

    3637:   Not collective

    3639:   Input Parameter:
    3640: . ts         - time stepping context

    3642:   Output Parameter:
    3643: . exactError - The function which computes the solution error

    3645:   Level: advanced

    3647:   Calling sequence for exactError:
    3648: $ PetscErrorCode exactError(TS ts, Vec u)

    3650: + ts - The timestepping context
    3651: . u  - The approximate solution vector
    3652: - e  - The input vector in which the error is stored

    3654: .seealso: TSGetComputeExactError(), TSComputeExactError()
    3655: @*/
    3656: PetscErrorCode TSGetComputeExactError(TS ts, PetscErrorCode (**exactError)(TS, Vec, Vec))
    3657: {
    3660:   *exactError = ts->ops->exacterror;
    3661:   return 0;
    3662: }

    3664: /*@C
    3665:   TSSetComputeExactError - Set the function used to automatically compute the exact error for the timestepping.

    3667:   Logically collective on ts

    3669:   Input Parameters:
    3670: + ts         - time stepping context
    3671: - exactError - The function which computes the solution error

    3673:   Level: advanced

    3675:   Calling sequence for exactError:
    3676: $ PetscErrorCode exactError(TS ts, Vec u)

    3678: + ts - The timestepping context
    3679: . u  - The approximate solution vector
    3680: - e  - The input vector in which the error is stored

    3682: .seealso: TSGetComputeExactError(), TSComputeExactError()
    3683: @*/
    3684: PetscErrorCode TSSetComputeExactError(TS ts, PetscErrorCode (*exactError)(TS, Vec, Vec))
    3685: {
    3688:   ts->ops->exacterror = exactError;
    3689:   return 0;
    3690: }

    3692: /*@
    3693:   TSComputeExactError - Compute the solution error for the timestepping using the function previously set.

    3695:   Collective on ts

    3697:   Input Parameters:
    3698: + ts - time stepping context
    3699: . u  - The approximate solution
    3700: - e  - The Vec used to store the error

    3702:   Level: advanced

    3704: .seealso: TSGetComputeInitialCondition(), TSSetComputeInitialCondition(), TSSolve()
    3705: @*/
    3706: PetscErrorCode TSComputeExactError(TS ts, Vec u, Vec e)
    3707: {
    3711:   if (ts->ops->exacterror) (*ts->ops->exacterror)(ts, u, e);
    3712:   return 0;
    3713: }

    3715: /*@
    3716:    TSSolve - Steps the requested number of timesteps.

    3718:    Collective on TS

    3720:    Input Parameters:
    3721: +  ts - the TS context obtained from TSCreate()
    3722: -  u - the solution vector  (can be null if TSSetSolution() was used and TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP) was not used,
    3723:                              otherwise must contain the initial conditions and will contain the solution at the final requested time

    3725:    Level: beginner

    3727:    Notes:
    3728:    The final time returned by this function may be different from the time of the internally
    3729:    held state accessible by TSGetSolution() and TSGetTime() because the method may have
    3730:    stepped over the final time.

    3732: .seealso: TSCreate(), TSSetSolution(), TSStep(), TSGetTime(), TSGetSolveTime()
    3733: @*/
    3734: PetscErrorCode TSSolve(TS ts,Vec u)
    3735: {
    3736:   Vec               solution;

    3741:   TSSetExactFinalTimeDefault(ts);
    3742:   if (ts->exact_final_time == TS_EXACTFINALTIME_INTERPOLATE && u) {   /* Need ts->vec_sol to be distinct so it is not overwritten when we interpolate at the end */
    3743:     if (!ts->vec_sol || u == ts->vec_sol) {
    3744:       VecDuplicate(u,&solution);
    3745:       TSSetSolution(ts,solution);
    3746:       VecDestroy(&solution); /* grant ownership */
    3747:     }
    3748:     VecCopy(u,ts->vec_sol);
    3750:   } else if (u) {
    3751:     TSSetSolution(ts,u);
    3752:   }
    3753:   TSSetUp(ts);
    3754:   TSTrajectorySetUp(ts->trajectory,ts);

    3760:   if (ts->forward_solve) {
    3761:     TSForwardSetUp(ts);
    3762:   }

    3764:   /* reset number of steps only when the step is not restarted. ARKIMEX
    3765:      restarts the step after an event. Resetting these counters in such case causes
    3766:      TSTrajectory to incorrectly save the output files
    3767:   */
    3768:   /* reset time step and iteration counters */
    3769:   if (!ts->steps) {
    3770:     ts->ksp_its           = 0;
    3771:     ts->snes_its          = 0;
    3772:     ts->num_snes_failures = 0;
    3773:     ts->reject            = 0;
    3774:     ts->steprestart       = PETSC_TRUE;
    3775:     ts->steprollback      = PETSC_FALSE;
    3776:     ts->rhsjacobian.time  = PETSC_MIN_REAL;
    3777:   }

    3779:   /* make sure initial time step does not overshoot final time */
    3780:   if (ts->exact_final_time == TS_EXACTFINALTIME_MATCHSTEP) {
    3781:     PetscReal maxdt = ts->max_time-ts->ptime;
    3782:     PetscReal dt = ts->time_step;

    3784:     ts->time_step = dt >= maxdt ? maxdt : (PetscIsCloseAtTol(dt,maxdt,10*PETSC_MACHINE_EPSILON,0) ? maxdt : dt);
    3785:   }
    3786:   ts->reason = TS_CONVERGED_ITERATING;

    3788:   {
    3789:     PetscViewer       viewer;
    3790:     PetscViewerFormat format;
    3791:     PetscBool         flg;
    3792:     static PetscBool  incall = PETSC_FALSE;

    3794:     if (!incall) {
    3795:       /* Estimate the convergence rate of the time discretization */
    3796:       PetscOptionsGetViewer(PetscObjectComm((PetscObject) ts),((PetscObject)ts)->options, ((PetscObject) ts)->prefix, "-ts_convergence_estimate", &viewer, &format, &flg);
    3797:       if (flg) {
    3798:         PetscConvEst conv;
    3799:         DM           dm;
    3800:         PetscReal   *alpha; /* Convergence rate of the solution error for each field in the L_2 norm */
    3801:         PetscInt     Nf;
    3802:         PetscBool    checkTemporal = PETSC_TRUE;

    3804:         incall = PETSC_TRUE;
    3805:         PetscOptionsGetBool(((PetscObject)ts)->options, ((PetscObject) ts)->prefix, "-ts_convergence_temporal", &checkTemporal, &flg);
    3806:         TSGetDM(ts, &dm);
    3807:         DMGetNumFields(dm, &Nf);
    3808:         PetscCalloc1(PetscMax(Nf, 1), &alpha);
    3809:         PetscConvEstCreate(PetscObjectComm((PetscObject) ts), &conv);
    3810:         PetscConvEstUseTS(conv, checkTemporal);
    3811:         PetscConvEstSetSolver(conv, (PetscObject) ts);
    3812:         PetscConvEstSetFromOptions(conv);
    3813:         PetscConvEstSetUp(conv);
    3814:         PetscConvEstGetConvRate(conv, alpha);
    3815:         PetscViewerPushFormat(viewer, format);
    3816:         PetscConvEstRateView(conv, alpha, viewer);
    3817:         PetscViewerPopFormat(viewer);
    3818:         PetscViewerDestroy(&viewer);
    3819:         PetscConvEstDestroy(&conv);
    3820:         PetscFree(alpha);
    3821:         incall = PETSC_FALSE;
    3822:       }
    3823:     }
    3824:   }

    3826:   TSViewFromOptions(ts,NULL,"-ts_view_pre");

    3828:   if (ts->ops->solve) { /* This private interface is transitional and should be removed when all implementations are updated. */
    3829:     (*ts->ops->solve)(ts);
    3830:     if (u) VecCopy(ts->vec_sol,u);
    3831:     ts->solvetime = ts->ptime;
    3832:     solution = ts->vec_sol;
    3833:   } else { /* Step the requested number of timesteps. */
    3834:     if (ts->steps >= ts->max_steps) ts->reason = TS_CONVERGED_ITS;
    3835:     else if (ts->ptime >= ts->max_time) ts->reason = TS_CONVERGED_TIME;

    3837:     if (!ts->steps) {
    3838:       TSTrajectorySet(ts->trajectory,ts,ts->steps,ts->ptime,ts->vec_sol);
    3839:       TSEventInitialize(ts->event,ts,ts->ptime,ts->vec_sol);
    3840:     }

    3842:     while (!ts->reason) {
    3843:       TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);
    3844:       if (!ts->steprollback) {
    3845:         TSPreStep(ts);
    3846:       }
    3847:       TSStep(ts);
    3848:       if (ts->testjacobian) {
    3849:         TSRHSJacobianTest(ts,NULL);
    3850:       }
    3851:       if (ts->testjacobiantranspose) {
    3852:         TSRHSJacobianTestTranspose(ts,NULL);
    3853:       }
    3854:       if (ts->quadraturets && ts->costintegralfwd) { /* Must evaluate the cost integral before event is handled. The cost integral value can also be rolled back. */
    3855:         if (ts->reason >= 0) ts->steps--; /* Revert the step number changed by TSStep() */
    3856:         TSForwardCostIntegral(ts);
    3857:         if (ts->reason >= 0) ts->steps++;
    3858:       }
    3859:       if (ts->forward_solve) { /* compute forward sensitivities before event handling because postevent() may change RHS and jump conditions may have to be applied */
    3860:         if (ts->reason >= 0) ts->steps--; /* Revert the step number changed by TSStep() */
    3861:         TSForwardStep(ts);
    3862:         if (ts->reason >= 0) ts->steps++;
    3863:       }
    3864:       TSPostEvaluate(ts);
    3865:       TSEventHandler(ts); /* The right-hand side may be changed due to event. Be careful with Any computation using the RHS information after this point. */
    3866:       if (ts->steprollback) {
    3867:         TSPostEvaluate(ts);
    3868:       }
    3869:       if (!ts->steprollback) {
    3870:         TSTrajectorySet(ts->trajectory,ts,ts->steps,ts->ptime,ts->vec_sol);
    3871:         TSPostStep(ts);
    3872:       }
    3873:     }
    3874:     TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);

    3876:     if (ts->exact_final_time == TS_EXACTFINALTIME_INTERPOLATE && ts->ptime > ts->max_time) {
    3877:       TSInterpolate(ts,ts->max_time,u);
    3878:       ts->solvetime = ts->max_time;
    3879:       solution = u;
    3880:       TSMonitor(ts,-1,ts->solvetime,solution);
    3881:     } else {
    3882:       if (u) VecCopy(ts->vec_sol,u);
    3883:       ts->solvetime = ts->ptime;
    3884:       solution = ts->vec_sol;
    3885:     }
    3886:   }

    3888:   TSViewFromOptions(ts,NULL,"-ts_view");
    3889:   VecViewFromOptions(solution,(PetscObject)ts,"-ts_view_solution");
    3890:   PetscObjectSAWsBlock((PetscObject)ts);
    3891:   if (ts->adjoint_solve) {
    3892:     TSAdjointSolve(ts);
    3893:   }
    3894:   return 0;
    3895: }

    3897: /*@
    3898:    TSGetTime - Gets the time of the most recently completed step.

    3900:    Not Collective

    3902:    Input Parameter:
    3903: .  ts - the TS context obtained from TSCreate()

    3905:    Output Parameter:
    3906: .  t  - the current time. This time may not corresponds to the final time set with TSSetMaxTime(), use TSGetSolveTime().

