Actual source code: ex7.c

  1: /*$Id: ex7.c,v 1.3 2001/04/14 03:58:23 bsmith Exp $*/

  3: /* Program usage:  mpirun -np <procs> ex5 [-help] [all PETSc options] */

  5: static char help[] = "Nonlinear, time-dependent PDE in 2d.n";


  8: /* 
  9:    Include "petscda.h" so that we can use distributed arrays (DAs).
 10:    Include "petscts.h" so that we can use SNES solvers.  Note that this
 11:    file automatically includes:
 12:      petsc.h       - base PETSc routines   petscvec.h - vectors
 13:      petscsys.h    - system routines       petscmat.h - matrices
 14:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 15:      petscviewer.h - viewers               petscpc.h  - preconditioners
 16:      petscsles.h   - linear solvers
 17: */
 18:  #include petscda.h
 19:  #include petscts.h


 22: /* 
 23:    User-defined routines
 24: */
 25: extern int FormFunction(TS,double,Vec,Vec,void*),FormInitialSolution(DA,Vec);
 26: extern int Monitor(TS,int,double,Vec,void*);

 28: int main(int argc,char **argv)
 29: {
 30:   TS                     ts;                 /* nonlinear solver */
 31:   Vec                    x,r;                  /* solution, residual vectors */
 32:   Mat                    J;                    /* Jacobian matrix */
 33:   int                    steps;                  /* iterations for convergence */
 34:   int                    ierr;
 35:   DA                     da;
 36:   MatFDColoring          matfdcoloring;
 37:   ISColoring             iscoloring;
 38:   double                 ftime;

 40:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 41:      Initialize program
 42:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 44:   PetscInitialize(&argc,&argv,(char *)0,help);


 47:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 48:      Create distributed array (DA) to manage parallel grid and vectors
 49:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 50:   DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,8,8,PETSC_DECIDE,PETSC_DECIDE,
 51:                     1,1,PETSC_NULL,PETSC_NULL,&da);

 53:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 54:      Extract global vectors from DA; then duplicate for remaining
 55:      vectors that are the same types
 56:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 57:   DACreateGlobalVector(da,&x);
 58:   VecDuplicate(x,&r);

 60:   TSCreate(PETSC_COMM_WORLD,TS_NONLINEAR,&ts);
 61:   TSSetRHSFunction(ts,FormFunction,da);


 64:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 65:      Create matrix data structure; set Jacobian evaluation routine

 67:      Set Jacobian matrix data structure and default Jacobian evaluation
 68:      routine. User can override with:
 69:      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
 70:                 (unless user explicitly sets preconditioner) 
 71:      -snes_mf_operator : form preconditioning matrix as set by the user,
 72:                          but use matrix-free approx for Jacobian-vector
 73:                          products within Newton-Krylov method

 75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 76:   DAGetColoring(da,IS_COLORING_GLOBAL,MATMPIAIJ,&iscoloring,&J);
 77:   MatFDColoringCreate(J,iscoloring,&matfdcoloring);
 78:   ISColoringDestroy(iscoloring);
 79:   MatFDColoringSetFunction(matfdcoloring,(int (*)(void))FormFunction,da);
 80:   MatFDColoringSetFromOptions(matfdcoloring);

 82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 83:      Customize nonlinear solver; set runtime options
 84:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 85:   TSSetInitialTimeStep(ts,0.0,.0001);
 86:   TSSetType(ts,TS_BEULER);
 87:   TSSetDuration(ts,100,1.0);
 88:   TSSetFromOptions(ts);
 89:   TSSetMonitor(ts,Monitor,0,0);

 91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 92:      Set initial conditions
 93:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 94:   FormInitialSolution(da,x);

 96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 97:      Solve nonlinear system
 98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 99:   TSSetSolution(ts,x);
100:   TSStep(ts,&steps,&ftime);


103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104:      Free work space.  All PETSc objects should be destroyed when they
105:      are no longer needed.
106:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

108:   MatDestroy(J);
109:   MatFDColoringDestroy(matfdcoloring);
110:   VecDestroy(x);
111:   VecDestroy(r);
112:   TSDestroy(ts);
113:   DADestroy(da);
114:   PetscFinalize();

116:   return(0);
117: }
118: /* ------------------------------------------------------------------- */
119: /* 
120:    FormFunction - Evaluates nonlinear function, F(x).

