Actual source code: ex2.c

  1: /*$Id: ex2.c,v 1.36 2001/08/07 21:31:27 bsmith Exp $*/
  2: /*
  3:        Formatted test for TS routines.

  5:           Solves U_t=F(t,u)
  6:           Where:
  7:           
  8:                   [2*u1+u2
  9:           F(t,u)= [u1+2*u2+u3
 10:                   [   u2+2*u3
 11:        We can compare the solutions from euler, beuler and PVODE to
 12:        see what is the difference.

 14: */

 16: static char help[] = "Solves a nonlinear ODE. nn";

 18:  #include petscsys.h
 19:  #include petscts.h
 20:  #include petscpc.h

 22: extern int RHSFunction(TS,PetscReal,Vec,Vec,void*);
 23: extern int RHSJacobian(TS,PetscReal,Vec,Mat*,Mat*,MatStructure *,void*);
 24: extern int Monitor(TS,int,PetscReal,Vec,void *);
 25: extern int Initial(Vec,void *);

 27: extern PetscReal solx(PetscReal);
 28: extern PetscReal soly(PetscReal);
 29: extern PetscReal solz(PetscReal);

 31: int main(int argc,char **argv)
 32: {
 33:   int           ierr,time_steps = 100,steps,size;
 34:   Vec           global;
 35:   PetscReal     dt,ftime;
 36:   TS            ts;
 37:   MatStructure  A_structure;
 38:   Mat           A = 0;
 39: 
 40:   PetscInitialize(&argc,&argv,(char*)0,help);
 41:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 42: 
 43:   PetscOptionsGetInt(PETSC_NULL,"-time",&time_steps,PETSC_NULL);
 44: 
 45:   /* set initial conditions */
 46:   VecCreate(PETSC_COMM_WORLD,&global);
 47:   VecSetSizes(global,PETSC_DECIDE,3);
 48:   VecSetFromOptions(global);
 49:   Initial(global,PETSC_NULL);
 50: 
 51:   /* make timestep context */
 52:   TSCreate(PETSC_COMM_WORLD,&ts);
 53:   TSSetProblemType(ts,TS_NONLINEAR);
 54:   TSSetMonitor(ts,Monitor,PETSC_NULL,PETSC_NULL);

 56:   dt = 0.1;

 58:   /*
 59:     The user provides the RHS and Jacobian
 60:   */
 61:   TSSetRHSFunction(ts,RHSFunction,NULL);
 62:   MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,3,3,&A);
 63:   MatSetFromOptions(A);
 64:   RHSJacobian(ts,0.0,global,&A,&A,&A_structure,NULL);
 65:   TSSetRHSJacobian(ts,A,A,RHSJacobian,NULL);
 66: 
 67:   TSSetFromOptions(ts);

 69:   TSSetInitialTimeStep(ts,0.0,dt);
 70:   TSSetDuration(ts,time_steps,1);
 71:   TSSetSolution(ts,global);


 74:   TSSetUp(ts);
 75:   TSStep(ts,&steps,&ftime);


 78:   /* free the memories */
 79: 
 80:   TSDestroy(ts);
 81:   VecDestroy(global);
 82:   ierr= MatDestroy(A);

 84:   PetscFinalize();
 85:   return 0;
 86: }

 88: /* -------------------------------------------------------------------*/
 89: /* this test problem has initial values (1,1,1).                      */
 90: int Initial(Vec global,void *ctx)
 91: {
 92:   PetscScalar *localptr;
 93:   int    i,mybase,myend,ierr,locsize;

 95:   /* determine starting point of each processor */
 96:   VecGetOwnershipRange(global,&mybase,&myend);
 97:   VecGetLocalSize(global,&locsize);

 99:   /* Initialize the array */
100:   VecGetArray(global,&localptr);
101:   for (i=0; i<locsize; i++) {
102:     localptr[i] = 1.0;
103:   }
104: 
105:   if (mybase == 0) localptr[0]=1.0;

107:   VecRestoreArray(global,&localptr);
108:   return 0;
109: }

111: int Monitor(TS ts,int step,PetscReal time,Vec global,void *ctx)
112: {
113:   VecScatter   scatter;
114:   IS           from,to;
115:   int          i,n,*idx;
116:   Vec          tmp_vec;
117:   int          ierr;
118:   PetscScalar  *tmp;

120:   /* Get the size of the vector */
121:   VecGetSize(global,&n);

123:   /* Set the index sets */
124:   PetscMalloc(n*sizeof(int),&idx);
125:   for(i=0; i<n; i++) idx[i]=i;
126: 
127:   /* Create local sequential vectors */
128:   VecCreateSeq(PETSC_COMM_SELF,n,&tmp_vec);

130:   /* Create scatter context */
131:   ISCreateGeneral(PETSC_COMM_SELF,n,idx,&from);
132:   ISCreateGeneral(PETSC_COMM_SELF,n,idx,&to);
133:   VecScatterCreate(global,from,tmp_vec,to,&scatter);
134:   VecScatterBegin(global,tmp_vec,INSERT_VALUES,SCATTER_FORWARD,scatter);
135:   VecScatterEnd(global,tmp_vec,INSERT_VALUES,SCATTER_FORWARD,scatter);

