Date: 2022-08-02T03:15:08+00:00

Actual source code: ex2.c

      1: static char help[] = "Basic problem for multi-rate method.\n";

\begin{eqnarray}
ys' = -sin(a*t)\\
yf' = bcos(b*t)ys-sin(b*t)sin(a*t)\\
\end{eqnarray}

     12: #include <petscts.h>

     14: typedef struct {
     15:   PetscReal a,b,Tf,dt;
     16: } AppCtx;

     18: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
     19: {
     20:   const PetscScalar *u;
     21:   PetscScalar       *f;

     23:   VecGetArrayRead(U,&u);
     24:   VecGetArray(F,&f);
     25:   f[0] = -PetscSinScalar(ctx->a*t);
     26:   f[1] = ctx->b*PetscCosScalar(ctx->b*t)*u[0]-PetscSinScalar(ctx->b*t)*PetscSinScalar(ctx->a*t);
     27:   VecRestoreArrayRead(U,&u);
     28:   VecRestoreArray(F,&f);
     29:   return 0;
     30:  }

     32: static PetscErrorCode RHSFunctionslow(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
     33: {
     34:   const PetscScalar *u;
     35:   PetscScalar       *f;

     37:   VecGetArrayRead(U,&u);
     38:   VecGetArray(F,&f);
     39:   f[0] = -PetscSinScalar(ctx->a*t);
     40:   VecRestoreArrayRead(U,&u);
     41:   VecRestoreArray(F,&f);
     42:   return 0;
     43: }

     45: static PetscErrorCode RHSFunctionfast(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
     46: {
     47:   const PetscScalar *u;
     48:   PetscScalar       *f;

     50:   VecGetArrayRead(U,&u);
     51:   VecGetArray(F,&f);
     52:   f[0] = ctx->b*PetscCosScalar(ctx->b*t)*u[0]-PetscSinScalar(ctx->b*t)*PetscSinScalar(ctx->a*t);
     53:   VecRestoreArrayRead(U,&u);
     54:   VecRestoreArray(F,&f);
     55:   return 0;
     56: }

     58: /*
     59:   Define the analytic solution for check method easily
     60: */
     61: static PetscErrorCode sol_true(PetscReal t,Vec U,AppCtx *ctx)
     62: {
     63:   PetscScalar    *u;

     65:   VecGetArray(U,&u);
     66:   u[0] = PetscCosScalar(ctx->a*t)/ctx->a;
     67:   u[1] = PetscSinScalar(ctx->b*t)*PetscCosScalar(ctx->a*t)/ctx->a;
     68:   VecRestoreArray(U,&u);
     69:   return 0;
     70: }

     72: int main(int argc,char **argv)
     73: {
     74:   TS             ts;            /* ODE integrator */
     75:   Vec            U;             /* solution will be stored here */
     76:   Vec            Utrue;
     78:   PetscMPIInt    size;
     79:   AppCtx         ctx;
     80:   PetscScalar    *u;
     81:   IS             iss;
     82:   IS             isf;
     83:   PetscInt       *indicess;
     84:   PetscInt       *indicesf;
     85:   PetscInt       n=2;
     86:   PetscScalar    error,tt;

     88:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     89:      Initialize program
     90:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     91:   PetscInitialize(&argc,&argv,(char*)0,help);
     92:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

     95:  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     96:     Create index for slow part and fast part
     97:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     98:   PetscMalloc1(1,&indicess);
     99:   indicess[0]=0;
    100:   PetscMalloc1(1,&indicesf);
    101:   indicesf[0]=1;
    102:   ISCreateGeneral(PETSC_COMM_SELF,1,indicess,PETSC_COPY_VALUES,&iss);
    103:   ISCreateGeneral(PETSC_COMM_SELF,1,indicesf,PETSC_COPY_VALUES,&isf);

    105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    106:     Create necessary vector
    107:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    108:   VecCreate(PETSC_COMM_WORLD,&U);
    109:   VecSetSizes(U,n,PETSC_DETERMINE);
    110:   VecSetFromOptions(U);
    111:   VecDuplicate(U,&Utrue);
    112:   VecCopy(U,Utrue);

    114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    115:     Set runtime options
    116:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    117:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ODE options","");
    118:   {
    119:     ctx.a  = 1.0;
    120:     ctx.b  = 25.0;
    121:     PetscOptionsScalar("-a","","",ctx.a,&ctx.a,NULL);
    122:     PetscOptionsScalar("-b","","",ctx.b,&ctx.b,NULL);
    123:     ctx.Tf = 5.0;
    124:     ctx.dt = 0.01;
    125:     PetscOptionsScalar("-Tf","","",ctx.Tf,&ctx.Tf,NULL);
    126:     PetscOptionsScalar("-dt","","",ctx.dt,&ctx.dt,NULL);
    127:   }
    128:   PetscOptionsEnd();

    130:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    131:      Initialize the solution
    132:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    133:   VecGetArray(U,&u);
    134:   u[0] = 1.0/ctx.a;
    135:   u[1] = 0.0;
    136:   VecRestoreArray(U,&u);

    138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    139:      Create timestepping solver context
    140:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    141:   TSCreate(PETSC_COMM_WORLD,&ts);
    142:   TSSetType(ts,TSMPRK);

    144:   TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
    145:   TSRHSSplitSetIS(ts,"slow",iss);
    146:   TSRHSSplitSetIS(ts,"fast",isf);
    147:   TSRHSSplitSetRHSFunction(ts,"slow",NULL,(TSRHSFunction)RHSFunctionslow,&ctx);
    148:   TSRHSSplitSetRHSFunction(ts,"fast",NULL,(TSRHSFunction)RHSFunctionfast,&ctx);

    150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    151:      Set initial conditions
    152:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    153:   TSSetSolution(ts,U);

    155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    156:      Set solver options
    157:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    158:   TSSetMaxTime(ts,ctx.Tf);
    159:   TSSetTimeStep(ts,ctx.dt);
    160:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
    161:   TSSetFromOptions(ts);

    163:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    164:      Solve linear system
    165:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    166:   TSSolve(ts,U);
    167:   VecView(U,PETSC_VIEWER_STDOUT_WORLD);

    169:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    170:      Check the error of the Petsc solution
    171:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    172:   TSGetTime(ts,&tt);
    173:   sol_true(tt,Utrue,&ctx);
    174:   VecAXPY(Utrue,-1.0,U);
    175:   VecNorm(Utrue,NORM_2,&error);

    177:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    178:      Print norm2 error
    179:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    180:   PetscPrintf(PETSC_COMM_WORLD,"l2 error norm: %g\n", error);

    182:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    183:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
    184:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    185:   VecDestroy(&U);
    186:   TSDestroy(&ts);
    187:   VecDestroy(&Utrue);
    188:   ISDestroy(&iss);
    189:   ISDestroy(&isf);
    190:   PetscFree(indicess);
    191:   PetscFree(indicesf);
    192:   PetscFinalize();
    193:   return 0;
    194: }

    196: /*TEST
    197:     build:
    198:       requires: !complex

    200:     test:

    202: TEST*/