Date: 2022-03-04T17:39:38+00:00

Actual source code: ex40.c

      1: static char help[] = "Serial bouncing ball example to test TS event feature.\n";

      3: /*
      4:   The dynamics of the bouncing ball is described by the ODE
      5:                   u1_t = u2
      6:                   u2_t = -9.8

      8:   There are two events set in this example. The first one checks for the ball hitting the
      9:   ground (u1 = 0). Every time the ball hits the ground, its velocity u2 is attenuated by
     10:   a factor of 0.9. The second event sets a limit on the number of ball bounces.
     11: */

     13: #include <petscts.h>

     15: typedef struct {
     16:   PetscInt maxbounces;
     17:   PetscInt nbounces;
     18: } AppCtx;

     20: PetscErrorCode EventFunction(TS ts,PetscReal t,Vec U,PetscScalar *fvalue,void *ctx)
     21: {
     22:   AppCtx            *app=(AppCtx*)ctx;
     23:   PetscErrorCode    ierr;
     24:   const PetscScalar *u;

     27:   /* Event for ball height */
     28:   VecGetArrayRead(U,&u);
     29:   fvalue[0] = u[0];
     30:   /* Event for number of bounces */
     31:   fvalue[1] = app->maxbounces - app->nbounces;
     32:   VecRestoreArrayRead(U,&u);
     33:   return(0);
     34: }

     36: PetscErrorCode PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec U,PetscBool forwardsolve,void* ctx)
     37: {
     38:   AppCtx         *app=(AppCtx*)ctx;
     40:   PetscScalar    *u;

     43:   if (event_list[0] == 0) {
     44:     PetscPrintf(PETSC_COMM_SELF,"Ball hit the ground at t = %5.2f seconds\n",(double)t);
     45:     /* Set new initial conditions with .9 attenuation */
     46:     VecGetArray(U,&u);
     47:     u[0] =  0.0;
     48:     u[1] = -0.9*u[1];
     49:     VecRestoreArray(U,&u);
     50:   } else if (event_list[0] == 1) {
     51:     PetscPrintf(PETSC_COMM_SELF,"Ball bounced %D times\n",app->nbounces);
     52:   }
     53:   app->nbounces++;
     54:   return(0);
     55: }

     57: /*
     58:      Defines the ODE passed to the ODE solver in explicit form: U_t = F(U)
     59: */
     60: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,void *ctx)
     61: {
     62:   PetscErrorCode    ierr;
     63:   PetscScalar       *f;
     64:   const PetscScalar *u;

     67:   /*  The next three lines allow us to access the entries of the vectors directly */
     68:   VecGetArrayRead(U,&u);
     69:   VecGetArray(F,&f);

     71:   f[0] = u[1];
     72:   f[1] = - 9.8;

     74:   VecRestoreArrayRead(U,&u);
     75:   VecRestoreArray(F,&f);
     76:   return(0);
     77: }

     79: /*
     80:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetRHSJacobian() for the meaning of the Jacobian.
     81: */
     82: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,void *ctx)
     83: {
     84:   PetscErrorCode    ierr;
     85:   PetscInt          rowcol[] = {0,1};
     86:   PetscScalar       J[2][2];
     87:   const PetscScalar *u;

     90:   VecGetArrayRead(U,&u);

     92:   J[0][0] = 0.0;     J[0][1] = 1.0;
     93:   J[1][0] = 0.0;     J[1][1] = 0.0;
     94:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);

     96:   VecRestoreArrayRead(U,&u);

     98:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     99:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    100:   if (A != B) {
    101:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    102:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    103:   }
    104:   return(0);
    105: }

    107: /*
    108:      Defines the ODE passed to the ODE solver in implicit form: F(U_t,U) = 0
    109: */
    110: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
    111: {
    112:   PetscErrorCode    ierr;
    113:   PetscScalar       *f;
    114:   const PetscScalar *u,*udot;

    117:   /*  The next three lines allow us to access the entries of the vectors directly */
    118:   VecGetArrayRead(U,&u);
    119:   VecGetArrayRead(Udot,&udot);
    120:   VecGetArray(F,&f);

    122:   f[0] = udot[0] - u[1];
    123:   f[1] = udot[1] + 9.8;

    125:   VecRestoreArrayRead(U,&u);
    126:   VecRestoreArrayRead(Udot,&udot);
    127:   VecRestoreArray(F,&f);
    128:   return(0);
    129: }

    131: /*
    132:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
    133: */
    134: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,void *ctx)
    135: {
    136:   PetscErrorCode    ierr;
    137:   PetscInt          rowcol[] = {0,1};
    138:   PetscScalar       J[2][2];
    139:   const PetscScalar *u,*udot;

    142:   VecGetArrayRead(U,&u);
    143:   VecGetArrayRead(Udot,&udot);

