ts/tutorials/ex40.c

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

/*
  The dynamics of the bouncing ball is described by the ODE
                  u1_t = u2
                  u2_t = -9.8

  There is one event set in this example, which checks for the ball hitting the
  ground (u1 = 0). Every time the ball hits the ground, its velocity u2 is attenuated by
  a factor of 0.9. On reaching the limit on the number of ball bounces,
  the TS run is requested to terminate from the PostEvent() callback.
*/

#include <petscts.h>

typedef struct {
  PetscInt maxbounces;
  PetscInt nbounces;
} AppCtx;

PetscErrorCode EventFunction(TS ts, PetscReal t, Vec U, PetscReal *fvalue, void *ctx)
{
  const PetscScalar *u;

  PetscFunctionBeginUser;
  /* Event for ball height */
  PetscCall(VecGetArrayRead(U, &u));
  fvalue[0] = PetscRealPart(u[0]);
  PetscCall(VecRestoreArrayRead(U, &u));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBeginUser;
  PetscCall(PetscPrintf(PETSC_COMM_SELF, "Ball hit the ground at t = %5.2f seconds\n", (double)t));
  /* Set new initial conditions with .9 attenuation */
  PetscCall(VecGetArray(U, &u));
  u[0] = 0.0;
  u[1] = -0.9 * u[1];
  PetscCall(VecRestoreArray(U, &u));
  app->nbounces++;
  if (app->nbounces >= app->maxbounces) {
    PetscCall(PetscPrintf(PETSC_COMM_SELF, "Ball bounced %" PetscInt_FMT " times\n", app->nbounces));
    PetscCall(TSSetConvergedReason(ts, TS_CONVERGED_USER)); // request TS to terminate; since the program is serial, no need to sync this call
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBeginUser;
  /*  The following lines allow us to access the entries of the vectors directly */
  PetscCall(VecGetArrayRead(U, &u));
  PetscCall(VecGetArray(F, &f));

  f[0] = u[1];
  f[1] = -9.8;

  PetscCall(VecRestoreArrayRead(U, &u));
  PetscCall(VecRestoreArray(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(U, &u));

  J[0][0] = 0.0;
  J[0][1] = 1.0;
  J[1][0] = 0.0;
  J[1][1] = 0.0;
  PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));

  PetscCall(VecRestoreArrayRead(U, &u));

  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  if (A != B) {
    PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

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

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

  PetscCall(VecRestoreArrayRead(U, &u));
  PetscCall(VecRestoreArrayRead(Udot, &udot));
  PetscCall(VecRestoreArray(F, &f));
  PetscFunctionReturn(PETSC_SUCCESS);
}

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

  PetscFunctionBeginUser;
  PetscCall(VecGetArrayRead(U, &u));
  PetscCall(VecGetArrayRead(Udot, &udot));

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

  PetscCall(VecRestoreArrayRead(U, &u));
  PetscCall(VecRestoreArrayRead(Udot, &udot));

  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  if (A != B) {
    PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

int main(int argc, char **argv)
{
  TS           ts; /* ODE integrator */
  Vec          U;  /* solution will be stored here */
  PetscMPIInt  size;
  PetscInt     n = 2;
  PetscScalar *u;
  AppCtx       app;
  PetscInt     direction[1];
  PetscBool    terminate[1];
  PetscBool    rhs_form = PETSC_FALSE, hist = PETSC_TRUE;
  TSAdapt      adapt;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
  PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");

  app.nbounces   = 0;
  app.maxbounces = 10;
  PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex40 options", "");
  PetscCall(PetscOptionsInt("-maxbounces", "", "", app.maxbounces, &app.maxbounces, NULL));
  PetscCall(PetscOptionsBool("-test_adapthistory", "", "", hist, &hist, NULL));
  PetscOptionsEnd();

