Actual source code: ex7.c

  1: /*$Id: ex7.c,v 1.7 2001/08/21 21:04:28 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,PetscReal,Vec,Vec,void*),FormInitialSolution(DA,Vec);
 26: extern int Monitor(TS,int,PetscReal,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:   PetscReal              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);
 61:   TSSetProblemType(ts,TS_NONLINEAR);
 62:   TSSetRHSFunction(ts,FormFunction,da);


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

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

 76:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 77:   DAGetColoring(da,IS_COLORING_LOCAL,&iscoloring);
 78:   DAGetMatrix(da,MATMPIAIJ,&J);
 79:   MatFDColoringCreate(J,iscoloring,&matfdcoloring);
 80:   ISColoringDestroy(iscoloring);
 81:   MatFDColoringSetFunction(matfdcoloring,(int (*)(void))FormFunction,da);
 82:   MatFDColoringSetFromOptions(matfdcoloring);
 83:   TSSetRHSJacobian(ts,J,J,TSDefaultComputeJacobianColor,matfdcoloring);
 84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 85:      Customize nonlinear solver; set runtime options
 86:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 87:   TSSetInitialTimeStep(ts,0.0,.0001);
 88:   TSSetType(ts,TS_BEULER);
 89:   TSSetDuration(ts,100,1.0);
 90:   TSSetFromOptions(ts);
 91:   TSSetMonitor(ts,Monitor,0,0);

 93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 94:      Set initial conditions
 95:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 96:   FormInitialSolution(da,x);

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


105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
106:      Free work space.  All PETSc objects should be destroyed when they
107:      are no longer needed.
108:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

118:   return(0);
119: }
120: /* ------------------------------------------------------------------- */
121: /* 
122:    FormFunction - Evaluates nonlinear function, F(x).

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

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

141:   DAGetLocalVector(da,&localX);
142:   DAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
143:                    PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

145:   hx     = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
146:   hy     = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
147:   hxdhy  = hx/hy;
148:   hydhx  = hy/hx;

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

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

165:   /*
166:      Get local grid boundaries
167:   */
168:   DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);

170:   /*
171:      Compute function over the locally owned part of the grid
172:   */
173:   for (j=ys; j<ys+ym; j++) {
174:     for (i=xs; i<xs+xm; i++) {
175:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
176:         f[j][i] = x[j][i];
177:         continue;
178:       }
179:       u       = x[j][i];
180:       uxx     = (two*u - x[j][i-1] - x[j][i+1])*sx;
181:       uyy     = (two*u - x[j-1][i] - x[j+1][i])*sy;
182:       /*      f[j][i] = -(uxx + uyy); */
183:       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 +
184:                                             (x[j+1][i] - x[j-1][i])*(x[j+1][i] - x[j-1][i])*.25*sy);
185:     }
186:   }

188:   /*
189:      Restore vectors
190:   */
191:   DAVecRestoreArray(da,localX,(void**)&x);
192:   DAVecRestoreArray(da,F,(void**)&f);
193:   DARestoreLocalVector(da,&localX);
194:   PetscLogFlops(11*ym*xm);
195:   return(0);
196: }

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

206:   DAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
207:                    PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

209:   hx     = 1.0/(PetscReal)(Mx-1);
210:   hy     = 1.0/(PetscReal)(My-1);

212:   /*
213:      Get pointers to vector data
214:   */
215:   DAVecGetArray(da,U,(void**)&u);

217:   /*
218:      Get local grid boundaries
219:   */
220:   DAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);

222:   /*
223:      Compute function over the locally owned part of the grid
224:   */
225:   for (j=ys; j<ys+ym; j++) {
226:     y = j*hy;
227:     for (i=xs; i<xs+xm; i++) {
228:       x = i*hx;
229:       r = PetscSqrtScalar((x-.5)*(x-.5) + (y-.5)*(y-.5));
230:       if (r < .125) {
231:         u[j][i] = PetscExpScalar(-30.0*r*r*r);
232:       } else {
233:         u[j][i] = 0.0;
234:       }
235:     }
236:   }

238:   /*
239:      Restore vectors
240:   */
241:   DAVecRestoreArray(da,U,(void**)&u);
242:   return(0);
243: }

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

252:   VecNorm(v,NORM_2,&norm);
253:   PetscObjectGetComm((PetscObject)ts,&comm);
254:   PetscPrintf(comm,"timestep %d time %g norm %gn",step,ptime,norm);
255:   return(0);
256: }