    145:   J[0][0] = a;      J[0][1] = -1.0;
    146:   J[1][0] = 0.0;    J[1][1] = a;
    147:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);

    149:   VecRestoreArrayRead(U,&u);
    150:   VecRestoreArrayRead(Udot,&udot);

    152:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    153:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    154:   if (A != B) {
    155:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    156:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    157:   }
    158:   return(0);
    159: }

    161: int main(int argc,char **argv)
    162: {
    163:   TS             ts;            /* ODE integrator */
    164:   Vec            U;             /* solution will be stored here */
    166:   PetscMPIInt    size;
    167:   PetscInt       n = 2;
    168:   PetscScalar    *u;
    169:   AppCtx         app;
    170:   PetscInt       direction[2];
    171:   PetscBool      terminate[2];
    172:   PetscBool      rhs_form=PETSC_FALSE,hist=PETSC_TRUE;
    173:   TSAdapt        adapt;

    175:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    176:      Initialize program
    177:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    178:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
    179:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
    180:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

    182:   app.nbounces = 0;
    183:   app.maxbounces = 10;
    184:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex40 options","");
    185:   PetscOptionsInt("-maxbounces","","",app.maxbounces,&app.maxbounces,NULL);
    186:   PetscOptionsBool("-test_adapthistory","","",hist,&hist,NULL);
    187:   PetscOptionsEnd();

    189:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    190:      Create timestepping solver context
    191:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    192:   TSCreate(PETSC_COMM_WORLD,&ts);
    193:   TSSetType(ts,TSROSW);

    195:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    196:      Set ODE routines
    197:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    198:   TSSetProblemType(ts,TS_NONLINEAR);
    199:   /* Users are advised against the following branching and code duplication.
    200:      For problems without a mass matrix like the one at hand, the RHSFunction
    201:      (and companion RHSJacobian) interface is enough to support both explicit
    202:      and implicit timesteppers. This tutorial example also deals with the
    203:      IFunction/IJacobian interface for demonstration and testing purposes. */
    204:   PetscOptionsGetBool(NULL,NULL,"-rhs-form",&rhs_form,NULL);
    205:   if (rhs_form) {
    206:     TSSetRHSFunction(ts,NULL,RHSFunction,NULL);
    207:     TSSetRHSJacobian(ts,NULL,NULL,RHSJacobian,NULL);
    208:   } else {
    209:     Mat A; /* Jacobian matrix */
    210:     MatCreate(PETSC_COMM_WORLD,&A);
    211:     MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
    212:     MatSetType(A,MATDENSE);
    213:     MatSetFromOptions(A);
    214:     MatSetUp(A);
    215:     TSSetIFunction(ts,NULL,IFunction,NULL);
    216:     TSSetIJacobian(ts,A,A,IJacobian,NULL);
    217:     MatDestroy(&A);
    218:   }

    220:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    221:      Set initial conditions
    222:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    223:   VecCreate(PETSC_COMM_WORLD,&U);
    224:   VecSetSizes(U,n,PETSC_DETERMINE);
    225:   VecSetUp(U);
    226:   VecGetArray(U,&u);
    227:   u[0] = 0.0;
    228:   u[1] = 20.0;
    229:   VecRestoreArray(U,&u);
    230:   TSSetSolution(ts,U);

    232:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    233:      Set solver options
    234:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    235:   if (hist) {TSSetSaveTrajectory(ts);}
    236:   TSSetMaxTime(ts,30.0);
    237:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
    238:   TSSetTimeStep(ts,0.1);
    239:   /* The adaptive time step controller could take very large timesteps resulting in
    240:      the same event occurring multiple times in the same interval. A maximum step size
    241:      limit is enforced here to avoid this issue. */
    242:   TSGetAdapt(ts,&adapt);
    243:   TSAdaptSetStepLimits(adapt,0.0,0.5);

    245:   /* Set directions and terminate flags for the two events */
    246:   direction[0] = -1;            direction[1] = -1;
    247:   terminate[0] = PETSC_FALSE;   terminate[1] = PETSC_TRUE;
    248:   TSSetEventHandler(ts,2,direction,terminate,EventFunction,PostEventFunction,(void*)&app);

    250:   TSSetFromOptions(ts);

    252:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    253:      Run timestepping solver
    254:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    255:   TSSolve(ts,U);

    257:   if (hist) { /* replay following history */
    258:     TSTrajectory tj;
    259:     PetscReal    tf,t0,dt;

