Actual source code: ex14.c

petsc-master 2016-05-26
Report Typos and Errors
  2: static char help[] = "Bratu nonlinear PDE in 3d.\n\
  3: We solve the  Bratu (SFI - solid fuel ignition) problem in a 3D rectangular\n\
  4: domain, using distributed arrays (DMDAs) to partition the parallel grid.\n\
  5: The command line options include:\n\
  6:   -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\
  7:      problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)\n\n";

  9: /*T
 10:    Concepts: SNES^parallel Bratu example
 11:    Concepts: DMDA^using distributed arrays;
 12:    Processors: n
 13: T*/

 15: /* ------------------------------------------------------------------------

 17:     Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 18:     the partial differential equation

 20:             -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,

 22:     with boundary conditions

 24:              u = 0  for  x = 0, x = 1, y = 0, y = 1, z = 0, z = 1

 26:     A finite difference approximation with the usual 7-point stencil
 27:     is used to discretize the boundary value problem to obtain a nonlinear
 28:     system of equations.


 31:   ------------------------------------------------------------------------- */

 33: /*
 34:    Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
 35:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
 36:    file automatically includes:
 37:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 38:      petscmat.h - matrices
 39:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 40:      petscviewer.h - viewers               petscpc.h  - preconditioners
 41:      petscksp.h   - linear solvers
 42: */
 43: #include <petscdm.h>
 44: #include <petscdmda.h>
 45: #include <petscsnes.h>


 48: /*
 49:    User-defined application context - contains data needed by the
 50:    application-provided call-back routines, FormJacobian() and
 51:    FormFunction().
 52: */
 53: typedef struct {
 54:   PetscReal param;             /* test problem parameter */
 55:   DM        da;                /* distributed array data structure */
 56: } AppCtx;

 58: /*
 59:    User-defined routines
 60: */
 61: extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*),FormInitialGuess(AppCtx*,Vec);
 62: extern PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);

 66: int main(int argc,char **argv)
 67: {
 68:   SNES           snes;                         /* nonlinear solver */
 69:   Vec            x,r;                          /* solution, residual vectors */
 70:   Mat            J = NULL;                            /* Jacobian matrix */
 71:   AppCtx         user;                         /* user-defined work context */
 72:   PetscInt       its;                          /* iterations for convergence */
 73:   MatFDColoring  matfdcoloring = NULL;
 74:   PetscBool      matrix_free = PETSC_FALSE,coloring = PETSC_FALSE;
 76:   PetscReal      bratu_lambda_max = 6.81,bratu_lambda_min = 0.,fnorm;

 78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 79:      Initialize program
 80:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 82:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

 84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 85:      Initialize problem parameters
 86:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 87:   user.param = 6.0;
 88:   PetscOptionsGetReal(NULL,NULL,"-par",&user.param,NULL);
 89:   if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) SETERRQ(PETSC_COMM_SELF,1,"Lambda is out of range");

 91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 92:      Create nonlinear solver context
 93:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 94:   SNESCreate(PETSC_COMM_WORLD,&snes);

 96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 97:      Create distributed array (DMDA) to manage parallel grid and vectors
 98:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 99:   DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-4,-4,-4,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,NULL,&user.da);

101:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102:      Extract global vectors from DMDA; then duplicate for remaining
103:      vectors that are the same types
104:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105:   DMCreateGlobalVector(user.da,&x);
106:   VecDuplicate(x,&r);

108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109:      Set function evaluation routine and vector
110:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
111:   SNESSetFunction(snes,r,FormFunction,(void*)&user);

113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114:      Create matrix data structure; set Jacobian evaluation routine

116:      Set Jacobian matrix data structure and default Jacobian evaluation
117:      routine. User can override with:
118:      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
119:                 (unless user explicitly sets preconditioner)
120:      -snes_mf_operator : form preconditioning matrix as set by the user,
121:                          but use matrix-free approx for Jacobian-vector
122:                          products within Newton-Krylov method
123:      -fdcoloring : using finite differences with coloring to compute the Jacobian

125:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
126:   PetscOptionsGetBool(NULL,NULL,"-snes_mf",&matrix_free,NULL);
127:   PetscOptionsGetBool(NULL,NULL,"-fdcoloring",&coloring,NULL);
128:   if (!matrix_free) {
129:     DMSetMatType(user.da,MATAIJ);
130:     DMCreateMatrix(user.da,&J);
131:     if (coloring) {
132:       ISColoring iscoloring;
133:       DMCreateColoring(user.da,IS_COLORING_GLOBAL,&iscoloring);
134:       MatFDColoringCreate(J,iscoloring,&matfdcoloring);
135:       MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))FormFunction,&user);
136:       MatFDColoringSetFromOptions(matfdcoloring);
137:       MatFDColoringSetUp(J,iscoloring,matfdcoloring);
138:       SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);
139:       ISColoringDestroy(&iscoloring);
140:     } else {
141:       SNESSetJacobian(snes,J,J,FormJacobian,&user);
142:     }
143:   }

145:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146:      Customize nonlinear solver; set runtime options
147:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
148:   SNESSetDM(snes,user.da);
149:   SNESSetFromOptions(snes);

151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152:      Evaluate initial guess
153:      Note: The user should initialize the vector, x, with the initial guess
154:      for the nonlinear solver prior to calling SNESSolve().  In particular,
155:      to employ an initial guess of zero, the user should explicitly set
156:      this vector to zero by calling VecSet().
157:   */
158:   FormInitialGuess(&user,x);

160:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161:      Solve nonlinear system
162:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
163:   SNESSolve(snes,NULL,x);
164:   SNESGetIterationNumber(snes,&its);

166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167:      Explicitly check norm of the residual of the solution
168:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169:   FormFunction(snes,x,r,(void*)&user);
170:   VecNorm(r,NORM_2,&fnorm);
171:   PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D fnorm %g\n",its,(double)fnorm);

173:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174:      Free work space.  All PETSc objects should be destroyed when they
175:      are no longer needed.
176:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

178:   MatDestroy(&J);
179:   VecDestroy(&x);
180:   VecDestroy(&r);
181:   SNESDestroy(&snes);
182:   DMDestroy(&user.da);
183:   MatFDColoringDestroy(&matfdcoloring);
184:   PetscFinalize();
185:   return ierr;
186: }
187: /* ------------------------------------------------------------------- */
190: /*
191:    FormInitialGuess - Forms initial approximation.

193:    Input Parameters:
194:    user - user-defined application context
195:    X - vector

197:    Output Parameter:
198:    X - vector
199:  */
200: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
201: {
202:   PetscInt       i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
204:   PetscReal      lambda,temp1,hx,hy,hz,tempk,tempj;
205:   PetscScalar    ***x;

208:   DMDAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

210:   lambda = user->param;
211:   hx     = 1.0/(PetscReal)(Mx-1);
212:   hy     = 1.0/(PetscReal)(My-1);
213:   hz     = 1.0/(PetscReal)(Mz-1);
214:   temp1  = lambda/(lambda + 1.0);

216:   /*
217:      Get a pointer to vector data.
218:        - For default PETSc vectors, VecGetArray() returns a pointer to
219:          the data array.  Otherwise, the routine is implementation dependent.
220:        - You MUST call VecRestoreArray() when you no longer need access to
221:          the array.
222:   */
223:   DMDAVecGetArray(user->da,X,&x);

225:   /*
226:      Get local grid boundaries (for 3-dimensional DMDA):
227:        xs, ys, zs   - starting grid indices (no ghost points)
228:        xm, ym, zm   - widths of local grid (no ghost points)

230:   */
231:   DMDAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);

233:   /*
234:      Compute initial guess over the locally owned part of the grid
235:   */
236:   for (k=zs; k<zs+zm; k++) {
237:     tempk = (PetscReal)(PetscMin(k,Mz-k-1))*hz;
238:     for (j=ys; j<ys+ym; j++) {
239:       tempj = PetscMin((PetscReal)(PetscMin(j,My-j-1))*hy,tempk);
240:       for (i=xs; i<xs+xm; i++) {
241:         if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
242:           /* boundary conditions are all zero Dirichlet */
243:           x[k][j][i] = 0.0;
244:         } else {
245:           x[k][j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,tempj));
246:         }
247:       }
248:     }
249:   }

251:   /*
252:      Restore vector
253:   */
254:   DMDAVecRestoreArray(user->da,X,&x);
255:   return(0);
256: }
257: /* ------------------------------------------------------------------- */
260: /*
261:    FormFunction - Evaluates nonlinear function, F(x).

