1: /*
  2:     Provides a PETSc interface to RADAU5 solver.

  4: */
  5: #include <petsc/private/tsimpl.h>

  7: typedef struct {
  8:   Vec work,workf;
  9: } TS_Radau5;

 11: void FVPOL(int *N,double *X,double *Y,double *F,double *RPAR,void *IPAR)
 12: {
 13:   TS             ts = (TS) IPAR;
 14:   TS_Radau5      *cvode = (TS_Radau5*)ts->data;
 15:   DM             dm;
 16:   DMTS           tsdm;
 17:   TSIFunction    ifunction;

 19:   PETSC_COMM_SELF,VecPlaceArray(cvode->work,Y);
 20:   PETSC_COMM_SELF,VecPlaceArray(cvode->workf,F);

 22:   /* Now compute the right hand side function, via IFunction unless only the more efficient RHSFunction is set */
 23:   PETSC_COMM_SELF,TSGetDM(ts,&dm);
 24:   PETSC_COMM_SELF,DMGetDMTS(dm,&tsdm);
 25:   PETSC_COMM_SELF,DMTSGetIFunction(dm,&ifunction,NULL);
 26:   if (!ifunction) {
 27:     PETSC_COMM_SELF,TSComputeRHSFunction(ts,*X,cvode->work,cvode->workf);
 28:   } else {       /* If rhsfunction is also set, this computes both parts and scale them to the right hand side */
 29:     Vec yydot;

 31:     PETSC_COMM_SELF,VecDuplicate(cvode->work,&yydot);
 32:     PETSC_COMM_SELF,VecZeroEntries(yydot);
 33:     PETSC_COMM_SELF,TSComputeIFunction(ts,*X,cvode->work,yydot,cvode->workf,PETSC_FALSE);
 34:     PETSC_COMM_SELF,VecScale(cvode->workf,-1.);
 35:     PETSC_COMM_SELF,VecDestroy(&yydot);
 36:   }

 38:   PETSC_COMM_SELF,VecResetArray(cvode->work);
 39:   PETSC_COMM_SELF,VecResetArray(cvode->workf);
 40: }

 42: void JVPOL(PetscInt *N,PetscScalar *X,PetscScalar *Y,PetscScalar *DFY,int *LDFY,PetscScalar *RPAR,void *IPAR)
 43: {
 44:   TS             ts = (TS) IPAR;
 45:   TS_Radau5      *cvode = (TS_Radau5*)ts->data;
 46:   Vec            yydot;
 47:   Mat            mat;
 48:   PetscInt       n;

 50:   PETSC_COMM_SELF,VecPlaceArray(cvode->work,Y);
 51:   PETSC_COMM_SELF,VecDuplicate(cvode->work,&yydot);
 52:   PETSC_COMM_SELF,VecGetSize(yydot,&n);
 53:   PETSC_COMM_SELF,MatCreateSeqDense(PETSC_COMM_SELF,n,n,DFY,&mat);
 54:   PETSC_COMM_SELF,VecZeroEntries(yydot);
 55:   PETSC_COMM_SELF,TSComputeIJacobian(ts,*X,cvode->work,yydot,0,mat,mat,PETSC_FALSE);
 56:   PETSC_COMM_SELF,MatScale(mat,-1.0);
 57:   PETSC_COMM_SELF,MatDestroy(&mat);
 58:   PETSC_COMM_SELF,VecDestroy(&yydot);
 59:   PETSC_COMM_SELF,VecResetArray(cvode->work);
 60: }

 62: void SOLOUT(int *NR,double *XOLD,double *X, double *Y,double *CONT,double *LRC,int *N,double *RPAR,void *IPAR,int *IRTRN)
 63: {
 64:   TS             ts = (TS) IPAR;
 65:   TS_Radau5      *cvode = (TS_Radau5*)ts->data;

 67:   PETSC_COMM_SELF,VecPlaceArray(cvode->work,Y);
 68:   ts->time_step = *X - *XOLD;
 69:   PETSC_COMM_SELF,TSMonitor(ts,*NR-1,*X,cvode->work);
 70:   PETSC_COMM_SELF,VecResetArray(cvode->work);
 71: }