    3908:    Level: beginner

    3910:    Note:
    3911:    When called during time step evaluation (e.g. during residual evaluation or via hooks set using TSSetPreStep(),
    3912:    TSSetPreStage(), TSSetPostStage(), or TSSetPostStep()), the time is the time at the start of the step being evaluated.

    3914: .seealso:  TSGetSolveTime(), TSSetTime(), TSGetTimeStep(), TSGetStepNumber()

    3916: @*/
    3917: PetscErrorCode  TSGetTime(TS ts,PetscReal *t)
    3918: {
    3921:   *t = ts->ptime;
    3922:   return 0;
    3923: }

    3925: /*@
    3926:    TSGetPrevTime - Gets the starting time of the previously completed step.

    3928:    Not Collective

    3930:    Input Parameter:
    3931: .  ts - the TS context obtained from TSCreate()

    3933:    Output Parameter:
    3934: .  t  - the previous time

    3936:    Level: beginner

    3938: .seealso: TSGetTime(), TSGetSolveTime(), TSGetTimeStep()

    3940: @*/
    3941: PetscErrorCode  TSGetPrevTime(TS ts,PetscReal *t)
    3942: {
    3945:   *t = ts->ptime_prev;
    3946:   return 0;
    3947: }

    3949: /*@
    3950:    TSSetTime - Allows one to reset the time.

    3952:    Logically Collective on TS

    3954:    Input Parameters:
    3955: +  ts - the TS context obtained from TSCreate()
    3956: -  time - the time

    3958:    Level: intermediate

    3960: .seealso: TSGetTime(), TSSetMaxSteps()

    3962: @*/
    3963: PetscErrorCode  TSSetTime(TS ts, PetscReal t)
    3964: {
    3967:   ts->ptime = t;
    3968:   return 0;
    3969: }

    3971: /*@C
    3972:    TSSetOptionsPrefix - Sets the prefix used for searching for all
    3973:    TS options in the database.

    3975:    Logically Collective on TS

    3977:    Input Parameters:
    3978: +  ts     - The TS context
    3979: -  prefix - The prefix to prepend to all option names

    3981:    Notes:
    3982:    A hyphen (-) must NOT be given at the beginning of the prefix name.
    3983:    The first character of all runtime options is AUTOMATICALLY the
    3984:    hyphen.

    3986:    Level: advanced

    3988: .seealso: TSSetFromOptions()

    3990: @*/
    3991: PetscErrorCode  TSSetOptionsPrefix(TS ts,const char prefix[])
    3992: {
    3993:   SNES           snes;

    3996:   PetscObjectSetOptionsPrefix((PetscObject)ts,prefix);
    3997:   TSGetSNES(ts,&snes);
    3998:   SNESSetOptionsPrefix(snes,prefix);
    3999:   return 0;
    4000: }

    4002: /*@C
    4003:    TSAppendOptionsPrefix - Appends to the prefix used for searching for all
    4004:    TS options in the database.

    4006:    Logically Collective on TS

    4008:    Input Parameters:
    4009: +  ts     - The TS context
    4010: -  prefix - The prefix to prepend to all option names

    4012:    Notes:
    4013:    A hyphen (-) must NOT be given at the beginning of the prefix name.
    4014:    The first character of all runtime options is AUTOMATICALLY the
    4015:    hyphen.

    4017:    Level: advanced

    4019: .seealso: TSGetOptionsPrefix()

    4021: @*/
    4022: PetscErrorCode  TSAppendOptionsPrefix(TS ts,const char prefix[])
    4023: {
    4024:   SNES           snes;

    4027:   PetscObjectAppendOptionsPrefix((PetscObject)ts,prefix);
    4028:   TSGetSNES(ts,&snes);
    4029:   SNESAppendOptionsPrefix(snes,prefix);
    4030:   return 0;
    4031: }

    4033: /*@C
    4034:    TSGetOptionsPrefix - Sets the prefix used for searching for all
    4035:    TS options in the database.

    4037:    Not Collective

    4039:    Input Parameter:
    4040: .  ts - The TS context

    4042:    Output Parameter:
    4043: .  prefix - A pointer to the prefix string used

    4045:    Notes:
    4046:     On the fortran side, the user should pass in a string 'prifix' of
    4047:    sufficient length to hold the prefix.

    4049:    Level: intermediate

    4051: .seealso: TSAppendOptionsPrefix()
    4052: @*/
    4053: PetscErrorCode  TSGetOptionsPrefix(TS ts,const char *prefix[])
    4054: {
    4057:   PetscObjectGetOptionsPrefix((PetscObject)ts,prefix);
    4058:   return 0;
    4059: }

    4061: /*@C
    4062:    TSGetRHSJacobian - Returns the Jacobian J at the present timestep.

    4064:    Not Collective, but parallel objects are returned if TS is parallel

    4066:    Input Parameter:
    4067: .  ts  - The TS context obtained from TSCreate()

    4069:    Output Parameters:
    4070: +  Amat - The (approximate) Jacobian J of G, where U_t = G(U,t)  (or NULL)
    4071: .  Pmat - The matrix from which the preconditioner is constructed, usually the same as Amat  (or NULL)
    4072: .  func - Function to compute the Jacobian of the RHS  (or NULL)
    4073: -  ctx - User-defined context for Jacobian evaluation routine  (or NULL)

    4075:    Notes:
    4076:     You can pass in NULL for any return argument you do not need.

    4078:    Level: intermediate

    4080: .seealso: TSGetTimeStep(), TSGetMatrices(), TSGetTime(), TSGetStepNumber()

    4082: @*/
    4083: PetscErrorCode  TSGetRHSJacobian(TS ts,Mat *Amat,Mat *Pmat,TSRHSJacobian *func,void **ctx)
    4084: {
    4085:   DM             dm;

    4087:   if (Amat || Pmat) {
    4088:     SNES snes;
    4089:     TSGetSNES(ts,&snes);
    4090:     SNESSetUpMatrices(snes);
    4091:     SNESGetJacobian(snes,Amat,Pmat,NULL,NULL);
    4092:   }
    4093:   TSGetDM(ts,&dm);
    4094:   DMTSGetRHSJacobian(dm,func,ctx);
    4095:   return 0;
    4096: }

    4098: /*@C
    4099:    TSGetIJacobian - Returns the implicit Jacobian at the present timestep.

    4101:    Not Collective, but parallel objects are returned if TS is parallel

    4103:    Input Parameter:
    4104: .  ts  - The TS context obtained from TSCreate()

    4106:    Output Parameters:
    4107: +  Amat  - The (approximate) Jacobian of F(t,U,U_t)
    4108: .  Pmat - The matrix from which the preconditioner is constructed, often the same as Amat
    4109: .  f   - The function to compute the matrices
    4110: - ctx - User-defined context for Jacobian evaluation routine

    4112:    Notes:
    4113:     You can pass in NULL for any return argument you do not need.

    4115:    Level: advanced

    4117: .seealso: TSGetTimeStep(), TSGetRHSJacobian(), TSGetMatrices(), TSGetTime(), TSGetStepNumber()

    4119: @*/
    4120: PetscErrorCode  TSGetIJacobian(TS ts,Mat *Amat,Mat *Pmat,TSIJacobian *f,void **ctx)
    4121: {
    4122:   DM             dm;

    4124:   if (Amat || Pmat) {
    4125:     SNES snes;
    4126:     TSGetSNES(ts,&snes);
    4127:     SNESSetUpMatrices(snes);
    4128:     SNESGetJacobian(snes,Amat,Pmat,NULL,NULL);
    4129:   }
    4130:   TSGetDM(ts,&dm);
    4131:   DMTSGetIJacobian(dm,f,ctx);
    4132:   return 0;
    4133: }

    4135: #include <petsc/private/dmimpl.h>
    4136: /*@
    4137:    TSSetDM - Sets the DM that may be used by some nonlinear solvers or preconditioners under the TS

    4139:    Logically Collective on ts

    4141:    Input Parameters:
    4142: +  ts - the ODE integrator object
    4143: -  dm - the dm, cannot be NULL

    4145:    Notes:
    4146:    A DM can only be used for solving one problem at a time because information about the problem is stored on the DM,
    4147:    even when not using interfaces like DMTSSetIFunction().  Use DMClone() to get a distinct DM when solving
    4148:    different problems using the same function space.

    4150:    Level: intermediate

    4152: .seealso: TSGetDM(), SNESSetDM(), SNESGetDM()
    4153: @*/
    4154: PetscErrorCode  TSSetDM(TS ts,DM dm)
    4155: {
    4156:   SNES           snes;
    4157:   DMTS           tsdm;

    4161:   PetscObjectReference((PetscObject)dm);
    4162:   if (ts->dm) {               /* Move the DMTS context over to the new DM unless the new DM already has one */
    4163:     if (ts->dm->dmts && !dm->dmts) {
    4164:       DMCopyDMTS(ts->dm,dm);
    4165:       DMGetDMTS(ts->dm,&tsdm);
    4166:       if (tsdm->originaldm == ts->dm) { /* Grant write privileges to the replacement DM */
    4167:         tsdm->originaldm = dm;
    4168:       }
    4169:     }
    4170:     DMDestroy(&ts->dm);
    4171:   }
    4172:   ts->dm = dm;

    4174:   TSGetSNES(ts,&snes);
    4175:   SNESSetDM(snes,dm);
    4176:   return 0;
    4177: }

    4179: /*@
    4180:    TSGetDM - Gets the DM that may be used by some preconditioners

    4182:    Not Collective

    4184:    Input Parameter:
    4185: . ts - the preconditioner context

    4187:    Output Parameter:
    4188: .  dm - the dm

    4190:    Level: intermediate

    4192: .seealso: TSSetDM(), SNESSetDM(), SNESGetDM()
    4193: @*/
    4194: PetscErrorCode  TSGetDM(TS ts,DM *dm)
    4195: {
    4197:   if (!ts->dm) {
    4198:     DMShellCreate(PetscObjectComm((PetscObject)ts),&ts->dm);
    4199:     if (ts->snes) SNESSetDM(ts->snes,ts->dm);
    4200:   }
    4201:   *dm = ts->dm;
    4202:   return 0;
    4203: }

    4205: /*@
    4206:    SNESTSFormFunction - Function to evaluate nonlinear residual

    4208:    Logically Collective on SNES

    4210:    Input Parameters:
    4211: + snes - nonlinear solver
    4212: . U - the current state at which to evaluate the residual
    4213: - ctx - user context, must be a TS

    4215:    Output Parameter:
    4216: . F - the nonlinear residual

    4218:    Notes:
    4219:    This function is not normally called by users and is automatically registered with the SNES used by TS.
    4220:    It is most frequently passed to MatFDColoringSetFunction().

    4222:    Level: advanced

    4224: .seealso: SNESSetFunction(), MatFDColoringSetFunction()
    4225: @*/
    4226: PetscErrorCode  SNESTSFormFunction(SNES snes,Vec U,Vec F,void *ctx)
    4227: {
    4228:   TS             ts = (TS)ctx;

    4234:   (ts->ops->snesfunction)(snes,U,F,ts);
    4235:   return 0;
    4236: }

    4238: /*@
    4239:    SNESTSFormJacobian - Function to evaluate the Jacobian

    4241:    Collective on SNES

    4243:    Input Parameters:
    4244: + snes - nonlinear solver
    4245: . U - the current state at which to evaluate the residual
    4246: - ctx - user context, must be a TS

    4248:    Output Parameters:
    4249: + A - the Jacobian
    4250: - B - the preconditioning matrix (may be the same as A)

    4252:    Notes:
    4253:    This function is not normally called by users and is automatically registered with the SNES used by TS.