263:    Input Parameters:
264: .  snes - the SNES context
265: .  X - input vector
266: .  ptr - optional user-defined context, as set by SNESSetFunction()

268:    Output Parameter:
269: .  F - function vector
270:  */
271: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ptr)
272: {
273:   AppCtx         *user = (AppCtx*)ptr;
275:   PetscInt       i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
276:   PetscReal      two = 2.0,lambda,hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc;
277:   PetscScalar    u_north,u_south,u_east,u_west,u_up,u_down,u,u_xx,u_yy,u_zz,***x,***f;
278:   Vec            localX;
279:   DM             da;

282:   SNESGetDM(snes,&da);
283:   DMGetLocalVector(da,&localX);
284:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

286:   lambda  = user->param;
287:   hx      = 1.0/(PetscReal)(Mx-1);
288:   hy      = 1.0/(PetscReal)(My-1);
289:   hz      = 1.0/(PetscReal)(Mz-1);
290:   sc      = hx*hy*hz*lambda;
291:   hxhzdhy = hx*hz/hy;
292:   hyhzdhx = hy*hz/hx;
293:   hxhydhz = hx*hy/hz;

295:   /*
296:      Scatter ghost points to local vector,using the 2-step process
297:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
298:      By placing code between these two statements, computations can be
299:      done while messages are in transition.
300:   */
301:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
302:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

304:   /*
305:      Get pointers to vector data
306:   */
307:   DMDAVecGetArrayRead(da,localX,&x);
308:   DMDAVecGetArray(da,F,&f);

310:   /*
311:      Get local grid boundaries
312:   */
313:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

315:   /*
316:      Compute function over the locally owned part of the grid
317:   */
318:   for (k=zs; k<zs+zm; k++) {
319:     for (j=ys; j<ys+ym; j++) {
320:       for (i=xs; i<xs+xm; i++) {
321:         if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
322:           f[k][j][i] = x[k][j][i];
323:         } else {
324:           u          = x[k][j][i];
325:           u_east     = x[k][j][i+1];
326:           u_west     = x[k][j][i-1];
327:           u_north    = x[k][j+1][i];
328:           u_south    = x[k][j-1][i];
329:           u_up       = x[k+1][j][i];
330:           u_down     = x[k-1][j][i];
331:           u_xx       = (-u_east + two*u - u_west)*hyhzdhx;
332:           u_yy       = (-u_north + two*u - u_south)*hxhzdhy;
333:           u_zz       = (-u_up + two*u - u_down)*hxhydhz;
334:           f[k][j][i] = u_xx + u_yy + u_zz - sc*PetscExpScalar(u);
335:         }
336:       }
337:     }
338:   }

340:   /*
341:      Restore vectors
342:   */
343:   DMDAVecRestoreArrayRead(da,localX,&x);
344:   DMDAVecRestoreArray(da,F,&f);
345:   DMRestoreLocalVector(da,&localX);
346:   PetscLogFlops(11.0*ym*xm);
347:   return(0);
348: }
349: /* ------------------------------------------------------------------- */
352: /*
353:    FormJacobian - Evaluates Jacobian matrix.

