Actual source code: ex5.c

  2: static char help[] = "Bratu nonlinear PDE in 2d.\n\
  3: We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular\n\
  4: domain, using distributed arrays (DAs) 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: DA^using distributed arrays;
 12:    Concepts: IS coloirng types;
 13:    Processors: n
 14: T*/

 16: /* ------------------------------------------------------------------------

 18:     Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 19:     the partial differential equation
 20:   
 21:             -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
 22:   
 23:     with boundary conditions
 24:    
 25:              u = 0  for  x = 0, x = 1, y = 0, y = 1.
 26:   
 27:     A finite difference approximation with the usual 5-point stencil
 28:     is used to discretize the boundary value problem to obtain a nonlinear 
 29:     system of equations.

 31:     Program usage:  mpiexec -n <procs> ex5 [-help] [all PETSc options] 
 32:      e.g.,
 33:       ./ex5 -fd_jacobian -mat_fd_coloring_view_draw -draw_pause -1
 34:       mpiexec -n 2 ./ex5 -fd_jacobian_ghosted -log_summary

 36:   ------------------------------------------------------------------------- */

 38: /* 
 39:    Include "petscda.h" so that we can use distributed arrays (DAs).
 40:    Include "petscsnes.h" so that we can use SNES solvers.  Note that this
 41:    file automatically includes:
 42:      petsc.h       - base PETSc routines   petscvec.h - vectors
 43:      petscsys.h    - system routines       petscmat.h - matrices
 44:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 45:      petscviewer.h - viewers               petscpc.h  - preconditioners
 46:      petscksp.h   - linear solvers
 47: */
 48:  #include petscda.h
 49:  #include petscsnes.h

 51: /* 
 52:    User-defined application context - contains data needed by the 
 53:    application-provided call-back routines, FormJacobianLocal() and
 54:    FormFunctionLocal().
 55: */
 56: typedef struct {
 57:    DA          da;             /* distributed array data structure */
 58:    PassiveReal param;          /* test problem parameter */
 59: } AppCtx;

 61: /* 
 62:    User-defined routines
 63: */

 71: int main(int argc,char **argv)
 72: {
 73:   SNES                   snes;                 /* nonlinear solver */
 74:   Vec                    x,r;                  /* solution, residual vectors */
 75:   Mat                    A,J;                    /* Jacobian matrix */
 76:   AppCtx                 user;                 /* user-defined work context */
 77:   PetscInt               its;                  /* iterations for convergence */
 78:   PetscTruth             matlab_function = PETSC_FALSE;
 79:   PetscTruth             fd_jacobian = PETSC_FALSE,adic_jacobian=PETSC_FALSE,fd_jacobian_ghosted=PETSC_FALSE;
 80:   PetscTruth             adicmf_jacobian = PETSC_FALSE;
 81:   PetscErrorCode         ierr;
 82:   PetscReal              bratu_lambda_max = 6.81,bratu_lambda_min = 0.;
 83:   MatFDColoring          matfdcoloring = 0;
 84:   ISColoring             iscoloring;

 86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 87:      Initialize program
 88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 93:      Initialize problem parameters
 94:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 95:   user.param = 6.0;
 96:   PetscOptionsGetReal(PETSC_NULL,"-par",&user.param,PETSC_NULL);
 97:   if (user.param >= bratu_lambda_max || user.param <= bratu_lambda_min) {
 98:     SETERRQ(1,"Lambda is out of range");
 99:   }

101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102:      Create nonlinear solver context
103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
104:   SNESCreate(PETSC_COMM_WORLD,&snes);

106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
107:      Create distributed array (DA) to manage parallel grid and vectors
108:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
109:   DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,-4,-4,PETSC_DECIDE,PETSC_DECIDE,
110:                     1,1,PETSC_NULL,PETSC_NULL,&user.da);

112:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113:      Extract global vectors from DA; then duplicate for remaining
114:      vectors that are the same types
115:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
116:   DACreateGlobalVector(user.da,&x);
117:   VecDuplicate(x,&r);

119:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
120:      Create matrix data structure; set Jacobian evaluation routine

122:      Set Jacobian matrix data structure and default Jacobian evaluation
123:      routine. User can override with:
124:      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
125:                 (unless user explicitly sets preconditioner) 
126:      -snes_mf_operator : form preconditioning matrix as set by the user,
127:                          but use matrix-free approx for Jacobian-vector
128:                          products within Newton-Krylov method

130:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131:   /* J can be type of MATAIJ,MATBAIJ or MATSBAIJ */
132:   DAGetMatrix(user.da,MATAIJ,&J);
133: 
134:   A    = J;
135:   PetscOptionsGetTruth(PETSC_NULL,"-fd_jacobian",&fd_jacobian,0);
136:   PetscOptionsGetTruth(PETSC_NULL,"-fd_jacobian_ghosted",&fd_jacobian_ghosted,0);
137:   PetscOptionsGetTruth(PETSC_NULL,"-adic_jacobian",&adic_jacobian,0);
138:   PetscOptionsGetTruth(PETSC_NULL,"-adicmf_jacobian",&adicmf_jacobian,0);
139: #if defined(PETSC_HAVE_ADIC)
140:   if (adicmf_jacobian) {
141:     DASetLocalAdicMFFunction(user.da,admf_FormFunctionLocal);
142:     MatRegisterDAAD();
143:     MatCreateDAAD(user.da,&A);
144:     MatDAADSetSNES(A,snes);
145:     MatDAADSetCtx(A,&user);
146:   }
147: #endif

149:   if (fd_jacobian) {
150:     DAGetColoring(user.da,IS_COLORING_GLOBAL,&iscoloring);
151:     MatFDColoringCreate(J,iscoloring,&matfdcoloring);
152:     ISColoringDestroy(iscoloring);
153:     MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESDAFormFunction,&user);
154:     MatFDColoringSetFromOptions(matfdcoloring);
155:     SNESSetJacobian(snes,A,J,SNESDefaultComputeJacobianColor,matfdcoloring);
156:   } else if (fd_jacobian_ghosted) {
157:     DAGetColoring(user.da,IS_COLORING_GHOSTED,&iscoloring);
158:     MatFDColoringCreate(J,iscoloring,&matfdcoloring);
159:     ISColoringDestroy(iscoloring);
160:     MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESDAFormFunction,&user);
161:     MatFDColoringSetFromOptions(matfdcoloring);
162:     /* now, call a customized SNESDefaultComputeJacobianColor() */
163:     SNESSetJacobian(snes,A,J,MySNESDefaultComputeJacobianColor,matfdcoloring);
164: #if defined(PETSC_HAVE_ADIC)
165:   } else if (adic_jacobian) {
166:     DAGetColoring(user.da,IS_COLORING_GHOSTED,&iscoloring);
167:     MatSetColoring(J,iscoloring);
168:     ISColoringDestroy(iscoloring);
169:     SNESSetJacobian(snes,A,J,SNESDAComputeJacobianWithAdic,&user);
170: #endif
171:   } else {
172:     SNESSetJacobian(snes,A,J,SNESDAComputeJacobian,&user);
173:   }

175:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176:      Set local function evaluation routine
177:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
178:   DASetLocalFunction(user.da,(DALocalFunction1)FormFunctionLocal);
179:   DASetLocalJacobian(user.da,(DALocalFunction1)FormJacobianLocal);
180:   DASetLocalAdicFunction(user.da,ad_FormFunctionLocal);

182:   /* Decide which FormFunction to use */
183:   PetscOptionsGetTruth(PETSC_NULL,"-matlab_function",&matlab_function,0);

185:   SNESSetFunction(snes,r,SNESDAFormFunction,&user);
186: #if defined(PETSC_HAVE_MATLAB_ENGINE)
187:   if (matlab_function) {
188:     SNESSetFunction(snes,r,FormFunctionMatlab,&user);
189:   }
190: #endif

192:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193:      Customize nonlinear solver; set runtime options
194:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195:   SNESSetFromOptions(snes);

197:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198:      Evaluate initial guess
199:      Note: The user should initialize the vector, x, with the initial guess
200:      for the nonlinear solver prior to calling SNESSolve().  In particular,
201:      to employ an initial guess of zero, the user should explicitly set
202:      this vector to zero by calling VecSet().
203:   */

205:   {
206:     PetscTruth test_appctx = PETSC_FALSE;
207:     PetscOptionsGetTruth(PETSC_NULL,"-test_appctx",&test_appctx,0);
208:     if (test_appctx) {
209:       AppCtx *puser;
210:       SNESSetApplicationContext(snes,&user);
211:       SNESGetApplicationContext(snes,(void **)&puser);
212:       FormInitialGuess(puser,x);
213:     } else {
214:       FormInitialGuess(&user,x);
215:     }
216:   }

218:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
219:      Solve nonlinear system
220:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
221:   SNESSolve(snes,PETSC_NULL,x);
222:   SNESGetIterationNumber(snes,&its);

224:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
225:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
226:   PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %D\n",its);

228:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
229:      Free work space.  All PETSc objects should be destroyed when they
230:      are no longer needed.
231:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

233:   if (A != J) {
234:     MatDestroy(A);
235:   }
236:   MatDestroy(J);
237:   if (matfdcoloring) {
238:     MatFDColoringDestroy(matfdcoloring);
239:   }
240:   VecDestroy(x);
241:   VecDestroy(r);
242:   SNESDestroy(snes);
243:   DADestroy(user.da);
244:   PetscFinalize();

246:   return(0);
247: }
248: /* ------------------------------------------------------------------- */
251: /* 
252:    FormInitialGuess - Forms initial approximation.

