xref: /petsc/src/ts/tutorials/ex19.c (revision b122ec5aa1bd4469eb4e0673542fb7de3f411254)

static char help[] = "Solves the van der Pol DAE.\n\
Input parameters include:\n";

/*
   Concepts: TS^time-dependent nonlinear problems
   Concepts: TS^van der Pol DAE
   Processors: 1
*/
/* ------------------------------------------------------------------------

   This program solves the van der Pol DAE
       y' = -z = f(y,z)        (1)
       0  = y-(z^3/3 - z) = g(y,z)
   on the domain 0 <= x <= 1, with the boundary conditions
       y(0) = -2, y'(0) = -2.355301397608119909925287735864250951918
   This is a nonlinear equation.

   Notes:
   This code demonstrates the TS solver interface with the Van der Pol DAE,
   namely it is the case when there is no RHS (meaning the RHS == 0), and the
   equations are converted to two variants of linear problems, u_t = f(u,t),
   namely turning (1) into a vector equation in terms of u,

   [     y' + z      ] = [ 0 ]
   [ (z^3/3 - z) - y ]   [ 0 ]

   which then we can write as a vector equation

   [      u_1' + u_2       ] = [ 0 ]  (2)
   [ (u_2^3/3 - u_2) - u_1 ]   [ 0 ]

   which is now in the desired form of u_t = f(u,t). As this is a DAE, and
   there is no u_2', there is no need for a split,

   so

   [ F(u',u,t) ] = [ u_1' ] + [         u_2           ]
                   [  0   ]   [ (u_2^3/3 - u_2) - u_1 ]

   Using the definition of the Jacobian of F (from the PETSc user manual),
   in the equation F(u',u,t) = G(u,t),

              dF   dF
   J(F) = a * -- - --
              du'  du

   where d is the partial derivative. In this example,

   dF   [ 1 ; 0 ]
   -- = [       ]
   du'  [ 0 ; 0 ]

   dF   [  0 ;      1     ]
   -- = [                 ]
   du   [ -1 ; 1 - u_2^2  ]

   Hence,

          [ a ;    -1     ]
   J(F) = [               ]
          [ 1 ; u_2^2 - 1 ]

  ------------------------------------------------------------------------- */

#include <petscts.h>

typedef struct _n_User *User;
struct _n_User {
  PetscReal next_output;
};

/*
   User-defined routines
*/

static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
{
  PetscScalar       *f;
  const PetscScalar *x,*xdot;

  PetscFunctionBeginUser;
  CHKERRQ(VecGetArrayRead(X,&x));
  CHKERRQ(VecGetArrayRead(Xdot,&xdot));
  CHKERRQ(VecGetArray(F,&f));
  f[0] = xdot[0] + x[1];
  f[1] = (x[1]*x[1]*x[1]/3.0 - x[1])-x[0];
  CHKERRQ(VecRestoreArrayRead(X,&x));
  CHKERRQ(VecRestoreArrayRead(Xdot,&xdot));
  CHKERRQ(VecRestoreArray(F,&f));
  PetscFunctionReturn(0);
}

static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
{
  PetscInt          rowcol[] = {0,1};
  PetscScalar       J[2][2];
  const PetscScalar *x;

  PetscFunctionBeginUser;
  CHKERRQ(VecGetArrayRead(X,&x));
  J[0][0] = a;    J[0][1] = -1.;
  J[1][0] = 1.;   J[1][1] = -1. + x[1]*x[1];
  CHKERRQ(MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES));
  CHKERRQ(VecRestoreArrayRead(X,&x));

  CHKERRQ(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
  CHKERRQ(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
  if (A != B) {
    CHKERRQ(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    CHKERRQ(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode RegisterMyARK2(void)
{
  PetscFunctionBeginUser;
  {
    const PetscReal
      A[3][3] = {{0,0,0},
                 {0.41421356237309504880,0,0},
                 {0.75,0.25,0}},
      At[3][3] = {{0,0,0},
                  {0.12132034355964257320,0.29289321881345247560,0},
                  {0.20710678118654752440,0.50000000000000000000,0.29289321881345247560}},
    *bembedt = NULL,*bembed = NULL;
    CHKERRQ(TSARKIMEXRegister("myark2",2,3,&At[0][0],NULL,NULL,&A[0][0],NULL,NULL,bembedt,bembed,0,NULL,NULL));
  }
  PetscFunctionReturn(0);
}

/* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
{
  const PetscScalar *x;
  PetscReal         tfinal, dt;
  User              user = (User)ctx;
  Vec               interpolatedX;

  PetscFunctionBeginUser;
  CHKERRQ(TSGetTimeStep(ts,&dt));
  CHKERRQ(TSGetMaxTime(ts,&tfinal));

  while (user->next_output <= t && user->next_output <= tfinal) {
    CHKERRQ(VecDuplicate(X,&interpolatedX));
    CHKERRQ(TSInterpolate(ts,user->next_output,interpolatedX));
    CHKERRQ(VecGetArrayRead(interpolatedX,&x));
    CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %3D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",(double)user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(x[0]),(double)PetscRealPart(x[1])));
    CHKERRQ(VecRestoreArrayRead(interpolatedX,&x));
    CHKERRQ(VecDestroy(&interpolatedX));
    user->next_output += PetscRealConstant(0.1);
  }
  PetscFunctionReturn(0);
}

int main(int argc,char **argv)
{
  TS             ts;            /* nonlinear solver */
  Vec            x;             /* solution, residual vectors */
  Mat            A;             /* Jacobian matrix */
  PetscInt       steps;
  PetscReal      ftime   = 0.5;
  PetscBool      monitor = PETSC_FALSE;
  PetscScalar    *x_ptr;
  PetscMPIInt    size;
  struct _n_User user;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(PetscInitialize(&argc,&argv,NULL,help));
  CHKERRMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
  PetscCheck(size == 1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");

  CHKERRQ(RegisterMyARK2());

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Set runtime options
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  user.next_output = 0.0;
  CHKERRQ(PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Create necessary matrix and vectors, solve same ODE on every process
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(MatCreate(PETSC_COMM_WORLD,&A));
  CHKERRQ(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2));
  CHKERRQ(MatSetFromOptions(A));
  CHKERRQ(MatSetUp(A));
  CHKERRQ(MatCreateVecs(A,&x,NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(TSCreate(PETSC_COMM_WORLD,&ts));
  CHKERRQ(TSSetType(ts,TSBEULER));
  CHKERRQ(TSSetIFunction(ts,NULL,IFunction,&user));
  CHKERRQ(TSSetIJacobian(ts,A,A,IJacobian,&user));
  CHKERRQ(TSSetMaxTime(ts,ftime));
  CHKERRQ(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER));
  if (monitor) {
    CHKERRQ(TSMonitorSet(ts,Monitor,&user,NULL));
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(VecGetArray(x,&x_ptr));
  x_ptr[0] = -2;   x_ptr[1] = -2.355301397608119909925287735864250951918;
  CHKERRQ(VecRestoreArray(x,&x_ptr));
  CHKERRQ(TSSetTimeStep(ts,.001));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(TSSetFromOptions(ts));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve nonlinear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(TSSolve(ts,x));
  CHKERRQ(TSGetSolveTime(ts,&ftime));
  CHKERRQ(TSGetStepNumber(ts,&steps));
  CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"steps %3D, ftime %g\n",steps,(double)ftime));
  CHKERRQ(VecView(x,PETSC_VIEWER_STDOUT_WORLD));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.  All PETSc objects should be destroyed when they
     are no longer needed.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(MatDestroy(&A));
  CHKERRQ(VecDestroy(&x));
  CHKERRQ(TSDestroy(&ts));

  CHKERRQ(PetscFinalize());
  return 0;
}

/*TEST

   test:
      requires: !single
      suffix: a
      args: -monitor -ts_type bdf -ts_rtol 1e-6 -ts_atol 1e-6 -ts_view -ts_adapt_type dsp
      output_file: output/ex19_pi42.out

   test:
      requires: !single
      suffix: b
      args: -monitor -ts_type bdf -ts_rtol 1e-6 -ts_atol 1e-6 -ts_view -ts_adapt_type dsp -ts_adapt_dsp_filter PI42
      output_file: output/ex19_pi42.out

   test:
      requires: !single
      suffix: c
      args: -monitor -ts_type bdf -ts_rtol 1e-6 -ts_atol 1e-6 -ts_view -ts_adapt_type dsp -ts_adapt_dsp_pid 0.4,0.2
      output_file: output/ex19_pi42.out

   test:
      requires: !single
      suffix: bdf_reject
      args: -ts_type bdf -ts_dt 0.5 -ts_max_steps 1 -ts_max_reject {{0 1 2}separate_output} -ts_error_if_step_fails false -ts_adapt_monitor

TEST*/