355:    Input Parameters:
356: .  snes - the SNES context
357: .  x - input vector
358: .  ptr - optional user-defined context, as set by SNESSetJacobian()

360:    Output Parameters:
361: .  A - Jacobian matrix
362: .  B - optionally different preconditioning matrix

364: */
365: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat J,Mat jac,void *ptr)
366: {
367:   AppCtx         *user = (AppCtx*)ptr;  /* user-defined application context */
368:   Vec            localX;
370:   PetscInt       i,j,k,Mx,My,Mz;
371:   MatStencil     col[7],row;
372:   PetscInt       xs,ys,zs,xm,ym,zm;
373:   PetscScalar    lambda,v[7],hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc,***x;
374:   DM             da;

377:   SNESGetDM(snes,&da);
378:   DMGetLocalVector(da,&localX);
379:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

381:   lambda  = user->param;
382:   hx      = 1.0/(PetscReal)(Mx-1);
383:   hy      = 1.0/(PetscReal)(My-1);
384:   hz      = 1.0/(PetscReal)(Mz-1);
385:   sc      = hx*hy*hz*lambda;
386:   hxhzdhy = hx*hz/hy;
387:   hyhzdhx = hy*hz/hx;
388:   hxhydhz = hx*hy/hz;

390:   /*
391:      Scatter ghost points to local vector, using the 2-step process
392:         DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
393:      By placing code between these two statements, computations can be
394:      done while messages are in transition.
395:   */
396:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
397:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

399:   /*
400:      Get pointer to vector data
401:   */
402:   DMDAVecGetArrayRead(da,localX,&x);

404:   /*
405:      Get local grid boundaries
406:   */
407:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

409:   /*
410:      Compute entries for the locally owned part of the Jacobian.
411:       - Currently, all PETSc parallel matrix formats are partitioned by
412:         contiguous chunks of rows across the processors.
413:       - Each processor needs to insert only elements that it owns
414:         locally (but any non-local elements will be sent to the
415:         appropriate processor during matrix assembly).
416:       - Here, we set all entries for a particular row at once.
417:       - We can set matrix entries either using either
418:         MatSetValuesLocal() or MatSetValues(), as discussed above.
419:   */
420:   for (k=zs; k<zs+zm; k++) {
421:     for (j=ys; j<ys+ym; j++) {
422:       for (i=xs; i<xs+xm; i++) {
423:         row.k = k; row.j = j; row.i = i;
424:         /* boundary points */
425:         if (i == 0 || j == 0 || k == 0|| i == Mx-1 || j == My-1 || k == Mz-1) {
426:           v[0] = 1.0;
427:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
428:         } else {
429:           /* interior grid points */
430:           v[0] = -hxhydhz; col[0].k=k-1;col[0].j=j;  col[0].i = i;
431:           v[1] = -hxhzdhy; col[1].k=k;  col[1].j=j-1;col[1].i = i;
432:           v[2] = -hyhzdhx; col[2].k=k;  col[2].j=j;  col[2].i = i-1;
433:           v[3] = 2.0*(hyhzdhx+hxhzdhy+hxhydhz)-sc*PetscExpScalar(x[k][j][i]);col[3].k=row.k;col[3].j=row.j;col[3].i = row.i;
434:           v[4] = -hyhzdhx; col[4].k=k;  col[4].j=j;  col[4].i = i+1;
435:           v[5] = -hxhzdhy; col[5].k=k;  col[5].j=j+1;col[5].i = i;
436:           v[6] = -hxhydhz; col[6].k=k+1;col[6].j=j;  col[6].i = i;
437:           MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
438:         }
439:       }
440:     }
441:   }
442:   DMDAVecRestoreArrayRead(da,localX,&x);
443:   DMRestoreLocalVector(da,&localX);

445:   /*
446:      Assemble matrix, using the 2-step process:
447:        MatAssemblyBegin(), MatAssemblyEnd().
448:   */
449:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
450:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);

452:   /*
453:      Normally since the matrix has already been assembled above; this
454:      would do nothing. But in the matrix free mode -snes_mf_operator
455:      this tells the "matrix-free" matrix that a new linear system solve
456:      is about to be done.
457:   */

459:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
460:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);

462:   /*
463:      Tell the matrix we will never add a new nonzero location to the
464:      matrix. If we do, it will generate an error.
465:   */
466:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
467:   return(0);
468: }