Actual source code: ex7.c

petsc-3.5.2 2014-09-08
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  2: static char help[] = "Nonlinear, time-dependent PDE in 2d.\n";


  5: /*
  6:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
  7:    Include "petscts.h" so that we can use SNES solvers.  Note that this
  8:    file automatically includes:
  9:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 10:      petscmat.h - matrices
 11:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 12:      petscviewer.h - viewers               petscpc.h  - preconditioners
 13:      petscksp.h   - linear solvers
 14: */
 15: #include <petscdm.h>
 16: #include <petscdmda.h>
 17: #include <petscts.h>


 20: /*
 21:    User-defined routines
 22: */
 23: extern PetscErrorCode FormFunction(TS,PetscReal,Vec,Vec,void*),FormInitialSolution(DM,Vec);
 24: extern PetscErrorCode MyTSMonitor(TS,PetscInt,PetscReal,Vec,void*);
 25: extern PetscErrorCode MySNESMonitor(SNES,PetscInt,PetscReal,void*);

 29: int main(int argc,char **argv)
 30: {
 31:   TS             ts;                         /* time integrator */
 32:   SNES           snes;
 33:   Vec            x,r;                        /* solution, residual vectors */
 34:   PetscInt       maxsteps = 100;             /* iterations for convergence */
 36:   DM             da;

 38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 39:      Initialize program
 40:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 41:   PetscInitialize(&argc,&argv,(char*)0,help);

 43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 44:      Create distributed array (DMDA) to manage parallel grid and vectors
 45:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 46:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-8,-8,PETSC_DECIDE,PETSC_DECIDE,
 47:                       1,1,NULL,NULL,&da);

 49:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 50:      Extract global vectors from DMDA; then duplicate for remaining
 51:      vectors that are the same types
 52:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 53:   DMCreateGlobalVector(da,&x);
 54:   VecDuplicate(x,&r);

 56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 57:      Create timestepping solver context
 58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 59:   TSCreate(PETSC_COMM_WORLD,&ts);
 60:   TSSetProblemType(ts,TS_NONLINEAR);
 61:   TSSetRHSFunction(ts,NULL,FormFunction,da);

 63:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 64:      Create matrix data structure; set Jacobian evaluation routine

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

 74:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 76:   TSSetDuration(ts,maxsteps,1.0);
 77:   TSMonitorSet(ts,MyTSMonitor,0,0);
 78:   TSSetDM(ts,da);
 79:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 80:      Customize nonlinear solver
 81:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 82:   TSSetType(ts,TSBEULER);
 83:   TSGetSNES(ts,&snes);
 84:   SNESMonitorSet(snes,MySNESMonitor,NULL,NULL);

 86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 87:      Set initial conditions
 88:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 89:   FormInitialSolution(da,x);
 90:   TSSetInitialTimeStep(ts,0.0,.0001);
 91:   TSSetSolution(ts,x);

 93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 94:      Set runtime options
 95:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 96:   TSSetFromOptions(ts);

 98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 99:      Solve nonlinear system
100:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101:   TSSolve(ts,x);

103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104:      Free work space.  All PETSc objects should be destroyed when they
105:      are no longer needed.
106:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
107:   VecDestroy(&x);
108:   VecDestroy(&r);
109:   TSDestroy(&ts);
110:   DMDestroy(&da);

112:   PetscFinalize();
113:   return(0);
114: }
115: /* ------------------------------------------------------------------- */
118: /*
119:    FormFunction - Evaluates nonlinear function, F(x).

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

126:    Output Parameter:
127: .  F - function vector
128:  */
129: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
130: {
131:   DM             da;
133:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
134:   PetscReal      two = 2.0,hx,hy,sx,sy;
135:   PetscScalar    u,uxx,uyy,**x,**f;
136:   Vec            localX;

139:   TSGetDM(ts,&da);
140:   DMGetLocalVector(da,&localX);
141:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
142:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

144:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
145:   hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);

147:   /*
148:      Scatter ghost points to local vector,using the 2-step process
149:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
150:      By placing code between these two statements, computations can be
151:      done while messages are in transition.
152:   */
153:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
154:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

156:   /*
157:      Get pointers to vector data
158:   */
159:   DMDAVecGetArray(da,localX,&x);
160:   DMDAVecGetArray(da,F,&f);

162:   /*
163:      Get local grid boundaries
164:   */
165:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

167:   /*
168:      Compute function over the locally owned part of the grid
169:   */
170:   for (j=ys; j<ys+ym; j++) {
171:     for (i=xs; i<xs+xm; i++) {
172:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
173:         f[j][i] = x[j][i];
174:         continue;
175:       }
176:       u   = x[j][i];
177:       uxx = (two*u - x[j][i-1] - x[j][i+1])*sx;
178:       uyy = (two*u - x[j-1][i] - x[j+1][i])*sy;
179:       /*      f[j][i] = -(uxx + uyy); */
180:       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 +
181:                                               (x[j+1][i] - x[j-1][i])*(x[j+1][i] - x[j-1][i])*.25*sy);
182:     }
183:   }

185:   /*
186:      Restore vectors
187:   */
188:   DMDAVecRestoreArray(da,localX,&x);
189:   DMDAVecRestoreArray(da,F,&f);
190:   DMRestoreLocalVector(da,&localX);
191:   PetscLogFlops(11.0*ym*xm);
192:   return(0);
193: }

195: /* ------------------------------------------------------------------- */
198: PetscErrorCode FormInitialSolution(DM da,Vec U)
199: {
201:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
202:   PetscScalar    **u;
203:   PetscReal      hx,hy,x,y,r;

206:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
207:                      PETSC_IGNORE,PETSC_IGNORE,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:   DMDAVecGetArray(da,U,&u);

217:   /*
218:      Get local grid boundaries
219:   */
220:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,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 = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
230:       if (r < .125) u[j][i] = PetscExpReal(-30.0*r*r*r);
231:       else          u[j][i] = 0.0;
232:     }
233:   }

235:   /*
236:      Restore vectors
237:   */
238:   DMDAVecRestoreArray(da,U,&u);
239:   return(0);
240: }

244: PetscErrorCode MyTSMonitor(TS ts,PetscInt step,PetscReal ptime,Vec v,void *ctx)
245: {
247:   PetscReal      norm;
248:   MPI_Comm       comm;

251:   VecNorm(v,NORM_2,&norm);
252:   PetscObjectGetComm((PetscObject)ts,&comm);
253:   PetscPrintf(comm,"timestep %D time %g norm %g\n",step,(double)ptime,(double)norm);
254:   return(0);
255: }

259: /*
260:    MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
261:    Input Parameters:
262:      snes - the SNES context
263:      its - iteration number
264:      fnorm - 2-norm function value (may be estimated)
265:      ctx - optional user-defined context for private data for the
266:          monitor routine, as set by SNESMonitorSet()
267:  */
268: PetscErrorCode MySNESMonitor(SNES snes,PetscInt its,PetscReal fnorm,void *ctx)
269: {

273:   SNESMonitorDefaultShort(snes,its,fnorm,ctx);
274:   return(0);
275: }