1: static char help[] = "Solves DAE with integrator only on non-algebraic terms \n";

  3:  #include <petscts.h>

  5: /*
  6:         \dot{U} = f(U,V)
  7:         F(U,V)  = 0

  9:     Same as ex6.c except the user provided functions take input values as a single vector instead of two vectors 
 10: */


 13: /*
 14:    f(U,V) = U + V

 16: */
 17: PetscErrorCode f(PetscReal t,Vec UV,Vec F)
 18: {
 19:   PetscErrorCode    ierr;
 20:   const PetscScalar *u,*v;
 21:   PetscScalar       *f;
 22:   PetscInt          n,i;

 25:   VecGetLocalSize(UV,&n);
 26:   n    = n/2;
 27:   VecGetArrayRead(UV,&u);
 28:   v    = u + n;
 29:   VecGetArray(F,&f);
 30:   for (i=0; i<n; i++) f[i] = u[i] + v[i];
 31:   VecRestoreArrayRead(UV,&u);
 32:   VecRestoreArray(F,&f);
 33:   return(0);
 34: }

 36: /*
 37:    F(U,V) = U - V

 39: */
 40: PetscErrorCode F(PetscReal t,Vec UV,Vec F)
 41: {
 42:   PetscErrorCode    ierr;
 43:   const PetscScalar *u,*v;
 44:   PetscScalar       *f;
 45:   PetscInt          n,i;

 48:   VecGetLocalSize(UV,&n);
 49:   n    = n/2;
 50:   VecGetArrayRead(UV,&u);
 51:   v    = u + n;
 52:   VecGetArray(F,&f);
 53:   for (i=0; i<n; i++) f[i] = u[i] - v[i];
 54:   VecRestoreArrayRead(UV,&u);
 55:   VecRestoreArray(F,&f);
 56:   return(0);
 57: }

 59: typedef struct {
 60:   PetscReal      t;
 61:   SNES           snes;
 62:   Vec            UV,V;
 63:   VecScatter     scatterU,scatterV;
 64:   PetscErrorCode (*f)(PetscReal,Vec,Vec);
 65:   PetscErrorCode (*F)(PetscReal,Vec,Vec);
 66: } AppCtx;

 68: extern PetscErrorCode TSFunction(TS,PetscReal,Vec,Vec,void*);
 69: extern PetscErrorCode SNESFunction(SNES,Vec,Vec,void*);

 71: int main(int argc,char **argv)
 72: {
 74:   AppCtx         ctx;
 75:   TS             ts;
 76:   Vec            tsrhs,U;
 77:   IS             is;
 78:   PetscInt       I;
 79:   PetscMPIInt    rank;

 81:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 82:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 83:   TSCreate(PETSC_COMM_WORLD,&ts);
 84:   TSSetProblemType(ts,TS_NONLINEAR);
 85:   TSSetType(ts,TSEULER);
 86:   TSSetFromOptions(ts);
 87:   VecCreateMPI(PETSC_COMM_WORLD,1,PETSC_DETERMINE,&tsrhs);
 88:   VecCreateMPI(PETSC_COMM_WORLD,1,PETSC_DETERMINE,&U);
 89:   TSSetRHSFunction(ts,tsrhs,TSFunction,&ctx);
 90:   ctx.f = f;

 92:   SNESCreate(PETSC_COMM_WORLD,&ctx.snes);
 93:   SNESSetFromOptions(ctx.snes);
 94:   SNESSetFunction(ctx.snes,NULL,SNESFunction,&ctx);
 95:   SNESSetJacobian(ctx.snes,NULL,NULL,SNESComputeJacobianDefault,&ctx);
 96:   ctx.F = F;
 97:   VecCreateMPI(PETSC_COMM_WORLD,1,PETSC_DETERMINE,&ctx.V);

 99:   /* Create scatters to move between separate U and V representation and UV representation of solution */
100:   VecCreateMPI(PETSC_COMM_WORLD,2,PETSC_DETERMINE,&ctx.UV);
101:   I    = 2*rank;
102:   ISCreateGeneral(PETSC_COMM_WORLD,1,&I,PETSC_COPY_VALUES,&is);
103:   VecScatterCreate(U,NULL,ctx.UV,is,&ctx.scatterU);
104:   ISDestroy(&is);
105:   I    = 2*rank + 1;
106:   ISCreateGeneral(PETSC_COMM_WORLD,1,&I,PETSC_COPY_VALUES,&is);
107:   VecScatterCreate(ctx.V,NULL,ctx.UV,is,&ctx.scatterV);
108:   ISDestroy(&is);

110:   VecSet(U,1.0);
111:   TSSolve(ts,U);

113:   VecDestroy(&ctx.V);
114:   VecDestroy(&ctx.UV);
115:   VecScatterDestroy(&ctx.scatterU);
116:   VecScatterDestroy(&ctx.scatterV);
117:   VecDestroy(&tsrhs);
118:   VecDestroy(&U);
119:   SNESDestroy(&ctx.snes);
120:   TSDestroy(&ts);
121:   PetscFinalize();
122:   return ierr;
123: }

125: /*
126:    Defines the RHS function that is passed to the time-integrator. 

128:    Solves F(U,V) for V and then computes f(U,V)

130: */
131: PetscErrorCode TSFunction(TS ts,PetscReal t,Vec U,Vec F,void *actx)
132: {
133:   AppCtx         *ctx = (AppCtx*)actx;

137:   ctx->t = t;
138:   VecScatterBegin(ctx->scatterU,U,ctx->UV,INSERT_VALUES,SCATTER_FORWARD);
139:   VecScatterEnd(ctx->scatterU,U,ctx->UV,INSERT_VALUES,SCATTER_FORWARD);
140:   SNESSolve(ctx->snes,NULL,ctx->V);
141:   VecScatterBegin(ctx->scatterV,ctx->V,ctx->UV,INSERT_VALUES,SCATTER_FORWARD);
142:   VecScatterEnd(ctx->scatterV,ctx->V,ctx->UV,INSERT_VALUES,SCATTER_FORWARD);
143:   (*ctx->f)(t,ctx->UV,F);
144:   return(0);
145: }

147: /*
148:    Defines the nonlinear function that is passed to the nonlinear solver

150: */
151: PetscErrorCode SNESFunction(SNES snes,Vec V,Vec F,void *actx)
152: {
153:   AppCtx         *ctx = (AppCtx*)actx;

157:   VecScatterBegin(ctx->scatterV,V,ctx->UV,INSERT_VALUES,SCATTER_FORWARD);
158:   VecScatterEnd(ctx->scatterV,V,ctx->UV,INSERT_VALUES,SCATTER_FORWARD);
159:   (*ctx->F)(ctx->t,ctx->UV,F);
160:   return(0);
161: }