Date: 2022-08-02T03:15:04+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:   const PetscScalar *u;

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

     34: PetscErrorCode PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec U,PetscBool forwardsolve,void* ctx)
     35: {
     36:   AppCtx         *app=(AppCtx*)ctx;
     37:   PetscScalar    *u;

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

     53: /*
     54:      Defines the ODE passed to the ODE solver in explicit form: U_t = F(U)
     55: */
     56: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,void *ctx)
     57: {
     58:   PetscScalar       *f;
     59:   const PetscScalar *u;

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

     65:   f[0] = u[1];
     66:   f[1] = - 9.8;

     68:   VecRestoreArrayRead(U,&u);
     69:   VecRestoreArray(F,&f);
     70:   return 0;
     71: }

     73: /*
     74:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetRHSJacobian() for the meaning of the Jacobian.
     75: */
     76: static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,void *ctx)
     77: {
     78:   PetscInt          rowcol[] = {0,1};
     79:   PetscScalar       J[2][2];
     80:   const PetscScalar *u;

     82:   VecGetArrayRead(U,&u);

     84:   J[0][0] = 0.0;     J[0][1] = 1.0;
     85:   J[1][0] = 0.0;     J[1][1] = 0.0;
     86:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);

     88:   VecRestoreArrayRead(U,&u);

     90:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     91:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     92:   if (A != B) {
     93:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     94:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     95:   }
     96:   return 0;
     97: }

     99: /*
    100:      Defines the ODE passed to the ODE solver in implicit form: F(U_t,U) = 0
    101: */
    102: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx)
    103: {
    104:   PetscScalar       *f;
    105:   const PetscScalar *u,*udot;

    107:   /*  The next three lines allow us to access the entries of the vectors directly */
    108:   VecGetArrayRead(U,&u);
    109:   VecGetArrayRead(Udot,&udot);
    110:   VecGetArray(F,&f);

    112:   f[0] = udot[0] - u[1];
    113:   f[1] = udot[1] + 9.8;

    115:   VecRestoreArrayRead(U,&u);
    116:   VecRestoreArrayRead(Udot,&udot);
    117:   VecRestoreArray(F,&f);
    118:   return 0;
    119: }

    121: /*
    122:      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
    123: */
    124: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,void *ctx)
    125: {
    126:   PetscInt          rowcol[] = {0,1};
    127:   PetscScalar       J[2][2];
    128:   const PetscScalar *u,*udot;

    130:   VecGetArrayRead(U,&u);
    131:   VecGetArrayRead(Udot,&udot);

    133:   J[0][0] = a;      J[0][1] = -1.0;
    134:   J[1][0] = 0.0;    J[1][1] = a;
    135:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);

    137:   VecRestoreArrayRead(U,&u);
    138:   VecRestoreArrayRead(Udot,&udot);

    140:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    141:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    142:   if (A != B) {
    143:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    144:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    145:   }
    146:   return 0;
    147: }

    149: int main(int argc,char **argv)
    150: {
    151:   TS             ts;            /* ODE integrator */
    152:   Vec            U;             /* solution will be stored here */
    154:   PetscMPIInt    size;
    155:   PetscInt       n = 2;
    156:   PetscScalar    *u;
    157:   AppCtx         app;
    158:   PetscInt       direction[2];
    159:   PetscBool      terminate[2];
    160:   PetscBool      rhs_form=PETSC_FALSE,hist=PETSC_TRUE;
    161:   TSAdapt        adapt;

    163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    164:      Initialize program
    165:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    166:   PetscInitialize(&argc,&argv,(char*)0,help);
    167:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

    170:   app.nbounces = 0;
    171:   app.maxbounces = 10;
    172:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex40 options","");
    173:   PetscOptionsInt("-maxbounces","","",app.maxbounces,&app.maxbounces,NULL);
    174:   PetscOptionsBool("-test_adapthistory","","",hist,&hist,NULL);
    175:   PetscOptionsEnd();

    177:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    178:      Create timestepping solver context
    179:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    180:   TSCreate(PETSC_COMM_WORLD,&ts);
    181:   TSSetType(ts,TSROSW);

    183:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    184:      Set ODE routines
    185:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    186:   TSSetProblemType(ts,TS_NONLINEAR);
    187:   /* Users are advised against the following branching and code duplication.
    188:      For problems without a mass matrix like the one at hand, the RHSFunction
    189:      (and companion RHSJacobian) interface is enough to support both explicit
    190:      and implicit timesteppers. This tutorial example also deals with the
    191:      IFunction/IJacobian interface for demonstration and testing purposes. */
    192:   PetscOptionsGetBool(NULL,NULL,"-rhs-form",&rhs_form,NULL);
    193:   if (rhs_form) {
    194:     TSSetRHSFunction(ts,NULL,RHSFunction,NULL);
    195:     TSSetRHSJacobian(ts,NULL,NULL,RHSJacobian,NULL);
    196:   } else {
    197:     Mat A; /* Jacobian matrix */
    198:     MatCreate(PETSC_COMM_WORLD,&A);
    199:     MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
    200:     MatSetType(A,MATDENSE);
    201:     MatSetFromOptions(A);
    202:     MatSetUp(A);
    203:     TSSetIFunction(ts,NULL,IFunction,NULL);
    204:     TSSetIJacobian(ts,A,A,IJacobian,NULL);
    205:     MatDestroy(&A);
    206:   }