    4255:    Level: developer

    4257: .seealso: SNESSetJacobian()
    4258: @*/
    4259: PetscErrorCode  SNESTSFormJacobian(SNES snes,Vec U,Mat A,Mat B,void *ctx)
    4260: {
    4261:   TS             ts = (TS)ctx;

    4270:   (ts->ops->snesjacobian)(snes,U,A,B,ts);
    4271:   return 0;
    4272: }

    4274: /*@C
    4275:    TSComputeRHSFunctionLinear - Evaluate the right hand side via the user-provided Jacobian, for linear problems Udot = A U only

    4277:    Collective on TS

    4279:    Input Parameters:
    4280: +  ts - time stepping context
    4281: .  t - time at which to evaluate
    4282: .  U - state at which to evaluate
    4283: -  ctx - context

    4285:    Output Parameter:
    4286: .  F - right hand side

    4288:    Level: intermediate

    4290:    Notes:
    4291:    This function is intended to be passed to TSSetRHSFunction() to evaluate the right hand side for linear problems.
    4292:    The matrix (and optionally the evaluation context) should be passed to TSSetRHSJacobian().

    4294: .seealso: TSSetRHSFunction(), TSSetRHSJacobian(), TSComputeRHSJacobianConstant()
    4295: @*/
    4296: PetscErrorCode TSComputeRHSFunctionLinear(TS ts,PetscReal t,Vec U,Vec F,void *ctx)
    4297: {
    4298:   Mat            Arhs,Brhs;

    4300:   TSGetRHSMats_Private(ts,&Arhs,&Brhs);
    4301:   /* undo the damage caused by shifting */
    4302:   TSRecoverRHSJacobian(ts,Arhs,Brhs);
    4303:   TSComputeRHSJacobian(ts,t,U,Arhs,Brhs);
    4304:   MatMult(Arhs,U,F);
    4305:   return 0;
    4306: }

    4308: /*@C
    4309:    TSComputeRHSJacobianConstant - Reuses a Jacobian that is time-independent.

    4311:    Collective on TS

    4313:    Input Parameters:
    4314: +  ts - time stepping context
    4315: .  t - time at which to evaluate
    4316: .  U - state at which to evaluate
    4317: -  ctx - context

    4319:    Output Parameters:
    4320: +  A - pointer to operator
    4321: -  B - pointer to preconditioning matrix

    4323:    Level: intermediate

    4325:    Notes:
    4326:    This function is intended to be passed to TSSetRHSJacobian() to evaluate the Jacobian for linear time-independent problems.

    4328: .seealso: TSSetRHSFunction(), TSSetRHSJacobian(), TSComputeRHSFunctionLinear()
    4329: @*/
    4330: PetscErrorCode TSComputeRHSJacobianConstant(TS ts,PetscReal t,Vec U,Mat A,Mat B,void *ctx)
    4331: {
    4332:   return 0;
    4333: }

    4335: /*@C
    4336:    TSComputeIFunctionLinear - Evaluate the left hand side via the user-provided Jacobian, for linear problems only

    4338:    Collective on TS

    4340:    Input Parameters:
    4341: +  ts - time stepping context
    4342: .  t - time at which to evaluate
    4343: .  U - state at which to evaluate
    4344: .  Udot - time derivative of state vector
    4345: -  ctx - context

    4347:    Output Parameter:
    4348: .  F - left hand side

    4350:    Level: intermediate

    4352:    Notes:
    4353:    The assumption here is that the left hand side is of the form A*Udot (and not A*Udot + B*U). For other cases, the
    4354:    user is required to write their own TSComputeIFunction.
    4355:    This function is intended to be passed to TSSetIFunction() to evaluate the left hand side for linear problems.
    4356:    The matrix (and optionally the evaluation context) should be passed to TSSetIJacobian().

    4358:    Note that using this function is NOT equivalent to using TSComputeRHSFunctionLinear() since that solves Udot = A U

    4360: .seealso: TSSetIFunction(), TSSetIJacobian(), TSComputeIJacobianConstant(), TSComputeRHSFunctionLinear()
    4361: @*/
    4362: PetscErrorCode TSComputeIFunctionLinear(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
    4363: {
    4364:   Mat            A,B;

    4366:   TSGetIJacobian(ts,&A,&B,NULL,NULL);
    4367:   TSComputeIJacobian(ts,t,U,Udot,1.0,A,B,PETSC_TRUE);
    4368:   MatMult(A,Udot,F);
    4369:   return 0;
    4370: }

    4372: /*@C
    4373:    TSComputeIJacobianConstant - Reuses a time-independent for a semi-implicit DAE or ODE

    4375:    Collective on TS

    4377:    Input Parameters:
    4378: +  ts - time stepping context
    4379: .  t - time at which to evaluate
    4380: .  U - state at which to evaluate
    4381: .  Udot - time derivative of state vector
    4382: .  shift - shift to apply
    4383: -  ctx - context

    4385:    Output Parameters:
    4386: +  A - pointer to operator
    4387: -  B - pointer to preconditioning matrix

    4389:    Level: advanced

    4391:    Notes:
    4392:    This function is intended to be passed to TSSetIJacobian() to evaluate the Jacobian for linear time-independent problems.

    4394:    It is only appropriate for problems of the form

    4396: $     M Udot = F(U,t)

    4398:   where M is constant and F is non-stiff.  The user must pass M to TSSetIJacobian().  The current implementation only
    4399:   works with IMEX time integration methods such as TSROSW and TSARKIMEX, since there is no support for de-constructing
    4400:   an implicit operator of the form

    4402: $    shift*M + J

    4404:   where J is the Jacobian of -F(U).  Support may be added in a future version of PETSc, but for now, the user must store
    4405:   a copy of M or reassemble it when requested.

    4407: .seealso: TSSetIFunction(), TSSetIJacobian(), TSComputeIFunctionLinear()
    4408: @*/
    4409: PetscErrorCode TSComputeIJacobianConstant(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat A,Mat B,void *ctx)
    4410: {
    4411:   MatScale(A, shift / ts->ijacobian.shift);
    4412:   ts->ijacobian.shift = shift;
    4413:   return 0;
    4414: }

    4416: /*@
    4417:    TSGetEquationType - Gets the type of the equation that TS is solving.

    4419:    Not Collective

    4421:    Input Parameter:
    4422: .  ts - the TS context

    4424:    Output Parameter:
    4425: .  equation_type - see TSEquationType

    4427:    Level: beginner

    4429: .seealso: TSSetEquationType(), TSEquationType
    4430: @*/
    4431: PetscErrorCode  TSGetEquationType(TS ts,TSEquationType *equation_type)
    4432: {
    4435:   *equation_type = ts->equation_type;
    4436:   return 0;
    4437: }

    4439: /*@
    4440:    TSSetEquationType - Sets the type of the equation that TS is solving.

    4442:    Not Collective

    4444:    Input Parameters:
    4445: +  ts - the TS context
    4446: -  equation_type - see TSEquationType

    4448:    Level: advanced

    4450: .seealso: TSGetEquationType(), TSEquationType
    4451: @*/
    4452: PetscErrorCode  TSSetEquationType(TS ts,TSEquationType equation_type)
    4453: {
    4455:   ts->equation_type = equation_type;
    4456:   return 0;
    4457: }

    4459: /*@
    4460:    TSGetConvergedReason - Gets the reason the TS iteration was stopped.

    4462:    Not Collective

    4464:    Input Parameter:
    4465: .  ts - the TS context

    4467:    Output Parameter:
    4468: .  reason - negative value indicates diverged, positive value converged, see TSConvergedReason or the
    4469:             manual pages for the individual convergence tests for complete lists

    4471:    Level: beginner

    4473:    Notes:
    4474:    Can only be called after the call to TSSolve() is complete.

    4476: .seealso: TSSetConvergenceTest(), TSConvergedReason
    4477: @*/
    4478: PetscErrorCode  TSGetConvergedReason(TS ts,TSConvergedReason *reason)
    4479: {
    4482:   *reason = ts->reason;
    4483:   return 0;
    4484: }

    4486: /*@
    4487:    TSSetConvergedReason - Sets the reason for handling the convergence of TSSolve.

    4489:    Logically Collective; reason must contain common value

    4491:    Input Parameters:
    4492: +  ts - the TS context
    4493: -  reason - negative value indicates diverged, positive value converged, see TSConvergedReason or the
    4494:             manual pages for the individual convergence tests for complete lists

    4496:    Level: advanced

    4498:    Notes:
    4499:    Can only be called while TSSolve() is active.

    4501: .seealso: TSConvergedReason
    4502: @*/
    4503: PetscErrorCode  TSSetConvergedReason(TS ts,TSConvergedReason reason)
    4504: {
    4506:   ts->reason = reason;
    4507:   return 0;
    4508: }

    4510: /*@
    4511:    TSGetSolveTime - Gets the time after a call to TSSolve()

    4513:    Not Collective

    4515:    Input Parameter:
    4516: .  ts - the TS context

    4518:    Output Parameter:
    4519: .  ftime - the final time. This time corresponds to the final time set with TSSetMaxTime()

    4521:    Level: beginner

    4523:    Notes:
    4524:    Can only be called after the call to TSSolve() is complete.

    4526: .seealso: TSSetConvergenceTest(), TSConvergedReason
    4527: @*/
    4528: PetscErrorCode  TSGetSolveTime(TS ts,PetscReal *ftime)
    4529: {
    4532:   *ftime = ts->solvetime;
    4533:   return 0;
    4534: }

    4536: /*@
    4537:    TSGetSNESIterations - Gets the total number of nonlinear iterations
    4538:    used by the time integrator.

    4540:    Not Collective

    4542:    Input Parameter:
    4543: .  ts - TS context

    4545:    Output Parameter:
    4546: .  nits - number of nonlinear iterations

    4548:    Notes:
    4549:    This counter is reset to zero for each successive call to TSSolve().

    4551:    Level: intermediate

    4553: .seealso:  TSGetKSPIterations()
    4554: @*/
    4555: PetscErrorCode TSGetSNESIterations(TS ts,PetscInt *nits)
    4556: {
    4559:   *nits = ts->snes_its;
    4560:   return 0;
    4561: }

    4563: /*@
    4564:    TSGetKSPIterations - Gets the total number of linear iterations
    4565:    used by the time integrator.

    4567:    Not Collective

    4569:    Input Parameter:
    4570: .  ts - TS context

    4572:    Output Parameter:
    4573: .  lits - number of linear iterations

    4575:    Notes:
    4576:    This counter is reset to zero for each successive call to TSSolve().

    4578:    Level: intermediate

    4580: .seealso:  TSGetSNESIterations(), SNESGetKSPIterations()
    4581: @*/
    4582: PetscErrorCode TSGetKSPIterations(TS ts,PetscInt *lits)
    4583: {
    4586:   *lits = ts->ksp_its;
    4587:   return 0;
    4588: }

    4590: /*@
    4591:    TSGetStepRejections - Gets the total number of rejected steps.

    4593:    Not Collective

    4595:    Input Parameter:
    4596: .  ts - TS context

    4598:    Output Parameter:
    4599: .  rejects - number of steps rejected

    4601:    Notes:
    4602:    This counter is reset to zero for each successive call to TSSolve().

