Date: 2021-03-03T22:27:56+00:00

Actual source code: ex20.c
petsc-3.14.5 2021-03-03
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      2: static char help[] = "Solves the van der Pol equation.\n\
      3: Input parameters include:\n";

      5: /*
      6:    Concepts: TS^time-dependent nonlinear problems
      7:    Concepts: TS^van der Pol equation DAE equivalent
      8:    Processors: 1
      9: */
     10: /* ------------------------------------------------------------------------

     12:    This program solves the van der Pol DAE ODE equivalent
     13:        y' = z                 (1)
     14:        z' = \mu ((1-y^2)z-y)
     15:    on the domain 0 <= x <= 1, with the boundary conditions
     16:        y(0) = 2, y'(0) = - 2/3 +10/(81*\mu) - 292/(2187*\mu^2),
     17:    and
     18:        \mu = 10^6 ( y'(0) ~ -0.6666665432100101).
     19:    This is a nonlinear equation. The well prepared initial condition gives errors that are not dominated by the first few steps of the method when \mu is large.

     21:    Notes:
     22:    This code demonstrates the TS solver interface to an ODE -- RHSFunction for explicit form and IFunction for implicit form.

     24:   ------------------------------------------------------------------------- */

     26: #include <petscts.h>

     28: typedef struct _n_User *User;
     29: struct _n_User {
     30:   PetscReal mu;
     31:   PetscReal next_output;
     32: };

     34: /*
     35: *  User-defined routines
     36: */
     37: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx)
     38: {
     39:   PetscErrorCode    ierr;
     40:   User              user = (User)ctx;
     41:   PetscScalar       *f;
     42:   const PetscScalar *x;

     45:   VecGetArrayRead(X,&x);
     46:   VecGetArray(F,&f);
     47:   f[0] = x[1];
     48:   f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0];
     49:   VecRestoreArrayRead(X,&x);
     50:   VecRestoreArray(F,&f);
     51:   return(0);
     52: }

     55: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
     56: {
     57:   PetscErrorCode    ierr;
     58:   User              user = (User)ctx;
     59:   const PetscScalar *x,*xdot;
     60:   PetscScalar       *f;

     63:   VecGetArrayRead(X,&x);
     64:   VecGetArrayRead(Xdot,&xdot);
     65:   VecGetArray(F,&f);
     66:   f[0] = xdot[0] - x[1];
     67:   f[1] = xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]);
     68:   VecRestoreArrayRead(X,&x);
     69:   VecRestoreArrayRead(Xdot,&xdot);
     70:   VecRestoreArray(F,&f);
     71:   return(0);
     72: }

     74: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
     75: {
     76:   PetscErrorCode    ierr;
     77:   User              user     = (User)ctx;
     78:   PetscInt          rowcol[] = {0,1};
     79:   const PetscScalar *x;
     80:   PetscScalar       J[2][2];

     83:   VecGetArrayRead(X,&x);
     84:   J[0][0] = a;     J[0][1] = -1.0;
     85:   J[1][0] = user->mu*(2.0*x[0]*x[1] + 1.0);   J[1][1] = a - user->mu*(1.0-x[0]*x[0]);
     86:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
     87:   VecRestoreArrayRead(X,&x);

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

     98: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
     99: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
    100: {
    101:   PetscErrorCode    ierr;
    102:   const PetscScalar *x;
    103:   PetscReal         tfinal, dt;
    104:   User              user = (User)ctx;
    105:   Vec               interpolatedX;

    108:   TSGetTimeStep(ts,&dt);
    109:   TSGetMaxTime(ts,&tfinal);

    111:   while (user->next_output <= t && user->next_output <= tfinal) {
    112:     VecDuplicate(X,&interpolatedX);
    113:     TSInterpolate(ts,user->next_output,interpolatedX);
    114:     VecGetArrayRead(interpolatedX,&x);
    115:     PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
    116:                        user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
    117:                        (double)PetscRealPart(x[1]));
    118:     VecRestoreArrayRead(interpolatedX,&x);
    119:     VecDestroy(&interpolatedX);
    120:     user->next_output += 0.1;
    121:   }
    122:   return(0);
    123: }

    125: int main(int argc,char **argv)
    126: {
    127:   TS             ts;            /* nonlinear solver */
    128:   Vec            x;             /* solution, residual vectors */
    129:   Mat            A;             /* Jacobian matrix */
    130:   PetscInt       steps;
    131:   PetscReal      ftime = 0.5;
    132:   PetscBool      monitor = PETSC_FALSE,implicitform = PETSC_TRUE;
    133:   PetscScalar    *x_ptr;
    134:   PetscMPIInt    size;
    135:   struct _n_User user;

    138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    139:      Initialize program
    140:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    141:   PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
    142:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
    143:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");

    145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    146:     Set runtime options
    147:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    148:   user.next_output = 0.0;
    149:   user.mu          = 1.0e3;
    150:   PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
    151:   PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL);
    152:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);
    153:   PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);
    154:   PetscOptionsEnd();

    156:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    157:     Create necessary matrix and vectors, solve same ODE on every process
    158:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    159:   MatCreate(PETSC_COMM_WORLD,&A);
    160:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);
    161:   MatSetFromOptions(A);
    162:   MatSetUp(A);

    164:   MatCreateVecs(A,&x,NULL);

    166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    167:      Create timestepping solver context
    168:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    169:   TSCreate(PETSC_COMM_WORLD,&ts);
    170:   if (implicitform) {
    171:     TSSetIFunction(ts,NULL,IFunction,&user);
    172:     TSSetIJacobian(ts,A,A,IJacobian,&user);
    173:     TSSetType(ts,TSBEULER);
    174:   } else {
    175:     TSSetRHSFunction(ts,NULL,RHSFunction,&user);
    176:     TSSetType(ts,TSRK);
    177:   }
    178:   TSSetMaxTime(ts,ftime);
    179:   TSSetTimeStep(ts,0.001);
    180:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
    181:   if (monitor) {
    182:     TSMonitorSet(ts,Monitor,&user,NULL);
    183:   }

    185:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    186:      Set initial conditions
    187:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    188:   VecGetArray(x,&x_ptr);
    189:   x_ptr[0] = 2.0;
    190:   x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu);
    191:   VecRestoreArray(x,&x_ptr);

    193:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    194:      Set runtime options
    195:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    196:   TSSetFromOptions(ts);

    198:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    199:      Solve nonlinear system
    200:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    201:   TSSolve(ts,x);
    202:   TSGetSolveTime(ts,&ftime);
    203:   TSGetStepNumber(ts,&steps);
    204:   PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);
    205:   VecView(x,PETSC_VIEWER_STDOUT_WORLD);

    207:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    208:      Free work space.  All PETSc objects should be destroyed when they
    209:      are no longer needed.
    210:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    211:   MatDestroy(&A);
    212:   VecDestroy(&x);
    213:   TSDestroy(&ts);

    215:   PetscFinalize();
    216:   return(ierr);
    217: }

    219: /*TEST

    221:     test:
    222:       requires: !single
    223:       args: -mu 1e6

    225:     test:
    226:       requires: !single
    227:       suffix: 2
    228:       args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp

    230:     test:
    231:       requires: !single
    232:       suffix: 3
    233:       args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp -ts_adapt_dsp_filter H0312

    235: TEST*/