    208:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    209:      Set initial conditions
    210:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    211:   VecCreate(PETSC_COMM_WORLD,&U);
    212:   VecSetSizes(U,n,PETSC_DETERMINE);
    213:   VecSetUp(U);
    214:   VecGetArray(U,&u);
    215:   u[0] = 0.0;
    216:   u[1] = 20.0;
    217:   VecRestoreArray(U,&u);
    218:   TSSetSolution(ts,U);

    220:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    221:      Set solver options
    222:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    223:   if (hist) TSSetSaveTrajectory(ts);
    224:   TSSetMaxTime(ts,30.0);
    225:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
    226:   TSSetTimeStep(ts,0.1);
    227:   /* The adaptive time step controller could take very large timesteps resulting in
    228:      the same event occurring multiple times in the same interval. A maximum step size
    229:      limit is enforced here to avoid this issue. */
    230:   TSGetAdapt(ts,&adapt);
    231:   TSAdaptSetStepLimits(adapt,0.0,0.5);

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

    238:   TSSetFromOptions(ts);

    240:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    241:      Run timestepping solver
    242:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    243:   TSSolve(ts,U);

    245:   if (hist) { /* replay following history */
    246:     TSTrajectory tj;
    247:     PetscReal    tf,t0,dt;

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

    282:   PetscFinalize();
    283:   return 0;
    284: }

    286: /*TEST

    288:     test:
    289:       suffix: a
    290:       args: -snes_stol 1e-4 -ts_trajectory_dirname ex40_a_dir
    291:       output_file: output/ex40.out

    293:     test:
    294:       suffix: b
    295:       args: -ts_type arkimex -snes_stol 1e-4 -ts_trajectory_dirname ex40_b_dir
    296:       output_file: output/ex40.out

    298:     test:
    299:       suffix: c
    300:       args: -ts_type theta -ts_adapt_type basic -ts_atol 1e-1 -snes_stol 1e-4 -ts_trajectory_dirname ex40_c_dir
    301:       output_file: output/ex40.out

    303:     test:
    304:       suffix: d
    305:       args: -ts_type alpha -ts_adapt_type basic -ts_atol 1e-1 -snes_stol 1e-4 -ts_trajectory_dirname ex40_d_dir
    306:       output_file: output/ex40.out

    308:     test:
    309:       suffix: e
    310:       args: -ts_type bdf -ts_adapt_dt_max 0.025 -ts_max_steps 1500 -ts_trajectory_dirname ex40_e_dir
    311:       output_file: output/ex40.out

    313:     test:
    314:       suffix: f
    315:       args: -rhs-form -ts_type rk -ts_rk_type 3bs -ts_trajectory_dirname ex40_f_dir
    316:       output_file: output/ex40.out

    318:     test:
    319:       suffix: g
    320:       args: -rhs-form -ts_type rk -ts_rk_type 5bs -ts_trajectory_dirname ex40_g_dir
    321:       output_file: output/ex40.out

    323:     test:
    324:       suffix: h
    325:       args: -rhs-form -ts_type rk -ts_rk_type 6vr -ts_trajectory_dirname ex40_h_dir
    326:       output_file: output/ex40.out

    328:     test:
    329:       suffix: i
    330:       args: -rhs-form -ts_type rk -ts_rk_type 7vr -ts_trajectory_dirname ex40_i_dir
    331:       output_file: output/ex40.out

    333:     test:
    334:       suffix: j
    335:       args: -rhs-form -ts_type rk -ts_rk_type 8vr -ts_trajectory_dirname ex40_j_dir
    336:       output_file: output/ex40.out

    338:     test:
    339:       suffix: k
    340:       args: -ts_type theta -ts_adapt_type dsp -ts_trajectory_dirname ex40_k_dir
    341:       output_file: output/ex40.out

    343:     test:
    344:       suffix: l
    345:       args: -rhs-form -ts_type rk -ts_rk_type 2a -ts_trajectory_dirname ex40_l_dir
    346:       args: -ts_adapt_type dsp -ts_adapt_always_accept {{false true}} -ts_adapt_dt_min 0.01
    347:       output_file: output/ex40.out

    349:     test:
    350:       suffix: m
    351:       args: -ts_type alpha -ts_adapt_type basic -ts_atol 1e-1 -snes_stol 1e-4 -test_adapthistory false
    352:       args: -ts_max_time 10 -ts_exact_final_time {{STEPOVER MATCHSTEP INTERPOLATE}}

    354:     test:
    355:       requires: !single
    356:       suffix: n
    357:       args: -test_adapthistory false
    358:       args: -ts_type alpha -ts_alpha_radius 1.0 -ts_view
    359:       args: -ts_dt 0.25 -ts_adapt_type basic -ts_adapt_wnormtype INFINITY -ts_adapt_monitor
    360:       args: -ts_max_steps 1 -ts_max_reject {{0 1 2}separate_output} -ts_error_if_step_fails false

    362:     test:
    363:       requires: !single
    364:       suffix: o
    365:       args: -rhs-form -ts_type rk -ts_rk_type 2b -ts_trajectory_dirname ex40_o_dir
    366:       output_file: output/ex40.out
    367: TEST*/