    4604:    Level: intermediate

    4606: .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetSNESFailures(), TSSetMaxSNESFailures(), TSSetErrorIfStepFails()
    4607: @*/
    4608: PetscErrorCode TSGetStepRejections(TS ts,PetscInt *rejects)
    4609: {
    4612:   *rejects = ts->reject;
    4613:   return 0;
    4614: }

    4616: /*@
    4617:    TSGetSNESFailures - Gets the total number of failed SNES solves

    4619:    Not Collective

    4621:    Input Parameter:
    4622: .  ts - TS context

    4624:    Output Parameter:
    4625: .  fails - number of failed nonlinear solves

    4627:    Notes:
    4628:    This counter is reset to zero for each successive call to TSSolve().

    4630:    Level: intermediate

    4632: .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSSetMaxSNESFailures()
    4633: @*/
    4634: PetscErrorCode TSGetSNESFailures(TS ts,PetscInt *fails)
    4635: {
    4638:   *fails = ts->num_snes_failures;
    4639:   return 0;
    4640: }

    4642: /*@
    4643:    TSSetMaxStepRejections - Sets the maximum number of step rejections before a step fails

    4645:    Not Collective

    4647:    Input Parameters:
    4648: +  ts - TS context
    4649: -  rejects - maximum number of rejected steps, pass -1 for unlimited

    4651:    Notes:
    4652:    The counter is reset to zero for each step

    4654:    Options Database Key:
    4655:  .  -ts_max_reject - Maximum number of step rejections before a step fails

    4657:    Level: intermediate

    4659: .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxSNESFailures(), TSGetStepRejections(), TSGetSNESFailures(), TSSetErrorIfStepFails(), TSGetConvergedReason()
    4660: @*/
    4661: PetscErrorCode TSSetMaxStepRejections(TS ts,PetscInt rejects)
    4662: {
    4664:   ts->max_reject = rejects;
    4665:   return 0;
    4666: }

    4668: /*@
    4669:    TSSetMaxSNESFailures - Sets the maximum number of failed SNES solves

    4671:    Not Collective

    4673:    Input Parameters:
    4674: +  ts - TS context
    4675: -  fails - maximum number of failed nonlinear solves, pass -1 for unlimited

    4677:    Notes:
    4678:    The counter is reset to zero for each successive call to TSSolve().

    4680:    Options Database Key:
    4681:  .  -ts_max_snes_failures - Maximum number of nonlinear solve failures

    4683:    Level: intermediate

    4685: .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSGetSNESFailures(), SNESGetConvergedReason(), TSGetConvergedReason()
    4686: @*/
    4687: PetscErrorCode TSSetMaxSNESFailures(TS ts,PetscInt fails)
    4688: {
    4690:   ts->max_snes_failures = fails;
    4691:   return 0;
    4692: }

    4694: /*@
    4695:    TSSetErrorIfStepFails - Error if no step succeeds

    4697:    Not Collective

    4699:    Input Parameters:
    4700: +  ts - TS context
    4701: -  err - PETSC_TRUE to error if no step succeeds, PETSC_FALSE to return without failure

    4703:    Options Database Key:
    4704:  .  -ts_error_if_step_fails - Error if no step succeeds

    4706:    Level: intermediate

    4708: .seealso:  TSGetSNESIterations(), TSGetKSPIterations(), TSSetMaxStepRejections(), TSGetStepRejections(), TSGetSNESFailures(), TSSetErrorIfStepFails(), TSGetConvergedReason()
    4709: @*/
    4710: PetscErrorCode TSSetErrorIfStepFails(TS ts,PetscBool err)
    4711: {
    4713:   ts->errorifstepfailed = err;
    4714:   return 0;
    4715: }

    4717: /*@
    4718:    TSGetAdapt - Get the adaptive controller context for the current method

    4720:    Collective on TS if controller has not been created yet

    4722:    Input Parameter:
    4723: .  ts - time stepping context

    4725:    Output Parameter:
    4726: .  adapt - adaptive controller

    4728:    Level: intermediate

    4730: .seealso: TSAdapt, TSAdaptSetType(), TSAdaptChoose()
    4731: @*/
    4732: PetscErrorCode TSGetAdapt(TS ts,TSAdapt *adapt)
    4733: {
    4736:   if (!ts->adapt) {
    4737:     TSAdaptCreate(PetscObjectComm((PetscObject)ts),&ts->adapt);
    4738:     PetscLogObjectParent((PetscObject)ts,(PetscObject)ts->adapt);
    4739:     PetscObjectIncrementTabLevel((PetscObject)ts->adapt,(PetscObject)ts,1);
    4740:   }
    4741:   *adapt = ts->adapt;
    4742:   return 0;
    4743: }

    4745: /*@
    4746:    TSSetTolerances - Set tolerances for local truncation error when using adaptive controller

    4748:    Logically Collective

    4750:    Input Parameters:
    4751: +  ts - time integration context
    4752: .  atol - scalar absolute tolerances, PETSC_DECIDE to leave current value
    4753: .  vatol - vector of absolute tolerances or NULL, used in preference to atol if present
    4754: .  rtol - scalar relative tolerances, PETSC_DECIDE to leave current value
    4755: -  vrtol - vector of relative tolerances or NULL, used in preference to atol if present

    4757:    Options Database keys:
    4758: +  -ts_rtol <rtol> - relative tolerance for local truncation error
    4759: -  -ts_atol <atol> - Absolute tolerance for local truncation error

    4761:    Notes:
    4762:    With PETSc's implicit schemes for DAE problems, the calculation of the local truncation error
    4763:    (LTE) includes both the differential and the algebraic variables. If one wants the LTE to be
    4764:    computed only for the differential or the algebraic part then this can be done using the vector of
    4765:    tolerances vatol. For example, by setting the tolerance vector with the desired tolerance for the
    4766:    differential part and infinity for the algebraic part, the LTE calculation will include only the
    4767:    differential variables.

    4769:    Level: beginner

    4771: .seealso: TS, TSAdapt, TSErrorWeightedNorm(), TSGetTolerances()
    4772: @*/
    4773: PetscErrorCode TSSetTolerances(TS ts,PetscReal atol,Vec vatol,PetscReal rtol,Vec vrtol)
    4774: {
    4775:   if (atol != PETSC_DECIDE && atol != PETSC_DEFAULT) ts->atol = atol;
    4776:   if (vatol) {
    4777:     PetscObjectReference((PetscObject)vatol);
    4778:     VecDestroy(&ts->vatol);
    4779:     ts->vatol = vatol;
    4780:   }
    4781:   if (rtol != PETSC_DECIDE && rtol != PETSC_DEFAULT) ts->rtol = rtol;
    4782:   if (vrtol) {
    4783:     PetscObjectReference((PetscObject)vrtol);
    4784:     VecDestroy(&ts->vrtol);
    4785:     ts->vrtol = vrtol;
    4786:   }
    4787:   return 0;
    4788: }

    4790: /*@
    4791:    TSGetTolerances - Get tolerances for local truncation error when using adaptive controller

    4793:    Logically Collective

    4795:    Input Parameter:
    4796: .  ts - time integration context

    4798:    Output Parameters:
    4799: +  atol - scalar absolute tolerances, NULL to ignore
    4800: .  vatol - vector of absolute tolerances, NULL to ignore
    4801: .  rtol - scalar relative tolerances, NULL to ignore
    4802: -  vrtol - vector of relative tolerances, NULL to ignore

    4804:    Level: beginner

    4806: .seealso: TS, TSAdapt, TSErrorWeightedNorm(), TSSetTolerances()
    4807: @*/
    4808: PetscErrorCode TSGetTolerances(TS ts,PetscReal *atol,Vec *vatol,PetscReal *rtol,Vec *vrtol)
    4809: {
    4810:   if (atol)  *atol  = ts->atol;
    4811:   if (vatol) *vatol = ts->vatol;
    4812:   if (rtol)  *rtol  = ts->rtol;
    4813:   if (vrtol) *vrtol = ts->vrtol;
    4814:   return 0;
    4815: }

    4817: /*@
    4818:    TSErrorWeightedNorm2 - compute a weighted 2-norm of the difference between two state vectors

    4820:    Collective on TS

    4822:    Input Parameters:
    4823: +  ts - time stepping context
    4824: .  U - state vector, usually ts->vec_sol
    4825: -  Y - state vector to be compared to U

    4827:    Output Parameters:
    4828: +  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
    4829: .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
    4830: -  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances

    4832:    Level: developer

    4834: .seealso: TSErrorWeightedNorm(), TSErrorWeightedNormInfinity()
    4835: @*/
    4836: PetscErrorCode TSErrorWeightedNorm2(TS ts,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
    4837: {
    4838:   PetscInt          i,n,N,rstart;
    4839:   PetscInt          n_loc,na_loc,nr_loc;
    4840:   PetscReal         n_glb,na_glb,nr_glb;
    4841:   const PetscScalar *u,*y;
    4842:   PetscReal         sum,suma,sumr,gsum,gsuma,gsumr,diff;
    4843:   PetscReal         tol,tola,tolr;
    4844:   PetscReal         err_loc[6],err_glb[6];

    4857:   VecGetSize(U,&N);
    4858:   VecGetLocalSize(U,&n);
    4859:   VecGetOwnershipRange(U,&rstart,NULL);
    4860:   VecGetArrayRead(U,&u);
    4861:   VecGetArrayRead(Y,&y);
    4862:   sum  = 0.; n_loc  = 0;
    4863:   suma = 0.; na_loc = 0;
    4864:   sumr = 0.; nr_loc = 0;
    4865:   if (ts->vatol && ts->vrtol) {
    4866:     const PetscScalar *atol,*rtol;
    4867:     VecGetArrayRead(ts->vatol,&atol);
    4868:     VecGetArrayRead(ts->vrtol,&rtol);
    4869:     for (i=0; i<n; i++) {
    4870:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    4871:       diff = PetscAbsScalar(y[i] - u[i]);
    4872:       tola = PetscRealPart(atol[i]);
    4873:       if (tola>0.) {
    4874:         suma  += PetscSqr(diff/tola);
    4875:         na_loc++;
    4876:       }
    4877:       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    4878:       if (tolr>0.) {
    4879:         sumr  += PetscSqr(diff/tolr);
    4880:         nr_loc++;
    4881:       }
    4882:       tol=tola+tolr;
    4883:       if (tol>0.) {
    4884:         sum  += PetscSqr(diff/tol);
    4885:         n_loc++;
    4886:       }
    4887:     }
    4888:     VecRestoreArrayRead(ts->vatol,&atol);
    4889:     VecRestoreArrayRead(ts->vrtol,&rtol);
    4890:   } else if (ts->vatol) {       /* vector atol, scalar rtol */
    4891:     const PetscScalar *atol;
    4892:     VecGetArrayRead(ts->vatol,&atol);
    4893:     for (i=0; i<n; i++) {
    4894:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    4895:       diff = PetscAbsScalar(y[i] - u[i]);
    4896:       tola = PetscRealPart(atol[i]);
    4897:       if (tola>0.) {
    4898:         suma  += PetscSqr(diff/tola);
    4899:         na_loc++;
    4900:       }
    4901:       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    4902:       if (tolr>0.) {
    4903:         sumr  += PetscSqr(diff/tolr);
    4904:         nr_loc++;
    4905:       }
    4906:       tol=tola+tolr;
    4907:       if (tol>0.) {
    4908:         sum  += PetscSqr(diff/tol);
    4909:         n_loc++;
    4910:       }
    4911:     }
    4912:     VecRestoreArrayRead(ts->vatol,&atol);
    4913:   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
    4914:     const PetscScalar *rtol;
    4915:     VecGetArrayRead(ts->vrtol,&rtol);
    4916:     for (i=0; i<n; i++) {
    4917:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    4918:       diff = PetscAbsScalar(y[i] - u[i]);
    4919:       tola = ts->atol;
    4920:       if (tola>0.) {
    4921:         suma  += PetscSqr(diff/tola);
    4922:         na_loc++;
    4923:       }
    4924:       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    4925:       if (tolr>0.) {
    4926:         sumr  += PetscSqr(diff/tolr);
    4927:         nr_loc++;
    4928:       }
    4929:       tol=tola+tolr;
    4930:       if (tol>0.) {
    4931:         sum  += PetscSqr(diff/tol);
    4932:         n_loc++;
    4933:       }
    4934:     }
    4935:     VecRestoreArrayRead(ts->vrtol,&rtol);
    4936:   } else {                      /* scalar atol, scalar rtol */
    4937:     for (i=0; i<n; i++) {
    4938:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    4939:       diff = PetscAbsScalar(y[i] - u[i]);
    4940:       tola = ts->atol;
    4941:       if (tola>0.) {
    4942:         suma  += PetscSqr(diff/tola);
    4943:         na_loc++;
    4944:       }
    4945:       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    4946:       if (tolr>0.) {
    4947:         sumr  += PetscSqr(diff/tolr);
    4948:         nr_loc++;
    4949:       }
    4950:       tol=tola+tolr;
    4951:       if (tol>0.) {
    4952:         sum  += PetscSqr(diff/tol);
    4953:         n_loc++;
    4954:       }
    4955:     }
    4956:   }
    4957:   VecRestoreArrayRead(U,&u);
    4958:   VecRestoreArrayRead(Y,&y);