 73: void radau5_(int *,void*,double*,double*,double*,double*,double*,double*,int*,void*,int*,int*,int*,void*,int*,int*,int*,void*,int*,double*,int*,int*,int*,double*,void*,int*);

 75: PetscErrorCode TSSolve_Radau5(TS ts)
 76: {
 77:   TS_Radau5      *cvode = (TS_Radau5*)ts->data;
 78:   PetscScalar    *Y,*WORK,X,XEND,RTOL,ATOL,H,RPAR;
 79:   PetscInt       ND,*IWORK,LWORK,LIWORK,MUJAC,MLMAS,MUMAS,IDID,ITOL;
 80:   int            IJAC,MLJAC,IMAS,IOUT;

 82:   VecGetArray(ts->vec_sol,&Y);
 83:   VecGetSize(ts->vec_sol,&ND);
 84:   VecCreateSeqWithArray(PETSC_COMM_SELF,1,ND,NULL,&cvode->work);
 85:   VecCreateSeqWithArray(PETSC_COMM_SELF,1,ND,NULL,&cvode->workf);

 87:   LWORK  = 4*ND*ND+12*ND+20;
 88:   LIWORK = 3*ND+20;

 90:   PetscCalloc2(LWORK,&WORK,LIWORK,&IWORK);

 92:   /* C --- PARAMETER IN THE DIFFERENTIAL EQUATION */
 93:   RPAR=1.0e-6;
 94:   /* C --- COMPUTE THE JACOBIAN ANALYTICALLY */
 95:   IJAC=1;
 96:   /* C --- JACOBIAN IS A FULL MATRIX */
 97:   MLJAC=ND;
 98:   /* C --- DIFFERENTIAL EQUATION IS IN EXPLICIT FORM*/
 99:   IMAS=0;
100:   /* C --- OUTPUT ROUTINE IS USED DURING INTEGRATION*/
101:   IOUT=1;
102:   /* C --- INITIAL VALUES*/
103:   X = ts->ptime;
104:   /* C --- ENDPOINT OF INTEGRATION */
105:   XEND = ts->max_time;
106:   /* C --- REQUIRED TOLERANCE */
107:   RTOL = ts->rtol;
108:   ATOL = ts->atol;
109:   ITOL=0;
110:   /* C --- INITIAL STEP SIZE */
111:   H = ts->time_step;

113:   /* output MUJAC MLMAS IDID; currently all ignored */

115:   radau5_(&ND,FVPOL,&X,Y,&XEND,&H,&RTOL,&ATOL,&ITOL,JVPOL,&IJAC,&MLJAC,&MUJAC,FVPOL,&IMAS,&MLMAS,&MUMAS,SOLOUT,&IOUT,WORK,&LWORK,IWORK,&LIWORK,&RPAR,(void*)ts,&IDID);

117:   PetscFree2(WORK,IWORK);
118:   return 0;
119: }

121: PetscErrorCode TSDestroy_Radau5(TS ts)
122: {
123:   TS_Radau5      *cvode = (TS_Radau5*)ts->data;

125:   VecDestroy(&cvode->work);
126:   VecDestroy(&cvode->workf);
127:   PetscFree(ts->data);
128:   return 0;
129: }

131: /*MC
132:       TSRADAU5 - ODE solver using the RADAU5 package

134:     Notes:
135:     This uses its own nonlinear solver and dense matrix direct solver so PETSc SNES and KSP options do not apply.
136:            Uses its own time-step adaptivity (but uses the TS rtol and atol, and initial timestep)
137:            Uses its own memory for the dense matrix storage and factorization
138:            Can only handle ODEs of the form \cdot{u} = -F(t,u) + G(t,u)

140:     Level: beginner

142: .seealso:  TSCreate(), TS, TSSetType()

144: M*/
145: PETSC_EXTERN PetscErrorCode TSCreate_Radau5(TS ts)
146: {
147:   TS_Radau5      *cvode;

149:   ts->ops->destroy        = TSDestroy_Radau5;
150:   ts->ops->solve          = TSSolve_Radau5;
151:   ts->default_adapt_type  = TSADAPTNONE;

153:   PetscNewLog(ts,&cvode);
154:   ts->data = (void*)cvode;
155:   return 0;
156: }