    261:     app.nbounces = 0;
    262:     TSGetTime(ts,&tf);
    263:     TSSetMaxTime(ts,tf);
    264:     TSSetStepNumber(ts,0);
    265:     TSRestartStep(ts);
    266:     TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
    267:     TSSetFromOptions(ts);
    268:     TSGetAdapt(ts,&adapt);
    269:     TSAdaptSetType(adapt,TSADAPTHISTORY);
    270:     TSGetTrajectory(ts,&tj);
    271:     TSAdaptHistorySetTrajectory(adapt,tj,PETSC_FALSE);
    272:     TSAdaptHistoryGetStep(adapt,0,&t0,&dt);
    273:     /* this example fails with single (or smaller) precision */
    274: #if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL__FP16)
    275:     TSAdaptSetType(adapt,TSADAPTBASIC);
    276:     TSAdaptSetStepLimits(adapt,0.0,0.5);
    277:     TSSetFromOptions(ts);
    278: #endif
    279:     TSSetTime(ts,t0);
    280:     TSSetTimeStep(ts,dt);
    281:     TSResetTrajectory(ts);
    282:     VecGetArray(U,&u);
    283:     u[0] = 0.0;
    284:     u[1] = 20.0;
    285:     VecRestoreArray(U,&u);
    286:     TSSolve(ts,U);
    287:   }
    288:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    289:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    290:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    291:   VecDestroy(&U);
    292:   TSDestroy(&ts);

    294:   PetscFinalize();
    295:   return ierr;
    296: }

    298: /*TEST

    300:     test:
    301:       suffix: a
    302:       args: -snes_stol 1e-4 -ts_trajectory_dirname ex40_a_dir
    303:       output_file: output/ex40.out

    305:     test:
    306:       suffix: b
    307:       args: -ts_type arkimex -snes_stol 1e-4 -ts_trajectory_dirname ex40_b_dir
    308:       output_file: output/ex40.out

    310:     test:
    311:       suffix: c
    312:       args: -ts_type theta -ts_adapt_type basic -ts_atol 1e-1 -snes_stol 1e-4 -ts_trajectory_dirname ex40_c_dir
    313:       output_file: output/ex40.out

    315:     test:
    316:       suffix: d
    317:       args: -ts_type alpha -ts_adapt_type basic -ts_atol 1e-1 -snes_stol 1e-4 -ts_trajectory_dirname ex40_d_dir
    318:       output_file: output/ex40.out

    320:     test:
    321:       suffix: e
    322:       args: -ts_type bdf -ts_adapt_dt_max 0.025 -ts_max_steps 1500 -ts_trajectory_dirname ex40_e_dir
    323:       output_file: output/ex40.out

    325:     test:
    326:       suffix: f
    327:       args: -rhs-form -ts_type rk -ts_rk_type 3bs -ts_trajectory_dirname ex40_f_dir
    328:       output_file: output/ex40.out

    330:     test:
    331:       suffix: g
    332:       args: -rhs-form -ts_type rk -ts_rk_type 5bs -ts_trajectory_dirname ex40_g_dir
    333:       output_file: output/ex40.out

    335:     test:
    336:       suffix: h
    337:       args: -rhs-form -ts_type rk -ts_rk_type 6vr -ts_trajectory_dirname ex40_h_dir
    338:       output_file: output/ex40.out

    340:     test:
    341:       suffix: i
    342:       args: -rhs-form -ts_type rk -ts_rk_type 7vr -ts_trajectory_dirname ex40_i_dir
    343:       output_file: output/ex40.out

    345:     test:
    346:       suffix: j
    347:       args: -rhs-form -ts_type rk -ts_rk_type 8vr -ts_trajectory_dirname ex40_j_dir
    348:       output_file: output/ex40.out

    350:     test:
    351:       suffix: k
    352:       args: -ts_type theta -ts_adapt_type dsp -ts_trajectory_dirname ex40_k_dir
    353:       output_file: output/ex40.out

    355:     test:
    356:       suffix: l
    357:       args: -rhs-form -ts_type rk -ts_rk_type 2a -ts_trajectory_dirname ex40_l_dir
    358:       args: -ts_adapt_type dsp -ts_adapt_always_accept {{false true}} -ts_adapt_dt_min 0.01
    359:       output_file: output/ex40.out

    361:     test:
    362:       suffix: m
    363:       args: -ts_type alpha -ts_adapt_type basic -ts_atol 1e-1 -snes_stol 1e-4 -test_adapthistory false
    364:       args: -ts_max_time 10 -ts_exact_final_time {{STEPOVER MATCHSTEP INTERPOLATE}}

    366:     test:
    367:       requires: !single
    368:       suffix: n
    369:       args: -test_adapthistory false
    370:       args: -ts_type alpha -ts_alpha_radius 1.0 -ts_view
    371:       args: -ts_dt 0.25 -ts_adapt_type basic -ts_adapt_wnormtype INFINITY -ts_adapt_monitor
    372:       args: -ts_max_steps 1 -ts_max_reject {{0 1 2}separate_output} -ts_error_if_step_fails false

    374: TEST*/