254:    Input Parameters:
255:    user - user-defined application context
256:    X - vector

258:    Output Parameter:
259:    X - vector
260:  */
261: PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
262: {
263:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
265:   PetscReal      lambda,temp1,temp,hx,hy;
266:   PetscScalar    **x;

269:   DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
270:                    PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

272:   lambda = user->param;
273:   hx     = 1.0/(PetscReal)(Mx-1);
274:   hy     = 1.0/(PetscReal)(My-1);
275:   temp1  = lambda/(lambda + 1.0);

277:   /*
278:      Get a pointer to vector data.
279:        - For default PETSc vectors, VecGetArray() returns a pointer to
280:          the data array.  Otherwise, the routine is implementation dependent.
281:        - You MUST call VecRestoreArray() when you no longer need access to
282:          the array.
283:   */
284:   DAVecGetArray(user->da,X,&x);

286:   /*
287:      Get local grid boundaries (for 2-dimensional DA):
288:        xs, ys   - starting grid indices (no ghost points)
289:        xm, ym   - widths of local grid (no ghost points)

291:   */
292:   DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);

294:   /*
295:      Compute initial guess over the locally owned part of the grid
296:   */
297:   for (j=ys; j<ys+ym; j++) {
298:     temp = (PetscReal)(PetscMin(j,My-j-1))*hy;
299:     for (i=xs; i<xs+xm; i++) {
300:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
301:         /* boundary conditions are all zero Dirichlet */
302:         x[j][i] = 0.0;
303:       } else {
304:         x[j][i] = temp1*sqrt(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,temp));
305:       }
306:     }
307:   }

309:   /*
310:      Restore vector
311:   */
312:   DAVecRestoreArray(user->da,X,&x);

314:   return(0);
315: }
316: /* ------------------------------------------------------------------- */
319: /* 
320:    FormFunctionLocal - Evaluates nonlinear function, F(x).

322:        Process adiC(36): FormFunctionLocal

324:  */
325: PetscErrorCode FormFunctionLocal(DALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user)
326: {
328:   PetscInt       i,j;
329:   PetscReal      lambda,hx,hy,hxdhy,hydhx,sc;
330:   PetscScalar    u,uxx,uyy;


334:   lambda = user->param;
335:   hx     = 1.0/(PetscReal)(info->mx-1);
336:   hy     = 1.0/(PetscReal)(info->my-1);
337:   sc     = hx*hy*lambda;
338:   hxdhy  = hx/hy;
339:   hydhx  = hy/hx;
340:   /*
341:      Compute function over the locally owned part of the grid
342:   */
343:   for (j=info->ys; j<info->ys+info->ym; j++) {
344:     for (i=info->xs; i<info->xs+info->xm; i++) {
345:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
346:         f[j][i] = x[j][i];
347:       } else {
348:         u       = x[j][i];
349:         uxx     = (2.0*u - x[j][i-1] - x[j][i+1])*hydhx;
350:         uyy     = (2.0*u - x[j-1][i] - x[j+1][i])*hxdhy;
351:         f[j][i] = uxx + uyy - sc*PetscExpScalar(u);
352:       }
353:     }
354:   }

356:   PetscLogFlops(11*info->ym*info->xm);
357:   return(0);
358: }

362: /*
363:    FormJacobianLocal - Evaluates Jacobian matrix.
364: */
365: PetscErrorCode FormJacobianLocal(DALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
366: {
368:   PetscInt       i,j;
369:   MatStencil     col[5],row;
370:   PetscScalar    lambda,v[5],hx,hy,hxdhy,hydhx,sc;

373:   lambda = user->param;
374:   hx     = 1.0/(PetscReal)(info->mx-1);
375:   hy     = 1.0/(PetscReal)(info->my-1);
376:   sc     = hx*hy*lambda;
377:   hxdhy  = hx/hy;
378:   hydhx  = hy/hx;


381:   /* 
382:      Compute entries for the locally owned part of the Jacobian.
383:       - Currently, all PETSc parallel matrix formats are partitioned by
384:         contiguous chunks of rows across the processors. 
385:       - Each processor needs to insert only elements that it owns
386:         locally (but any non-local elements will be sent to the
387:         appropriate processor during matrix assembly). 
388:       - Here, we set all entries for a particular row at once.
389:       - We can set matrix entries either using either
390:         MatSetValuesLocal() or MatSetValues(), as discussed above.
391:   */
392:   for (j=info->ys; j<info->ys+info->ym; j++) {
393:     for (i=info->xs; i<info->xs+info->xm; i++) {
394:       row.j = j; row.i = i;
395:       /* boundary points */
396:       if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
397:         v[0] = 1.0;
398:         MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
399:       } else {
400:       /* interior grid points */
401:         v[0] = -hxdhy;                                           col[0].j = j - 1; col[0].i = i;
402:         v[1] = -hydhx;                                           col[1].j = j;     col[1].i = i-1;
403:         v[2] = 2.0*(hydhx + hxdhy) - sc*PetscExpScalar(x[j][i]); col[2].j = row.j; col[2].i = row.i;
404:         v[3] = -hydhx;                                           col[3].j = j;     col[3].i = i+1;
405:         v[4] = -hxdhy;                                           col[4].j = j + 1; col[4].i = i;
406:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
407:       }
408:     }
409:   }