    4960:   err_loc[0] = sum;
    4961:   err_loc[1] = suma;
    4962:   err_loc[2] = sumr;
    4963:   err_loc[3] = (PetscReal)n_loc;
    4964:   err_loc[4] = (PetscReal)na_loc;
    4965:   err_loc[5] = (PetscReal)nr_loc;

    4967:   MPIU_Allreduce(err_loc,err_glb,6,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));

    4969:   gsum   = err_glb[0];
    4970:   gsuma  = err_glb[1];
    4971:   gsumr  = err_glb[2];
    4972:   n_glb  = err_glb[3];
    4973:   na_glb = err_glb[4];
    4974:   nr_glb = err_glb[5];

    4976:   *norm  = 0.;
    4977:   if (n_glb>0.) {*norm  = PetscSqrtReal(gsum  / n_glb);}
    4978:   *norma = 0.;
    4979:   if (na_glb>0.) {*norma = PetscSqrtReal(gsuma / na_glb);}
    4980:   *normr = 0.;
    4981:   if (nr_glb>0.) {*normr = PetscSqrtReal(gsumr / nr_glb);}

    4986:   return 0;
    4987: }

    4989: /*@
    4990:    TSErrorWeightedNormInfinity - compute a weighted infinity-norm of the difference between two state vectors

    4992:    Collective on TS

    4994:    Input Parameters:
    4995: +  ts - time stepping context
    4996: .  U - state vector, usually ts->vec_sol
    4997: -  Y - state vector to be compared to U

    4999:    Output Parameters:
    5000: +  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
    5001: .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
    5002: -  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances

    5004:    Level: developer

    5006: .seealso: TSErrorWeightedNorm(), TSErrorWeightedNorm2()
    5007: @*/
    5008: PetscErrorCode TSErrorWeightedNormInfinity(TS ts,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
    5009: {
    5010:   PetscInt          i,n,N,rstart;
    5011:   const PetscScalar *u,*y;
    5012:   PetscReal         max,gmax,maxa,gmaxa,maxr,gmaxr;
    5013:   PetscReal         tol,tola,tolr,diff;
    5014:   PetscReal         err_loc[3],err_glb[3];

    5027:   VecGetSize(U,&N);
    5028:   VecGetLocalSize(U,&n);
    5029:   VecGetOwnershipRange(U,&rstart,NULL);
    5030:   VecGetArrayRead(U,&u);
    5031:   VecGetArrayRead(Y,&y);

    5033:   max=0.;
    5034:   maxa=0.;
    5035:   maxr=0.;

    5037:   if (ts->vatol && ts->vrtol) {     /* vector atol, vector rtol */
    5038:     const PetscScalar *atol,*rtol;
    5039:     VecGetArrayRead(ts->vatol,&atol);
    5040:     VecGetArrayRead(ts->vrtol,&rtol);

    5042:     for (i=0; i<n; i++) {
    5043:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5044:       diff = PetscAbsScalar(y[i] - u[i]);
    5045:       tola = PetscRealPart(atol[i]);
    5046:       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5047:       tol  = tola+tolr;
    5048:       if (tola>0.) {
    5049:         maxa = PetscMax(maxa,diff / tola);
    5050:       }
    5051:       if (tolr>0.) {
    5052:         maxr = PetscMax(maxr,diff / tolr);
    5053:       }
    5054:       if (tol>0.) {
    5055:         max = PetscMax(max,diff / tol);
    5056:       }
    5057:     }
    5058:     VecRestoreArrayRead(ts->vatol,&atol);
    5059:     VecRestoreArrayRead(ts->vrtol,&rtol);
    5060:   } else if (ts->vatol) {       /* vector atol, scalar rtol */
    5061:     const PetscScalar *atol;
    5062:     VecGetArrayRead(ts->vatol,&atol);
    5063:     for (i=0; i<n; i++) {
    5064:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5065:       diff = PetscAbsScalar(y[i] - u[i]);
    5066:       tola = PetscRealPart(atol[i]);
    5067:       tolr = ts->rtol  * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5068:       tol  = tola+tolr;
    5069:       if (tola>0.) {
    5070:         maxa = PetscMax(maxa,diff / tola);
    5071:       }
    5072:       if (tolr>0.) {
    5073:         maxr = PetscMax(maxr,diff / tolr);
    5074:       }
    5075:       if (tol>0.) {
    5076:         max = PetscMax(max,diff / tol);
    5077:       }
    5078:     }
    5079:     VecRestoreArrayRead(ts->vatol,&atol);
    5080:   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
    5081:     const PetscScalar *rtol;
    5082:     VecGetArrayRead(ts->vrtol,&rtol);

    5084:     for (i=0; i<n; i++) {
    5085:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5086:       diff = PetscAbsScalar(y[i] - u[i]);
    5087:       tola = ts->atol;
    5088:       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5089:       tol  = tola+tolr;
    5090:       if (tola>0.) {
    5091:         maxa = PetscMax(maxa,diff / tola);
    5092:       }
    5093:       if (tolr>0.) {
    5094:         maxr = PetscMax(maxr,diff / tolr);
    5095:       }
    5096:       if (tol>0.) {
    5097:         max = PetscMax(max,diff / tol);
    5098:       }
    5099:     }
    5100:     VecRestoreArrayRead(ts->vrtol,&rtol);
    5101:   } else {                      /* scalar atol, scalar rtol */

    5103:     for (i=0; i<n; i++) {
    5104:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5105:       diff = PetscAbsScalar(y[i] - u[i]);
    5106:       tola = ts->atol;
    5107:       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5108:       tol  = tola+tolr;
    5109:       if (tola>0.) {
    5110:         maxa = PetscMax(maxa,diff / tola);
    5111:       }
    5112:       if (tolr>0.) {
    5113:         maxr = PetscMax(maxr,diff / tolr);
    5114:       }
    5115:       if (tol>0.) {
    5116:         max = PetscMax(max,diff / tol);
    5117:       }
    5118:     }
    5119:   }
    5120:   VecRestoreArrayRead(U,&u);
    5121:   VecRestoreArrayRead(Y,&y);
    5122:   err_loc[0] = max;
    5123:   err_loc[1] = maxa;
    5124:   err_loc[2] = maxr;
    5125:   MPIU_Allreduce(err_loc,err_glb,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
    5126:   gmax   = err_glb[0];
    5127:   gmaxa  = err_glb[1];
    5128:   gmaxr  = err_glb[2];

    5130:   *norm = gmax;
    5131:   *norma = gmaxa;
    5132:   *normr = gmaxr;
    5136:   return 0;
    5137: }

    5139: /*@
    5140:    TSErrorWeightedNorm - compute a weighted norm of the difference between two state vectors based on supplied absolute and relative tolerances

    5142:    Collective on TS

    5144:    Input Parameters:
    5145: +  ts - time stepping context
    5146: .  U - state vector, usually ts->vec_sol
    5147: .  Y - state vector to be compared to U
    5148: -  wnormtype - norm type, either NORM_2 or NORM_INFINITY

    5150:    Output Parameters:
    5151: +  norm  - weighted norm, a value of 1.0 achieves a balance between absolute and relative tolerances
    5152: .  norma - weighted norm, a value of 1.0 means that the error meets the absolute tolerance set by the user
    5153: -  normr - weighted norm, a value of 1.0 means that the error meets the relative tolerance set by the user

    5155:    Options Database Keys:
    5156: .  -ts_adapt_wnormtype <wnormtype> - 2, INFINITY

    5158:    Level: developer

    5160: .seealso: TSErrorWeightedNormInfinity(), TSErrorWeightedNorm2(), TSErrorWeightedENorm
    5161: @*/
    5162: PetscErrorCode TSErrorWeightedNorm(TS ts,Vec U,Vec Y,NormType wnormtype,PetscReal *norm,PetscReal *norma,PetscReal *normr)
    5163: {
    5164:   if (wnormtype == NORM_2) {
    5165:     TSErrorWeightedNorm2(ts,U,Y,norm,norma,normr);
    5166:   } else if (wnormtype == NORM_INFINITY) {
    5167:     TSErrorWeightedNormInfinity(ts,U,Y,norm,norma,normr);
    5168:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
    5169:   return 0;
    5170: }

    5172: /*@
    5173:    TSErrorWeightedENorm2 - compute a weighted 2 error norm based on supplied absolute and relative tolerances

    5175:    Collective on TS

    5177:    Input Parameters:
    5178: +  ts - time stepping context
    5179: .  E - error vector
    5180: .  U - state vector, usually ts->vec_sol
    5181: -  Y - state vector, previous time step

    5183:    Output Parameters:
    5184: +  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
    5185: .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
    5186: -  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances

    5188:    Level: developer

    5190: .seealso: TSErrorWeightedENorm(), TSErrorWeightedENormInfinity()
    5191: @*/
    5192: PetscErrorCode TSErrorWeightedENorm2(TS ts,Vec E,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
    5193: {
    5194:   PetscInt          i,n,N,rstart;
    5195:   PetscInt          n_loc,na_loc,nr_loc;
    5196:   PetscReal         n_glb,na_glb,nr_glb;
    5197:   const PetscScalar *e,*u,*y;
    5198:   PetscReal         err,sum,suma,sumr,gsum,gsuma,gsumr;
    5199:   PetscReal         tol,tola,tolr;
    5200:   PetscReal         err_loc[6],err_glb[6];

