Actual source code: ex7.c

petsc-3.5.4 2015-05-23
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  2: static char help[] = ".\n";

  4: /*

  6:         u_t =  u_xx + R(u)

  8:       Where u(t,x,i)    for i=0, .... N-1 where i+1 represents the void size

 10:       ex9.c is the 2d version of this code
 11: */

 13: #include <petscdm.h>
 14: #include <petscdmda.h>
 15: #include <petscts.h>

 17: /*
 18:    User-defined data structures and routines
 19: */

 21: /* AppCtx */
 22: typedef struct {
 23:   PetscInt N;               /* number of dofs */
 24: } AppCtx;

 26: extern PetscErrorCode IFunction(TS,PetscReal,Vec,Vec,Vec,void*);
 27: extern PetscErrorCode InitialConditions(DM,Vec);
 28: extern PetscErrorCode IJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);


 33: int main(int argc,char **argv)
 34: {
 35:   TS             ts;                  /* nonlinear solver */
 36:   Vec            U;                   /* solution, residual vectors */
 37:   Mat            J;                   /* Jacobian matrix */
 38:   PetscInt       maxsteps = 1000;
 40:   DM             da;
 41:   AppCtx         user;
 42:   PetscInt       i;
 43:   char           Name[16];

 45:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 46:      Initialize program
 47:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 48:   PetscInitialize(&argc,&argv,(char*)0,help);
 49:   user.N = 1;
 50:   PetscOptionsGetInt(NULL,"-N",&user.N,NULL);

 52:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 53:      Create distributed array (DMDA) to manage parallel grid and vectors
 54:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 55:   DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_MIRROR,-8,user.N,1,NULL,&da);

 57:   for (i=0; i<user.N; i++) {
 58:     PetscSNPrintf(Name,16,"Void size %d",(int)(i+1));
 59:     DMDASetFieldName(da,i,Name);
 60:   }

 62:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 63:    Extract global vectors from DMDA; then duplicate for remaining
 64:      vectors that are the same types
 65:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 66:   DMCreateGlobalVector(da,&U);
 67:   DMSetMatType(da,MATAIJ);
 68:   DMCreateMatrix(da,&J);

 70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 71:      Create timestepping solver context
 72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 73:   TSCreate(PETSC_COMM_WORLD,&ts);
 74:   TSSetType(ts,TSARKIMEX);
 75:   TSSetDM(ts,da);
 76:   TSSetProblemType(ts,TS_NONLINEAR);
 77:   TSSetIFunction(ts,NULL,IFunction,&user);
 78:   TSSetIJacobian(ts,J,J,IJacobian,&user);


 81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 82:      Set initial conditions
 83:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 84:   InitialConditions(da,U);
 85:   TSSetSolution(ts,U);

 87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 88:      Set solver options
 89:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 90:   TSSetInitialTimeStep(ts,0.0,.001);
 91:   TSSetDuration(ts,maxsteps,1.0);
 92:   TSSetFromOptions(ts);

 94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 95:      Solve nonlinear system
 96:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 97:   TSSolve(ts,U);

 99:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100:      Free work space.  All PETSc objects should be destroyed when they
101:      are no longer needed.
102:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
103:   VecDestroy(&U);
104:   MatDestroy(&J);
105:   TSDestroy(&ts);
106:   DMDestroy(&da);

108:   PetscFinalize();
109:   return(0);
110: }
111: /* ------------------------------------------------------------------- */
114: /*
115:    IFunction - Evaluates nonlinear function, F(U).

117:    Input Parameters:
118: .  ts - the TS context
119: .  U - input vector
120: .  ptr - optional user-defined context, as set by SNESSetFunction()

122:    Output Parameter:
123: .  F - function vector
124:  */
125: PetscErrorCode IFunction(TS ts,PetscReal ftime,Vec U,Vec Udot,Vec F,void *ptr)
126: {
127:   DM             da;
129:   PetscInt       i,c,Mx,xs,xm,N;
130:   PetscReal      hx,sx,x;
131:   PetscScalar    uxx;
132:   PetscScalar    **u,**f,**udot;
133:   Vec            localU;

136:   TSGetDM(ts,&da);
137:   DMGetLocalVector(da,&localU);
138:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,&N,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

140:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);

142:   /*
143:      Scatter ghost points to local vector,using the 2-step process
144:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
145:      By placing code between these two statements, computations can be
146:      done while messages are in transition.
147:   */
148:   DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
149:   DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);

151:   /*
152:     Get pointers to vector data
153:   */
154:   DMDAVecGetArrayDOF(da,localU,&u);
155:   DMDAVecGetArrayDOF(da,Udot,&udot);
156:   DMDAVecGetArrayDOF(da,F,&f);

158:   /*
159:      Get local grid boundaries
160:   */
161:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

163:   /*
164:      Compute function over the locally owned part of the grid
165:   */
166:   for (i=xs; i<xs+xm; i++) {
167:     x = i*hx;