  Mat A; /* Jacobian matrix */
  PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
  PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
  PetscCall(MatSetType(A, MATDENSE));
  PetscCall(MatSetFromOptions(A));
  PetscCall(MatSetUp(A));
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
  PetscCall(TSSetType(ts, TSROSW));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set ODE routines
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
  /* Users are advised against the following branching and code duplication.
     For problems without a mass matrix like the one at hand, the RHSFunction
     (and companion RHSJacobian) interface is enough to support both explicit
     and implicit timesteppers. This tutorial example also deals with the
     IFunction/IJacobian interface for demonstration and testing purposes. */
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-rhs-form", &rhs_form, NULL));
  if (rhs_form) {
    PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, NULL));
    PetscCall(TSSetRHSJacobian(ts, A, A, RHSJacobian, NULL));
  } else {
    PetscCall(TSSetIFunction(ts, NULL, IFunction, NULL));
    PetscCall(TSSetIJacobian(ts, A, A, IJacobian, NULL));
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(VecCreate(PETSC_COMM_WORLD, &U));
  PetscCall(VecSetSizes(U, n, PETSC_DETERMINE));
  PetscCall(VecSetUp(U));
  PetscCall(VecGetArray(U, &u));
  u[0] = 0.0;
  u[1] = 20.0;
  PetscCall(VecRestoreArray(U, &u));
  PetscCall(TSSetSolution(ts, U));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set solver options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  if (hist) PetscCall(TSSetSaveTrajectory(ts));
  PetscCall(TSSetMaxTime(ts, 30.0));
  PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
  PetscCall(TSSetTimeStep(ts, 0.1));
  /* The adaptive time step controller could take very large timesteps
     jumping over the next event zero-crossing point. A maximum step size
     limit is enforced here to avoid this issue. */
  PetscCall(TSGetAdapt(ts, &adapt));
  PetscCall(TSAdaptSetStepLimits(adapt, 0.0, 0.5));

  /* Set direction and terminate flag for the event */
  direction[0] = -1;
  terminate[0] = PETSC_FALSE;
  PetscCall(TSSetEventHandler(ts, 1, direction, terminate, EventFunction, PostEventFunction, (void *)&app));

  PetscCall(TSSetFromOptions(ts));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Run timestepping solver
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSolve(ts, U));

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

    app.nbounces = 0;
    PetscCall(TSGetTime(ts, &tf));
    PetscCall(TSSetMaxTime(ts, tf));
    PetscCall(TSSetStepNumber(ts, 0));
    PetscCall(TSRestartStep(ts));
    PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
    PetscCall(TSSetFromOptions(ts));
    PetscCall(TSGetAdapt(ts, &adapt));
    PetscCall(TSAdaptSetType(adapt, TSADAPTHISTORY));
    PetscCall(TSGetTrajectory(ts, &tj));
    PetscCall(TSAdaptHistorySetTrajectory(adapt, tj, PETSC_FALSE));
    PetscCall(TSAdaptHistoryGetStep(adapt, 0, &t0, &dt));
    /* this example fails with single (or smaller) precision */
#if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16)
    /*
       In the first TSSolve() the final time 'tf' is the event location found after a few event handler iterations.
       If 'tf' is set as the max time for the second run, the TS solver may approach this point by
       slightly different steps, resulting in a slightly different solution and fvalue[] at 'tf',
       so that the event may not be triggered at 'tf' anymore. Fix: apply safety factor 1.05
    */
    PetscCall(TSSetMaxTime(ts, tf * 1.05));
    PetscCall(TSAdaptSetType(adapt, TSADAPTBASIC));
    PetscCall(TSAdaptSetStepLimits(adapt, 0.0, 0.5));
    PetscCall(TSSetFromOptions(ts));
#endif
    PetscCall(TSSetTime(ts, t0));
    PetscCall(TSSetTimeStep(ts, dt));
    PetscCall(TSResetTrajectory(ts));
    PetscCall(VecGetArray(U, &u));
    u[0] = 0.0;
    u[1] = 20.0;
    PetscCall(VecRestoreArray(U, &u));
    PetscCall(TSSolve(ts, U));
  }
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.  All PETSc objects should be destroyed when they are no longer needed.
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(MatDestroy(&A));
  PetscCall(VecDestroy(&U));
  PetscCall(TSDestroy(&ts));

  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

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

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

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

    test:
      suffix: cr
      args: -rhs-form -ts_type theta -ts_adapt_type basic -ts_atol 1e-1 -snes_stol 1e-4 -ts_trajectory_dirname ex40_cr_dir
      output_file: output/ex40.out

    test:
      suffix: crmf
      args: -rhs-form -snes_mf_operator -ts_type theta -ts_adapt_type basic -ts_atol 1e-1 -snes_stol 1e-4 -ts_trajectory_dirname ex40_crmf_dir
      output_file: output/ex40.out

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

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

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

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

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

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

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

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

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

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

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

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