    5215:   VecGetSize(E,&N);
    5216:   VecGetLocalSize(E,&n);
    5217:   VecGetOwnershipRange(E,&rstart,NULL);
    5218:   VecGetArrayRead(E,&e);
    5219:   VecGetArrayRead(U,&u);
    5220:   VecGetArrayRead(Y,&y);
    5221:   sum  = 0.; n_loc  = 0;
    5222:   suma = 0.; na_loc = 0;
    5223:   sumr = 0.; nr_loc = 0;
    5224:   if (ts->vatol && ts->vrtol) {
    5225:     const PetscScalar *atol,*rtol;
    5226:     VecGetArrayRead(ts->vatol,&atol);
    5227:     VecGetArrayRead(ts->vrtol,&rtol);
    5228:     for (i=0; i<n; i++) {
    5229:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5230:       err = PetscAbsScalar(e[i]);
    5231:       tola = PetscRealPart(atol[i]);
    5232:       if (tola>0.) {
    5233:         suma  += PetscSqr(err/tola);
    5234:         na_loc++;
    5235:       }
    5236:       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5237:       if (tolr>0.) {
    5238:         sumr  += PetscSqr(err/tolr);
    5239:         nr_loc++;
    5240:       }
    5241:       tol=tola+tolr;
    5242:       if (tol>0.) {
    5243:         sum  += PetscSqr(err/tol);
    5244:         n_loc++;
    5245:       }
    5246:     }
    5247:     VecRestoreArrayRead(ts->vatol,&atol);
    5248:     VecRestoreArrayRead(ts->vrtol,&rtol);
    5249:   } else if (ts->vatol) {       /* vector atol, scalar rtol */
    5250:     const PetscScalar *atol;
    5251:     VecGetArrayRead(ts->vatol,&atol);
    5252:     for (i=0; i<n; i++) {
    5253:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5254:       err = PetscAbsScalar(e[i]);
    5255:       tola = PetscRealPart(atol[i]);
    5256:       if (tola>0.) {
    5257:         suma  += PetscSqr(err/tola);
    5258:         na_loc++;
    5259:       }
    5260:       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5261:       if (tolr>0.) {
    5262:         sumr  += PetscSqr(err/tolr);
    5263:         nr_loc++;
    5264:       }
    5265:       tol=tola+tolr;
    5266:       if (tol>0.) {
    5267:         sum  += PetscSqr(err/tol);
    5268:         n_loc++;
    5269:       }
    5270:     }
    5271:     VecRestoreArrayRead(ts->vatol,&atol);
    5272:   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
    5273:     const PetscScalar *rtol;
    5274:     VecGetArrayRead(ts->vrtol,&rtol);
    5275:     for (i=0; i<n; i++) {
    5276:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5277:       err = PetscAbsScalar(e[i]);
    5278:       tola = ts->atol;
    5279:       if (tola>0.) {
    5280:         suma  += PetscSqr(err/tola);
    5281:         na_loc++;
    5282:       }
    5283:       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5284:       if (tolr>0.) {
    5285:         sumr  += PetscSqr(err/tolr);
    5286:         nr_loc++;
    5287:       }
    5288:       tol=tola+tolr;
    5289:       if (tol>0.) {
    5290:         sum  += PetscSqr(err/tol);
    5291:         n_loc++;
    5292:       }
    5293:     }
    5294:     VecRestoreArrayRead(ts->vrtol,&rtol);
    5295:   } else {                      /* scalar atol, scalar rtol */
    5296:     for (i=0; i<n; i++) {
    5297:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5298:       err = PetscAbsScalar(e[i]);
    5299:       tola = ts->atol;
    5300:       if (tola>0.) {
    5301:         suma  += PetscSqr(err/tola);
    5302:         na_loc++;
    5303:       }
    5304:       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5305:       if (tolr>0.) {
    5306:         sumr  += PetscSqr(err/tolr);
    5307:         nr_loc++;
    5308:       }
    5309:       tol=tola+tolr;
    5310:       if (tol>0.) {
    5311:         sum  += PetscSqr(err/tol);
    5312:         n_loc++;
    5313:       }
    5314:     }
    5315:   }
    5316:   VecRestoreArrayRead(E,&e);
    5317:   VecRestoreArrayRead(U,&u);
    5318:   VecRestoreArrayRead(Y,&y);

    5320:   err_loc[0] = sum;
    5321:   err_loc[1] = suma;
    5322:   err_loc[2] = sumr;
    5323:   err_loc[3] = (PetscReal)n_loc;
    5324:   err_loc[4] = (PetscReal)na_loc;
    5325:   err_loc[5] = (PetscReal)nr_loc;

    5327:   MPIU_Allreduce(err_loc,err_glb,6,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ts));

    5329:   gsum   = err_glb[0];
    5330:   gsuma  = err_glb[1];
    5331:   gsumr  = err_glb[2];
    5332:   n_glb  = err_glb[3];
    5333:   na_glb = err_glb[4];
    5334:   nr_glb = err_glb[5];

    5336:   *norm  = 0.;
    5337:   if (n_glb>0.) {*norm  = PetscSqrtReal(gsum  / n_glb);}
    5338:   *norma = 0.;
    5339:   if (na_glb>0.) {*norma = PetscSqrtReal(gsuma / na_glb);}
    5340:   *normr = 0.;
    5341:   if (nr_glb>0.) {*normr = PetscSqrtReal(gsumr / nr_glb);}

    5346:   return 0;
    5347: }

    5349: /*@
    5350:    TSErrorWeightedENormInfinity - compute a weighted infinity error norm based on supplied absolute and relative tolerances
    5351:    Collective on TS

    5353:    Input Parameters:
    5354: +  ts - time stepping context
    5355: .  E - error vector
    5356: .  U - state vector, usually ts->vec_sol
    5357: -  Y - state vector, previous time step

    5359:    Output Parameters:
    5360: +  norm - weighted norm, a value of 1.0 means that the error matches the tolerances
    5361: .  norma - weighted norm based on the absolute tolerance, a value of 1.0 means that the error matches the tolerances
    5362: -  normr - weighted norm based on the relative tolerance, a value of 1.0 means that the error matches the tolerances

    5364:    Level: developer

    5366: .seealso: TSErrorWeightedENorm(), TSErrorWeightedENorm2()
    5367: @*/
    5368: PetscErrorCode TSErrorWeightedENormInfinity(TS ts,Vec E,Vec U,Vec Y,PetscReal *norm,PetscReal *norma,PetscReal *normr)
    5369: {
    5370:   PetscInt          i,n,N,rstart;
    5371:   const PetscScalar *e,*u,*y;
    5372:   PetscReal         err,max,gmax,maxa,gmaxa,maxr,gmaxr;
    5373:   PetscReal         tol,tola,tolr;
    5374:   PetscReal         err_loc[3],err_glb[3];

    5389:   VecGetSize(E,&N);
    5390:   VecGetLocalSize(E,&n);
    5391:   VecGetOwnershipRange(E,&rstart,NULL);
    5392:   VecGetArrayRead(E,&e);
    5393:   VecGetArrayRead(U,&u);
    5394:   VecGetArrayRead(Y,&y);

    5396:   max=0.;
    5397:   maxa=0.;
    5398:   maxr=0.;

    5400:   if (ts->vatol && ts->vrtol) {     /* vector atol, vector rtol */
    5401:     const PetscScalar *atol,*rtol;
    5402:     VecGetArrayRead(ts->vatol,&atol);
    5403:     VecGetArrayRead(ts->vrtol,&rtol);

    5405:     for (i=0; i<n; i++) {
    5406:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5407:       err = PetscAbsScalar(e[i]);
    5408:       tola = PetscRealPart(atol[i]);
    5409:       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5410:       tol  = tola+tolr;
    5411:       if (tola>0.) {
    5412:         maxa = PetscMax(maxa,err / tola);
    5413:       }
    5414:       if (tolr>0.) {
    5415:         maxr = PetscMax(maxr,err / tolr);
    5416:       }
    5417:       if (tol>0.) {
    5418:         max = PetscMax(max,err / tol);
    5419:       }
    5420:     }
    5421:     VecRestoreArrayRead(ts->vatol,&atol);
    5422:     VecRestoreArrayRead(ts->vrtol,&rtol);
    5423:   } else if (ts->vatol) {       /* vector atol, scalar rtol */
    5424:     const PetscScalar *atol;
    5425:     VecGetArrayRead(ts->vatol,&atol);
    5426:     for (i=0; i<n; i++) {
    5427:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5428:       err = PetscAbsScalar(e[i]);
    5429:       tola = PetscRealPart(atol[i]);
    5430:       tolr = ts->rtol  * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5431:       tol  = tola+tolr;
    5432:       if (tola>0.) {
    5433:         maxa = PetscMax(maxa,err / tola);
    5434:       }
    5435:       if (tolr>0.) {
    5436:         maxr = PetscMax(maxr,err / tolr);
    5437:       }
    5438:       if (tol>0.) {
    5439:         max = PetscMax(max,err / tol);
    5440:       }
    5441:     }
    5442:     VecRestoreArrayRead(ts->vatol,&atol);
    5443:   } else if (ts->vrtol) {       /* scalar atol, vector rtol */
    5444:     const PetscScalar *rtol;
    5445:     VecGetArrayRead(ts->vrtol,&rtol);

    5447:     for (i=0; i<n; i++) {
    5448:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5449:       err = PetscAbsScalar(e[i]);
    5450:       tola = ts->atol;
    5451:       tolr = PetscRealPart(rtol[i]) * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5452:       tol  = tola+tolr;
    5453:       if (tola>0.) {
    5454:         maxa = PetscMax(maxa,err / tola);
    5455:       }
    5456:       if (tolr>0.) {
    5457:         maxr = PetscMax(maxr,err / tolr);
    5458:       }
    5459:       if (tol>0.) {
    5460:         max = PetscMax(max,err / tol);
    5461:       }
    5462:     }
    5463:     VecRestoreArrayRead(ts->vrtol,&rtol);
    5464:   } else {                      /* scalar atol, scalar rtol */

    5466:     for (i=0; i<n; i++) {
    5467:       SkipSmallValue(y[i],u[i],ts->adapt->ignore_max);
    5468:       err = PetscAbsScalar(e[i]);
    5469:       tola = ts->atol;
    5470:       tolr = ts->rtol * PetscMax(PetscAbsScalar(u[i]),PetscAbsScalar(y[i]));
    5471:       tol  = tola+tolr;
    5472:       if (tola>0.) {
    5473:         maxa = PetscMax(maxa,err / tola);
    5474:       }
    5475:       if (tolr>0.) {
    5476:         maxr = PetscMax(maxr,err / tolr);
    5477:       }
    5478:       if (tol>0.) {
    5479:         max = PetscMax(max,err / tol);
    5480:       }
    5481:     }
    5482:   }
    5483:   VecRestoreArrayRead(E,&e);
    5484:   VecRestoreArrayRead(U,&u);
    5485:   VecRestoreArrayRead(Y,&y);
    5486:   err_loc[0] = max;
    5487:   err_loc[1] = maxa;
    5488:   err_loc[2] = maxr;
    5489:   MPIU_Allreduce(err_loc,err_glb,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)ts));
    5490:   gmax   = err_glb[0];
    5491:   gmaxa  = err_glb[1];
    5492:   gmaxr  = err_glb[2];

    5494:   *norm = gmax;
    5495:   *norma = gmaxa;
    5496:   *normr = gmaxr;
    5500:   return 0;
    5501: }

    5503: /*@
    5504:    TSErrorWeightedENorm - compute a weighted error norm based on supplied absolute and relative tolerances

    5506:    Collective on TS

    5508:    Input Parameters:
    5509: +  ts - time stepping context
    5510: .  E - error vector
    5511: .  U - state vector, usually ts->vec_sol
    5512: .  Y - state vector, previous time step
    5513: -  wnormtype - norm type, either NORM_2 or NORM_INFINITY

    5515:    Output Parameters:
    5516: +  norm  - weighted norm, a value of 1.0 achieves a balance between absolute and relative tolerances
    5517: .  norma - weighted norm, a value of 1.0 means that the error meets the absolute tolerance set by the user
    5518: -  normr - weighted norm, a value of 1.0 means that the error meets the relative tolerance set by the user