137:   VecGetArray(tmp_vec,&tmp);
138:   PetscPrintf(PETSC_COMM_WORLD,"At t =%14.6e u = %14.6e  %14.6e  %14.6e n",
139:                      time,PetscRealPart(tmp[0]),PetscRealPart(tmp[1]),PetscRealPart(tmp[2]));
140:   PetscPrintf(PETSC_COMM_WORLD,"At t =%14.6e errors = %14.6e  %14.6e  %14.6e n",
141:                      time,PetscRealPart(tmp[0]-solx(time)),PetscRealPart(tmp[1]-soly(time)),PetscRealPart(tmp[2]-solz(time)));
142:   VecRestoreArray(tmp_vec,&tmp);
143:   VecScatterDestroy(scatter);
144:   ISDestroy(from);
145:   ISDestroy(to);
146:   PetscFree(idx);
147:   VecDestroy(tmp_vec);
148:   return 0;
149: }

151: int RHSFunction(TS ts,PetscReal t,Vec globalin,Vec globalout,void *ctx)
152: {
153:   PetscScalar  *inptr,*outptr;
154:   int          i,n,ierr,*idx;
155:   IS           from,to;
156:   VecScatter   scatter;
157:   Vec          tmp_in,tmp_out;

159:   /* Get the length of parallel vector */
160:   VecGetSize(globalin,&n);

162:   /* Set the index sets */
163:   PetscMalloc(n*sizeof(int),&idx);
164:   for(i=0; i<n; i++) idx[i]=i;
165: 
166:   /* Create local sequential vectors */
167:   VecCreateSeq(PETSC_COMM_SELF,n,&tmp_in);
168:   VecDuplicate(tmp_in,&tmp_out);

170:   /* Create scatter context */
171:   ISCreateGeneral(PETSC_COMM_SELF,n,idx,&from);
172:   ISCreateGeneral(PETSC_COMM_SELF,n,idx,&to);
173:   VecScatterCreate(globalin,from,tmp_in,to,&scatter);
174:   VecScatterBegin(globalin,tmp_in,INSERT_VALUES,SCATTER_FORWARD,scatter);
175:   VecScatterEnd(globalin,tmp_in,INSERT_VALUES,SCATTER_FORWARD,scatter);
176:   VecScatterDestroy(scatter);

178:   /*Extract income array */
179:   VecGetArray(tmp_in,&inptr);

181:   /* Extract outcome array*/
182:   VecGetArray(tmp_out,&outptr);

184:   outptr[0] = 2.0*inptr[0]+inptr[1];
185:   outptr[1] = inptr[0]+2.0*inptr[1]+inptr[2];
186:   outptr[2] = inptr[1]+2.0*inptr[2];

188:   VecRestoreArray(tmp_in,&inptr);
189:   VecRestoreArray(tmp_out,&outptr);

191:   VecScatterCreate(tmp_out,from,globalout,to,&scatter);
192:   VecScatterBegin(tmp_out,globalout,INSERT_VALUES,SCATTER_FORWARD,scatter);
193:   VecScatterEnd(tmp_out,globalout,INSERT_VALUES,SCATTER_FORWARD,scatter);

195:   /* Destroy idx aand scatter */
196:   ISDestroy(from);
197:   ISDestroy(to);
198:   VecScatterDestroy(scatter);
199:   VecDestroy(tmp_in);
200:   VecDestroy(tmp_out);
201:   PetscFree(idx);
202:   return 0;
203: }

205: int RHSJacobian(TS ts,PetscReal t,Vec x,Mat *AA,Mat *BB,MatStructure *str,void *ctx)
206: {
207:   Mat    A = *AA;
208:   PetscScalar v[3],*tmp;
209:   int    idx[3],i,ierr;
210: 
211:   *str = SAME_NONZERO_PATTERN;

213:   idx[0]=0; idx[1]=1; idx[2]=2;
214:   VecGetArray(x,&tmp);

216:   i = 0;
217:   v[0] = 2.0; v[1] = 1.0; v[2] = 0.0;
218:   MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);

220:   i = 1;
221:   v[0] = 1.0; v[1] = 2.0; v[2] = 1.0;
222:   MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
223: 
224:   i = 2;
225:   v[0]= 0.0; v[1] = 1.0; v[2] = 2.0;
226:   MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);

228:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
229:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

231:   VecRestoreArray(x,&tmp);

233:   return 0;
234: }

236: /*
237:       The exact solutions 
238: */
239: PetscReal solx(PetscReal t)
240: {
241:   return exp((2.0 - sqrt(2.0))*t)/2.0 - exp((2.0 - sqrt(2.0))*t)/(2.0*sqrt(2.0)) +
242:          exp((2.0 + sqrt(2.0))*t)/2.0 + exp((2.0 + sqrt(2.0))*t)/(2.0*sqrt(2.0));
243: }

245: PetscReal soly(PetscReal t)
246: {
247:   return exp((2.0 - sqrt(2.0))*t)/2.0 - exp((2.0 - sqrt(2.0))*t)/sqrt(2.0) +
248:          exp((2.0 + sqrt(2.0))*t)/2.0 + exp((2.0 + sqrt(2.0))*t)/sqrt(2.0);
249: }
250: 
251: PetscReal solz(PetscReal t)
252: {
253:   return exp((2.0 - sqrt(2.0))*t)/2.0 - exp((2.0 - sqrt(2.0))*t)/(2.0*sqrt(2.0)) +
254:          exp((2.0 + sqrt(2.0))*t)/2.0 + exp((2.0 + sqrt(2.0))*t)/(2.0*sqrt(2.0));
255: }