411:   /* 
412:      Assemble matrix, using the 2-step process:
413:        MatAssemblyBegin(), MatAssemblyEnd().
414:   */
415:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
416:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
417:   /*
418:      Tell the matrix we will never add a new nonzero location to the
419:      matrix. If we do, it will generate an error.
420:   */
421:   MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
422:   return(0);
423: }

425: /*
426:       Variant of FormFunction() that computes the function in Matlab
427: */
428: #if defined(PETSC_HAVE_MATLAB_ENGINE)
429: PetscErrorCode FormFunctionMatlab(SNES snes,Vec X,Vec F,void *ptr)
430: {
431:   AppCtx         *user = (AppCtx*)ptr;
433:   PetscInt       Mx,My;
434:   PetscReal      lambda,hx,hy;
435:   Vec            localX,localF;
436:   MPI_Comm       comm;

439:   DAGetLocalVector(user->da,&localX);
440:   DAGetLocalVector(user->da,&localF);
441:   PetscObjectSetName((PetscObject)localX,"localX");
442:   PetscObjectSetName((PetscObject)localF,"localF");
443:   DAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
444:                    PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

446:   lambda = user->param;
447:   hx     = 1.0/(PetscReal)(Mx-1);
448:   hy     = 1.0/(PetscReal)(My-1);

450:   PetscObjectGetComm((PetscObject)snes,&comm);
451:   /*
452:      Scatter ghost points to local vector,using the 2-step process
453:         DAGlobalToLocalBegin(),DAGlobalToLocalEnd().
454:      By placing code between these two statements, computations can be
455:      done while messages are in transition.
456:   */
457:   DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
458:   DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
459:   PetscMatlabEnginePut(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localX);
460:   PetscMatlabEngineEvaluate(PETSC_MATLAB_ENGINE_(comm),"localF=ex5m(localX,%18.16e,%18.16e,%18.16e)",hx,hy,lambda);
461:   PetscMatlabEngineGet(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localF);

463:   /*
464:      Insert values into global vector
465:   */
466:   DALocalToGlobal(user->da,localF,INSERT_VALUES,F);
467:   DARestoreLocalVector(user->da,&localX);
468:   DARestoreLocalVector(user->da,&localF);
469:   return(0);
470: }
471: #endif

475: /*
476:   MySNESDefaultComputeJacobianColor - Computes the Jacobian using
477:     finite differences and coloring to exploit matrix sparsity. 
478:     It is customized from SNESDefaultComputeJacobianColor.
479:     The input global vector x1 is scattered to x1_local
480:     which then is passed into MatFDColoringApply() for reducing the
481:     VecScatterBingin/End.
482: */
483: PetscErrorCode MySNESDefaultComputeJacobianColor(SNES snes,Vec x1,Mat *J,Mat *B,MatStructure *flag,void *ctx)
484: {
485:   MatFDColoring  color = (MatFDColoring) ctx;
487:   Vec            f;
488:   PetscErrorCode (*ff)(void),(*fd)(void);
489:   void           *fctx;
490:   DA             da;
491:   Vec            x1_loc;

494:   *flag = SAME_NONZERO_PATTERN;
495:   SNESGetFunction(snes,&f,(PetscErrorCode (**)(SNES,Vec,Vec,void*))&ff,0);
496:   MatFDColoringGetFunction(color,&fd,&fctx);
497:   if (fd == ff) { /* reuse function value computed in SNES */
498:     MatFDColoringSetF(color,f);
499:   }
500:   /* Now, get x1_loc and scatter global x1 onto x1_loc */
501:   da = *(DA*)fctx;
502:   DAGetLocalVector(da,&x1_loc);
503:   DAGlobalToLocalBegin(da,x1,INSERT_VALUES,x1_loc);
504:   DAGlobalToLocalEnd(da,x1,INSERT_VALUES,x1_loc);
505:   MatFDColoringApply(*B,color,x1_loc,flag,snes);
506:   DARestoreLocalVector(da,&x1_loc);
507:   if (*J != *B) {
508:     MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
509:     MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
510:   }
511:   return(0);
512: }