    5520:    Options Database Keys:
    5521: .  -ts_adapt_wnormtype <wnormtype> - 2, INFINITY

    5523:    Level: developer

    5525: .seealso: TSErrorWeightedENormInfinity(), TSErrorWeightedENorm2(), TSErrorWeightedNormInfinity(), TSErrorWeightedNorm2()
    5526: @*/
    5527: PetscErrorCode TSErrorWeightedENorm(TS ts,Vec E,Vec U,Vec Y,NormType wnormtype,PetscReal *norm,PetscReal *norma,PetscReal *normr)
    5528: {
    5529:   if (wnormtype == NORM_2) {
    5530:     TSErrorWeightedENorm2(ts,E,U,Y,norm,norma,normr);
    5531:   } else if (wnormtype == NORM_INFINITY) {
    5532:     TSErrorWeightedENormInfinity(ts,E,U,Y,norm,norma,normr);
    5533:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for norm type %s",NormTypes[wnormtype]);
    5534:   return 0;
    5535: }

    5537: /*@
    5538:    TSSetCFLTimeLocal - Set the local CFL constraint relative to forward Euler

    5540:    Logically Collective on TS

    5542:    Input Parameters:
    5543: +  ts - time stepping context
    5544: -  cfltime - maximum stable time step if using forward Euler (value can be different on each process)

    5546:    Note:
    5547:    After calling this function, the global CFL time can be obtained by calling TSGetCFLTime()

    5549:    Level: intermediate

    5551: .seealso: TSGetCFLTime(), TSADAPTCFL
    5552: @*/
    5553: PetscErrorCode TSSetCFLTimeLocal(TS ts,PetscReal cfltime)
    5554: {
    5556:   ts->cfltime_local = cfltime;
    5557:   ts->cfltime       = -1.;
    5558:   return 0;
    5559: }

    5561: /*@
    5562:    TSGetCFLTime - Get the maximum stable time step according to CFL criteria applied to forward Euler

    5564:    Collective on TS

    5566:    Input Parameter:
    5567: .  ts - time stepping context

    5569:    Output Parameter:
    5570: .  cfltime - maximum stable time step for forward Euler

    5572:    Level: advanced

    5574: .seealso: TSSetCFLTimeLocal()
    5575: @*/
    5576: PetscErrorCode TSGetCFLTime(TS ts,PetscReal *cfltime)
    5577: {
    5578:   if (ts->cfltime < 0) {
    5579:     MPIU_Allreduce(&ts->cfltime_local,&ts->cfltime,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)ts));
    5580:   }
    5581:   *cfltime = ts->cfltime;
    5582:   return 0;
    5583: }

    5585: /*@
    5586:    TSVISetVariableBounds - Sets the lower and upper bounds for the solution vector. xl <= x <= xu

    5588:    Input Parameters:
    5589: +  ts   - the TS context.
    5590: .  xl   - lower bound.
    5591: -  xu   - upper bound.

    5593:    Notes:
    5594:    If this routine is not called then the lower and upper bounds are set to
    5595:    PETSC_NINFINITY and PETSC_INFINITY respectively during SNESSetUp().

    5597:    Level: advanced

    5599: @*/
    5600: PetscErrorCode TSVISetVariableBounds(TS ts, Vec xl, Vec xu)
    5601: {
    5602:   SNES           snes;

    5604:   TSGetSNES(ts,&snes);
    5605:   SNESVISetVariableBounds(snes,xl,xu);
    5606:   return 0;
    5607: }

    5609: /*@
    5610:    TSComputeLinearStability - computes the linear stability function at a point

    5612:    Collective on TS

    5614:    Input Parameters:
    5615: +  ts - the TS context
    5616: -  xr,xi - real and imaginary part of input arguments

    5618:    Output Parameters:
    5619: .  yr,yi - real and imaginary part of function value

    5621:    Level: developer

    5623: .seealso: TSSetRHSFunction(), TSComputeIFunction()
    5624: @*/
    5625: PetscErrorCode TSComputeLinearStability(TS ts,PetscReal xr,PetscReal xi,PetscReal *yr,PetscReal *yi)
    5626: {
    5629:   (*ts->ops->linearstability)(ts,xr,xi,yr,yi);
    5630:   return 0;
    5631: }

    5633: /*@
    5634:    TSRestartStep - Flags the solver to restart the next step

    5636:    Collective on TS

    5638:    Input Parameter:
    5639: .  ts - the TS context obtained from TSCreate()

    5641:    Level: advanced

    5643:    Notes:
    5644:    Multistep methods like BDF or Runge-Kutta methods with FSAL property require restarting the solver in the event of
    5645:    discontinuities. These discontinuities may be introduced as a consequence of explicitly modifications to the solution
    5646:    vector (which PETSc attempts to detect and handle) or problem coefficients (which PETSc is not able to detect). For
    5647:    the sake of correctness and maximum safety, users are expected to call TSRestart() whenever they introduce
    5648:    discontinuities in callback routines (e.g. prestep and poststep routines, or implicit/rhs function routines with
    5649:    discontinuous source terms).

    5651: .seealso: TSSolve(), TSSetPreStep(), TSSetPostStep()
    5652: @*/
    5653: PetscErrorCode TSRestartStep(TS ts)
    5654: {
    5656:   ts->steprestart = PETSC_TRUE;
    5657:   return 0;
    5658: }

    5660: /*@
    5661:    TSRollBack - Rolls back one time step

    5663:    Collective on TS

    5665:    Input Parameter:
    5666: .  ts - the TS context obtained from TSCreate()

    5668:    Level: advanced

    5670: .seealso: TSCreate(), TSSetUp(), TSDestroy(), TSSolve(), TSSetPreStep(), TSSetPreStage(), TSInterpolate()
    5671: @*/
    5672: PetscErrorCode  TSRollBack(TS ts)
    5673: {
    5677:   (*ts->ops->rollback)(ts);
    5678:   ts->time_step = ts->ptime - ts->ptime_prev;
    5679:   ts->ptime = ts->ptime_prev;
    5680:   ts->ptime_prev = ts->ptime_prev_rollback;
    5681:   ts->steps--;
    5682:   ts->steprollback = PETSC_TRUE;
    5683:   return 0;
    5684: }

    5686: /*@
    5687:    TSGetStages - Get the number of stages and stage values

    5689:    Input Parameter:
    5690: .  ts - the TS context obtained from TSCreate()

    5692:    Output Parameters:
    5693: +  ns - the number of stages
    5694: -  Y - the current stage vectors

    5696:    Level: advanced

    5698:    Notes: Both ns and Y can be NULL.

    5700: .seealso: TSCreate()
    5701: @*/
    5702: PetscErrorCode  TSGetStages(TS ts,PetscInt *ns,Vec **Y)
    5703: {
    5707:   if (!ts->ops->getstages) {
    5708:     if (ns) *ns = 0;
    5709:     if (Y) *Y = NULL;
    5710:   } else {
    5711:     (*ts->ops->getstages)(ts,ns,Y);
    5712:   }
    5713:   return 0;
    5714: }

    5716: /*@C
    5717:   TSComputeIJacobianDefaultColor - Computes the Jacobian using finite differences and coloring to exploit matrix sparsity.

    5719:   Collective on SNES

    5721:   Input Parameters:
    5722: + ts - the TS context
    5723: . t - current timestep
    5724: . U - state vector
    5725: . Udot - time derivative of state vector
    5726: . shift - shift to apply, see note below
    5727: - ctx - an optional user context

    5729:   Output Parameters:
    5730: + J - Jacobian matrix (not altered in this routine)
    5731: - B - newly computed Jacobian matrix to use with preconditioner (generally the same as J)

    5733:   Level: intermediate

    5735:   Notes:
    5736:   If F(t,U,Udot)=0 is the DAE, the required Jacobian is

    5738:   dF/dU + shift*dF/dUdot

    5740:   Most users should not need to explicitly call this routine, as it
    5741:   is used internally within the nonlinear solvers.

    5743:   This will first try to get the coloring from the DM.  If the DM type has no coloring
    5744:   routine, then it will try to get the coloring from the matrix.  This requires that the
    5745:   matrix have nonzero entries precomputed.

    5747: .seealso: TSSetIJacobian(), MatFDColoringCreate(), MatFDColoringSetFunction()
    5748: @*/
    5749: PetscErrorCode TSComputeIJacobianDefaultColor(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal shift,Mat J,Mat B,void *ctx)
    5750: {
    5751:   SNES           snes;
    5752:   MatFDColoring  color;
    5753:   PetscBool      hascolor, matcolor = PETSC_FALSE;

    5755:   PetscOptionsGetBool(((PetscObject)ts)->options,((PetscObject) ts)->prefix, "-ts_fd_color_use_mat", &matcolor, NULL);
    5756:   PetscObjectQuery((PetscObject) B, "TSMatFDColoring", (PetscObject *) &color);
    5757:   if (!color) {
    5758:     DM         dm;
    5759:     ISColoring iscoloring;

    5761:     TSGetDM(ts, &dm);
    5762:     DMHasColoring(dm, &hascolor);
    5763:     if (hascolor && !matcolor) {
    5764:       DMCreateColoring(dm, IS_COLORING_GLOBAL, &iscoloring);
    5765:       MatFDColoringCreate(B, iscoloring, &color);
    5766:       MatFDColoringSetFunction(color, (PetscErrorCode (*)(void)) SNESTSFormFunction, (void *) ts);
    5767:       MatFDColoringSetFromOptions(color);
    5768:       MatFDColoringSetUp(B, iscoloring, color);
    5769:       ISColoringDestroy(&iscoloring);
    5770:     } else {
    5771:       MatColoring mc;

    5773:       MatColoringCreate(B, &mc);
    5774:       MatColoringSetDistance(mc, 2);
    5775:       MatColoringSetType(mc, MATCOLORINGSL);
    5776:       MatColoringSetFromOptions(mc);
    5777:       MatColoringApply(mc, &iscoloring);
    5778:       MatColoringDestroy(&mc);
    5779:       MatFDColoringCreate(B, iscoloring, &color);
    5780:       MatFDColoringSetFunction(color, (PetscErrorCode (*)(void)) SNESTSFormFunction, (void *) ts);
    5781:       MatFDColoringSetFromOptions(color);
    5782:       MatFDColoringSetUp(B, iscoloring, color);
    5783:       ISColoringDestroy(&iscoloring);
    5784:     }
    5785:     PetscObjectCompose((PetscObject) B, "TSMatFDColoring", (PetscObject) color);
    5786:     PetscObjectDereference((PetscObject) color);
    5787:   }
    5788:   TSGetSNES(ts, &snes);
    5789:   MatFDColoringApply(B, color, U, snes);
    5790:   if (J != B) {
    5791:     MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);
    5792:     MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);
    5793:   }
    5794:   return 0;
    5795: }

    5797: /*@
    5798:     TSSetFunctionDomainError - Set a function that tests if the current state vector is valid

    5800:     Input Parameters:
    5801: +    ts - the TS context
    5802: -    func - function called within TSFunctionDomainError

    5804:     Calling sequence of func:
    5805: $     PetscErrorCode func(TS ts,PetscReal time,Vec state,PetscBool reject)

    5807: +   ts - the TS context
    5808: .   time - the current time (of the stage)
    5809: .   state - the state to check if it is valid
    5810: -   reject - (output parameter) PETSC_FALSE if the state is acceptable, PETSC_TRUE if not acceptable

    5812:     Level: intermediate

    5814:     Notes:
    5815:       If an implicit ODE solver is being used then, in addition to providing this routine, the
    5816:       user's code should call SNESSetFunctionDomainError() when domain errors occur during
    5817:       function evaluations where the functions are provided by TSSetIFunction() or TSSetRHSFunction().
    5818:       Use TSGetSNES() to obtain the SNES object

    5820:     Developer Notes:
    5821:       The naming of this function is inconsistent with the SNESSetFunctionDomainError()
    5822:       since one takes a function pointer and the other does not.