122:    Input Parameters:
123: .  ts - the TS context
124: .  X - input vector
125: .  ptr - optional user-defined context, as set by SNESSetFunction()

127:    Output Parameter:
128: .  F - function vector
129:  */
130: int FormFunction(TS ts,double time,Vec X,Vec F,void *ptr)
131: {
132:   DA      da = (DA)ptr;
133:   int     ierr,i,j,Mx,My,xs,ys,xm,ym;
134:   double  two = 2.0,hx,hy,hxdhy,hydhx,sx,sy;
135:   Scalar  u,uxx,uyy,**x,**f;
136:   Vec     localX;

139:   DAGetLocalVector(da,&localX);
140:   DAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
141:                    PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

143:   hx     = 1.0/(double)(Mx-1); sx = 1.0/(hx*hx);
144:   hy     = 1.0/(double)(My-1); sy = 1.0/(hy*hy);
145:   hxdhy  = hx/hy;
146:   hydhx  = hy/hx;

148:   /*
149:      Scatter ghost points to local vector,using the 2-step process
150:         DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
151:      By placing code between these two statements, computations can be
152:      done while messages are in transition.
153:   */
154:   DAGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
155:   DAGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

157:   /*
158:      Get pointers to vector data
159:   */
160:   DAVecGetArray(da,localX,(void**)&x);
161:   DAVecGetArray(da,F,(void**)&f);

163:   /*
164:      Get local grid boundaries
165:   */
166:   DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);

168:   /*
169:      Compute function over the locally owned part of the grid
170:   */
171:   for (j=ys; j<ys+ym; j++) {
172:     for (i=xs; i<xs+xm; i++) {
173:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
174:         f[j][i] = x[j][i];
175:         continue;
176:       }
177:       u       = x[j][i];
178:       uxx     = (two*u - x[j][i-1] - x[j][i+1])*sx;
179:       uyy     = (two*u - x[j-1][i] - x[j+1][i])*sy;
180:       /*      f[j][i] = -(uxx + uyy); */
181:       f[j][i] = -u*(uxx + uyy) - (4.0 - 1.0)*((x[j][i+1] - x[j][i-1])*(x[j][i+1] - x[j][i-1])*.25*sx +
182:                                             (x[j+1][i] - x[j-1][i])*(x[j+1][i] - x[j-1][i])*.25*sy);
183:     }
184:   }

186:   /*
187:      Restore vectors
188:   */
189:   DAVecRestoreArray(da,localX,(void**)&x);
190:   DAVecRestoreArray(da,F,(void**)&f);
191:   DARestoreLocalVector(da,&localX);
192:   PetscLogFlops(11*ym*xm);
193:   return(0);
194: }

196: /* ------------------------------------------------------------------- */
197: int FormInitialSolution(DA da,Vec U)
198: {
199:   int     ierr,i,j,xs,ys,xm,ym,Mx,My;
200:   Scalar  **u;
201:   double  hx,hy,x,y,r;

204:   DAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
205:                    PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

207:   hx     = 1.0/(double)(Mx-1);
208:   hy     = 1.0/(double)(My-1);

210:   /*
211:      Get pointers to vector data
212:   */
213:   DAVecGetArray(da,U,(void**)&u);

215:   /*
216:      Get local grid boundaries
217:   */
218:   DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);

220:   /*
221:      Compute function over the locally owned part of the grid
222:   */
223:   for (j=ys; j<ys+ym; j++) {
224:     y = j*hy;
225:     for (i=xs; i<xs+xm; i++) {
226:       x = i*hx;
227:       r = PetscSqrtScalar((x-.5)*(x-.5) + (y-.5)*(y-.5));
228:       if (r < .125) {
229:         u[j][i] = PetscExpScalar(-30.0*r*r*r);
230:       } else {
231:         u[j][i] = 0.0;
232:       }
233:     }
234:   }

236:   /*
237:      Restore vectors
238:   */
239:   DAVecRestoreArray(da,U,(void**)&u);
240:   return(0);
241: }

243: int Monitor(TS ts,int step,double ptime,Vec v,void *ctx)
244: {
245:   int      ierr;
246:   double   norm;
247:   MPI_Comm comm;

250:   VecNorm(v,NORM_2,&norm);
251:   PetscObjectGetComm((PetscObject)ts,&comm);
252:   PetscPrintf(comm,"timestep %d time %g norm %gn",step,ptime,norm);
253:   return(0);
254: }