169:     /*  diffusion term */
170:     for (c=0; c<N; c++) {
171:       uxx     = (-2.0*u[i][c] + u[i-1][c] + u[i+1][c])*sx;
172:       f[i][c] = udot[i][c] - uxx;
173:     }

175:     /* reaction terms */

177:     for (c=0; c<N/3; c++) {
178:       f[i][c]   +=  500*u[i][c]*u[i][c] + 500*u[i][c]*u[i][c+1];
179:       f[i][c+1] += -500*u[i][c]*u[i][c] + 500*u[i][c]*u[i][c+1];
180:       f[i][c+2] -=                        500*u[i][c]*u[i][c+1];
181:     }


184:     /* forcing term */

186:     f[i][0] -= 5*PetscExpScalar((1.0 - x)*(1.0 - x));

188:   }

190:   /*
191:      Restore vectors
192:   */
193:   DMDAVecRestoreArrayDOF(da,localU,&u);
194:   DMDAVecRestoreArrayDOF(da,Udot,&udot);
195:   DMDAVecRestoreArrayDOF(da,F,&f);
196:   DMRestoreLocalVector(da,&localU);
197:   return(0);
198: }

202: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx)
203: {
205:   PetscInt       i,c,Mx,xs,xm,nc;
206:   DM             da;
207:   MatStencil     col[3],row;
208:   PetscScalar    vals[3],hx,sx;
209:   AppCtx         *user = (AppCtx*)ctx;
210:   PetscInt       N     = user->N;
211:   PetscScalar    **u;

214:   TSGetDM(ts,&da);
215:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
216:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

218:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);

220:   DMDAVecGetArrayDOF(da,U,&u);

222:   MatZeroEntries(Jpre);
223:   for (i=xs; i<xs+xm; i++) {
224:     for (c=0; c<N; c++) {
225:       nc        = 0;
226:       row.c     = c; row.i = i;
227:       col[nc].c = c; col[nc].i = i-1; vals[nc++] = -sx;
228:       col[nc].c = c; col[nc].i = i;   vals[nc++] = 2.0*sx + a;
229:       col[nc].c = c; col[nc].i = i+1; vals[nc++] = -sx;
230:       MatSetValuesStencil(Jpre,1,&row,nc,col,vals,ADD_VALUES);
231:     }

233:     for (c=0; c<N/3; c++) {
234:       nc        = 0;
235:       row.c     = c;   row.i = i;
236:       col[nc].c = c;   col[nc].i = i; vals[nc++] = 1000*u[i][c] + 500*u[i][c+1];
237:       col[nc].c = c+1; col[nc].i = i; vals[nc++] =  500*u[i][c];
238:       MatSetValuesStencil(Jpre,1,&row,nc,col,vals,ADD_VALUES);

240:       nc        = 0;
241:       row.c     = c+1; row.i = i;
242:       col[nc].c = c;   col[nc].i = i; vals[nc++] = -1000*u[i][c] + 500*u[i][c+1];
243:       col[nc].c = c+1; col[nc].i = i; vals[nc++] =   500*u[i][c];
244:       MatSetValuesStencil(Jpre,1,&row,nc,col,vals,ADD_VALUES);

246:       nc        = 0;
247:       row.c     = c+2; row.i = i;
248:       col[nc].c = c;   col[nc].i = i; vals[nc++] =  -500*u[i][c+1];
249:       col[nc].c = c+1; col[nc].i = i; vals[nc++] =  -500*u[i][c];
250:       MatSetValuesStencil(Jpre,1,&row,nc,col,vals,ADD_VALUES);

252:     }
253:   }
254:   MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
255:   MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
256:   if (J != Jpre) {
257:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
258:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
259:   }
260:   DMDAVecRestoreArrayDOF(da,U,&u);
261:   return(0);
262: }

264: /* ------------------------------------------------------------------- */
267: PetscErrorCode InitialConditions(DM da,Vec U)
268: {
270:   PetscInt       i,c,xs,xm,Mx,N;
271:   PetscScalar    **u;
272:   PetscReal      hx,x;

275:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,&N,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

277:   hx = 1.0/(PetscReal)(Mx-1);

279:   /*
280:      Get pointers to vector data
281:   */
282:   DMDAVecGetArrayDOF(da,U,&u);

284:   /*
285:      Get local grid boundaries
286:   */
287:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

289:   /*
290:      Compute function over the locally owned part of the grid
291:   */
292:   for (i=xs; i<xs+xm; i++) {
293:     x = i*hx;
294:     for (c=0; c<N; c++) u[i][c] = 0.0; /*PetscCosScalar(PETSC_PI*x);*/
295:   }

297:   /*
298:      Restore vectors
299:   */
300:   DMDAVecRestoreArrayDOF(da,U,&u);
301:   return(0);
302: }