    5824: .seealso: TSAdaptCheckStage(), TSFunctionDomainError(), SNESSetFunctionDomainError(), TSGetSNES()
    5825: @*/

    5827: PetscErrorCode TSSetFunctionDomainError(TS ts, PetscErrorCode (*func)(TS,PetscReal,Vec,PetscBool*))
    5828: {
    5830:   ts->functiondomainerror = func;
    5831:   return 0;
    5832: }

    5834: /*@
    5835:     TSFunctionDomainError - Checks if the current state is valid

    5837:     Input Parameters:
    5838: +    ts - the TS context
    5839: .    stagetime - time of the simulation
    5840: -    Y - state vector to check.

    5842:     Output Parameter:
    5843: .    accept - Set to PETSC_FALSE if the current state vector is valid.

    5845:     Note:
    5846:     This function is called by the TS integration routines and calls the user provided function (set with TSSetFunctionDomainError())
    5847:     to check if the current state is valid.

    5849:     Level: developer

    5851: .seealso: TSSetFunctionDomainError()
    5852: @*/
    5853: PetscErrorCode TSFunctionDomainError(TS ts,PetscReal stagetime,Vec Y,PetscBool* accept)
    5854: {
    5856:   *accept = PETSC_TRUE;
    5857:   if (ts->functiondomainerror) {
    5858:     PetscStackCallStandard((*ts->functiondomainerror),ts,stagetime,Y,accept);
    5859:   }
    5860:   return 0;
    5861: }

    5863: /*@C
    5864:   TSClone - This function clones a time step object.

    5866:   Collective

    5868:   Input Parameter:
    5869: . tsin    - The input TS

    5871:   Output Parameter:
    5872: . tsout   - The output TS (cloned)

    5874:   Notes:
    5875:   This function is used to create a clone of a TS object. It is used in ARKIMEX for initializing the slope for first stage explicit methods. It will likely be replaced in the future with a mechanism of switching methods on the fly.

    5877:   When using TSDestroy() on a clone the user has to first reset the correct TS reference in the embedded SNES object: e.g.: by running SNES snes_dup=NULL; TSGetSNES(ts,&snes_dup); TSSetSNES(ts,snes_dup);

    5879:   Level: developer

    5881: .seealso: TSCreate(), TSSetType(), TSSetUp(), TSDestroy(), TSSetProblemType()
    5882: @*/
    5883: PetscErrorCode  TSClone(TS tsin, TS *tsout)
    5884: {
    5885:   TS             t;
    5886:   SNES           snes_start;
    5887:   DM             dm;
    5888:   TSType         type;

    5891:   *tsout = NULL;

    5893:   PetscHeaderCreate(t, TS_CLASSID, "TS", "Time stepping", "TS", PetscObjectComm((PetscObject)tsin), TSDestroy, TSView);

    5895:   /* General TS description */
    5896:   t->numbermonitors    = 0;
    5897:   t->monitorFrequency  = 1;
    5898:   t->setupcalled       = 0;
    5899:   t->ksp_its           = 0;
    5900:   t->snes_its          = 0;
    5901:   t->nwork             = 0;
    5902:   t->rhsjacobian.time  = PETSC_MIN_REAL;
    5903:   t->rhsjacobian.scale = 1.;
    5904:   t->ijacobian.shift   = 1.;

    5906:   TSGetSNES(tsin,&snes_start);
    5907:   TSSetSNES(t,snes_start);

    5909:   TSGetDM(tsin,&dm);
    5910:   TSSetDM(t,dm);

    5912:   t->adapt = tsin->adapt;
    5913:   PetscObjectReference((PetscObject)t->adapt);

    5915:   t->trajectory = tsin->trajectory;
    5916:   PetscObjectReference((PetscObject)t->trajectory);

    5918:   t->event = tsin->event;
    5919:   if (t->event) t->event->refct++;

    5921:   t->problem_type      = tsin->problem_type;
    5922:   t->ptime             = tsin->ptime;
    5923:   t->ptime_prev        = tsin->ptime_prev;
    5924:   t->time_step         = tsin->time_step;
    5925:   t->max_time          = tsin->max_time;
    5926:   t->steps             = tsin->steps;
    5927:   t->max_steps         = tsin->max_steps;
    5928:   t->equation_type     = tsin->equation_type;
    5929:   t->atol              = tsin->atol;
    5930:   t->rtol              = tsin->rtol;
    5931:   t->max_snes_failures = tsin->max_snes_failures;
    5932:   t->max_reject        = tsin->max_reject;
    5933:   t->errorifstepfailed = tsin->errorifstepfailed;

    5935:   TSGetType(tsin,&type);
    5936:   TSSetType(t,type);

    5938:   t->vec_sol           = NULL;

    5940:   t->cfltime          = tsin->cfltime;
    5941:   t->cfltime_local    = tsin->cfltime_local;
    5942:   t->exact_final_time = tsin->exact_final_time;

    5944:   PetscMemcpy(t->ops,tsin->ops,sizeof(struct _TSOps));

    5946:   if (((PetscObject)tsin)->fortran_func_pointers) {
    5947:     PetscInt i;
    5948:     PetscMalloc((10)*sizeof(void(*)(void)),&((PetscObject)t)->fortran_func_pointers);
    5949:     for (i=0; i<10; i++) {
    5950:       ((PetscObject)t)->fortran_func_pointers[i] = ((PetscObject)tsin)->fortran_func_pointers[i];
    5951:     }
    5952:   }
    5953:   *tsout = t;
    5954:   return 0;
    5955: }

    5957: static PetscErrorCode RHSWrapperFunction_TSRHSJacobianTest(void* ctx,Vec x,Vec y)
    5958: {
    5959:   TS             ts = (TS) ctx;

    5961:   TSComputeRHSFunction(ts,0,x,y);
    5962:   return 0;
    5963: }

    5965: /*@
    5966:     TSRHSJacobianTest - Compares the multiply routine provided to the MATSHELL with differencing on the TS given RHS function.

    5968:    Logically Collective on TS

    5970:     Input Parameters:
    5971:     TS - the time stepping routine

    5973:    Output Parameter:
    5974: .   flg - PETSC_TRUE if the multiply is likely correct

    5976:    Options Database:
    5977:  .   -ts_rhs_jacobian_test_mult -mat_shell_test_mult_view - run the test at each timestep of the integrator

    5979:    Level: advanced

    5981:    Notes:
    5982:     This only works for problems defined only the RHS function and Jacobian NOT IFunction and IJacobian

    5984: .seealso: MatCreateShell(), MatShellGetContext(), MatShellGetOperation(), MatShellTestMultTranspose(), TSRHSJacobianTestTranspose()
    5985: @*/
    5986: PetscErrorCode  TSRHSJacobianTest(TS ts,PetscBool *flg)
    5987: {
    5988:   Mat            J,B;
    5989:   TSRHSJacobian  func;
    5990:   void*          ctx;

    5992:   TSGetRHSJacobian(ts,&J,&B,&func,&ctx);
    5993:   (*func)(ts,0.0,ts->vec_sol,J,B,ctx);
    5994:   MatShellTestMult(J,RHSWrapperFunction_TSRHSJacobianTest,ts->vec_sol,ts,flg);
    5995:   return 0;
    5996: }

    5998: /*@C
    5999:     TSRHSJacobianTestTranspose - Compares the multiply transpose routine provided to the MATSHELL with differencing on the TS given RHS function.

    6001:    Logically Collective on TS

    6003:     Input Parameters:
    6004:     TS - the time stepping routine

    6006:    Output Parameter:
    6007: .   flg - PETSC_TRUE if the multiply is likely correct

    6009:    Options Database:
    6010: .   -ts_rhs_jacobian_test_mult_transpose -mat_shell_test_mult_transpose_view - run the test at each timestep of the integrator

    6012:    Notes:
    6013:     This only works for problems defined only the RHS function and Jacobian NOT IFunction and IJacobian

    6015:    Level: advanced

    6017: .seealso: MatCreateShell(), MatShellGetContext(), MatShellGetOperation(), MatShellTestMultTranspose(), TSRHSJacobianTest()
    6018: @*/
    6019: PetscErrorCode  TSRHSJacobianTestTranspose(TS ts,PetscBool *flg)
    6020: {
    6021:   Mat            J,B;
    6022:   void           *ctx;
    6023:   TSRHSJacobian  func;

    6025:   TSGetRHSJacobian(ts,&J,&B,&func,&ctx);
    6026:   (*func)(ts,0.0,ts->vec_sol,J,B,ctx);
    6027:   MatShellTestMultTranspose(J,RHSWrapperFunction_TSRHSJacobianTest,ts->vec_sol,ts,flg);
    6028:   return 0;
    6029: }

    6031: /*@
    6032:   TSSetUseSplitRHSFunction - Use the split RHSFunction when a multirate method is used.

    6034:   Logically collective

    6036:   Input Parameters:
    6037: +  ts - timestepping context
    6038: -  use_splitrhsfunction - PETSC_TRUE indicates that the split RHSFunction will be used

    6040:   Options Database:
    6041: .   -ts_use_splitrhsfunction - <true,false>

    6043:   Notes:
    6044:     This is only useful for multirate methods

    6046:   Level: intermediate

    6048: .seealso: TSGetUseSplitRHSFunction()
    6049: @*/
    6050: PetscErrorCode TSSetUseSplitRHSFunction(TS ts, PetscBool use_splitrhsfunction)
    6051: {
    6053:   ts->use_splitrhsfunction = use_splitrhsfunction;
    6054:   return 0;
    6055: }

    6057: /*@
    6058:   TSGetUseSplitRHSFunction - Gets whether to use the split RHSFunction when a multirate method is used.

    6060:   Not collective

    6062:   Input Parameter:
    6063: .  ts - timestepping context

    6065:   Output Parameter:
    6066: .  use_splitrhsfunction - PETSC_TRUE indicates that the split RHSFunction will be used

    6068:   Level: intermediate

    6070: .seealso: TSSetUseSplitRHSFunction()
    6071: @*/
    6072: PetscErrorCode TSGetUseSplitRHSFunction(TS ts, PetscBool *use_splitrhsfunction)
    6073: {
    6075:   *use_splitrhsfunction = ts->use_splitrhsfunction;
    6076:   return 0;
    6077: }

    6079: /*@
    6080:     TSSetMatStructure - sets the relationship between the nonzero structure of the RHS Jacobian matrix to the IJacobian matrix.

    6082:    Logically  Collective on ts

    6084:    Input Parameters:
    6085: +  ts - the time-stepper
    6086: -  str - the structure (the default is UNKNOWN_NONZERO_PATTERN)

    6088:    Level: intermediate

    6090:    Notes:
    6091:      When the relationship between the nonzero structures is known and supplied the solution process can be much faster

    6093: .seealso: MatAXPY(), MatStructure
    6094:  @*/
    6095: PetscErrorCode TSSetMatStructure(TS ts,MatStructure str)
    6096: {
    6098:   ts->axpy_pattern = str;
    6099:   return 0;
    6100: }