Actual source code: ex14f.F

petsc-master 2014-12-19
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  1: !
  2: !
  3: !  Solves a nonlinear system in parallel with a user-defined
  4: !  Newton method that uses KSP to solve the linearized Newton sytems.  This solver
  5: !  is a very simplistic inexact Newton method.  The intent of this code is to
  6: !  demonstrate the repeated solution of linear sytems with the same nonzero pattern.
  7: !
  8: !  This is NOT the recommended approach for solving nonlinear problems with PETSc!
  9: !  We urge users to employ the SNES component for solving nonlinear problems whenever
 10: !  possible, as it offers many advantages over coding nonlinear solvers independently.
 11: !
 12: !  We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
 13: !  domain, using distributed arrays (DMDAs) to partition the parallel grid.
 14: !
 15: !  The command line options include:
 16: !  -par <parameter>, where <parameter> indicates the problem's nonlinearity
 17: !     problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)
 18: !  -mx <xg>, where <xg> = number of grid points in the x-direction
 19: !  -my <yg>, where <yg> = number of grid points in the y-direction
 20: !  -Nx <npx>, where <npx> = number of processors in the x-direction
 21: !  -Ny <npy>, where <npy> = number of processors in the y-direction
 22: !  -mf use matrix free for matrix vector product
 23: !
 24: !/*T
 25: !   Concepts: KSP^writing a user-defined nonlinear solver
 26: !   Concepts: DMDA^using distributed arrays
 27: !   Processors: n
 28: !T*/
 29: !  ------------------------------------------------------------------------
 30: !
 31: !    Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 32: !    the partial differential equation
 33: !
 34: !            -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
 35: !
 36: !    with boundary conditions
 37: !
 38: !             u = 0  for  x = 0, x = 1, y = 0, y = 1.
 39: !
 40: !    A finite difference approximation with the usual 5-point stencil
 41: !    is used to discretize the boundary value problem to obtain a nonlinear
 42: !    system of equations.
 43: !
 44: !    The SNES version of this problem is:  snes/examples/tutorials/ex5f.F
 45: !
 46: !  -------------------------------------------------------------------------

 48:       program main
 49:       implicit none

 51: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 52: !                    Include files
 53: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 54: !
 55: !     petscsys.h       - base PETSc routines   petscvec.h - vectors
 56: !     petscmat.h - matrices
 57: !     petscis.h     - index sets            petscksp.h - Krylov subspace methods
 58: !     petscviewer.h - viewers               petscpc.h  - preconditioners

 60: #include <finclude/petscsys.h>
 61: #include <finclude/petscis.h>
 62: #include <finclude/petscvec.h>
 63: #include <finclude/petscmat.h>
 64: #include <finclude/petscpc.h>
 65: #include <finclude/petscksp.h>
 66: #include <finclude/petscdm.h>
 67: #include <finclude/petscdmda.h>

 69:       MPI_Comm comm
 70:       Vec      X,Y,F,localX
 71:       Mat      J,B
 72:       DM       da
 73:       KSP      ksp

 75:       PetscInt  Nx,Ny,N,mx,my,ifive,ithree
 76:       PetscBool  flg,nooutput,usemf
 77:       common   /mycommon/ mx,my,B,localX,da
 78: !
 79: !
 80: !      This is the routine to use for matrix-free approach
 81: !
 82:       external mymult

 84: !     --------------- Data to define nonlinear solver --------------
 85:       PetscReal   rtol,ttol
 86:       PetscReal   fnorm,ynorm,xnorm
 87:       PetscInt            max_nonlin_its,one
 88:       PetscInt            lin_its
 89:       PetscInt           i,m
 90:       PetscScalar        mone
 91:       PetscErrorCode ierr

 93:       mone           = -1.d0
 94:       rtol           = 1.d-8
 95:       max_nonlin_its = 10
 96:       one            = 1
 97:       ifive          = 5
 98:       ithree         = 3

100:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
101:       comm = PETSC_COMM_WORLD

103: !  Initialize problem parameters

105: !
106:       mx = 4
107:       my = 4
108:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-mx',mx,flg,ierr)
109:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-my',my,flg,ierr)
110:       N = mx*my

112:       nooutput = .false.
113:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-no_output',       &
114:      &     nooutput,ierr)

116: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117: !     Create linear solver context
118: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

120:       call KSPCreate(comm,ksp,ierr)

122: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
123: !     Create vector data structures
124: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

126: !
127: !  Create distributed array (DMDA) to manage parallel grid and vectors
128: !
129:       Nx = PETSC_DECIDE
130:       Ny = PETSC_DECIDE
131:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-Nx',Nx,flg,ierr)
132:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-Ny',Ny,flg,ierr)
133:       call DMDACreate2d(comm,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,         &
134:      &     DMDA_STENCIL_STAR,mx,my,Nx,Ny,one,one,                        &
135:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)

137: !
138: !  Extract global and local vectors from DMDA then duplicate for remaining
139: !  vectors that are the same types
140: !
141:        call DMCreateGlobalVector(da,X,ierr)
142:        call DMCreateLocalVector(da,localX,ierr)
143:        call VecDuplicate(X,F,ierr)
144:        call VecDuplicate(X,Y,ierr)


147: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: !     Create matrix data structure for Jacobian
149: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: !
151: !     Note:  For the parallel case, vectors and matrices MUST be partitioned
152: !     accordingly.  When using distributed arrays (DMDAs) to create vectors,
153: !     the DMDAs determine the problem partitioning.  We must explicitly
154: !     specify the local matrix dimensions upon its creation for compatibility
155: !     with the vector distribution.
156: !
157: !     Note: Here we only approximately preallocate storage space for the
158: !     Jacobian.  See the users manual for a discussion of better techniques
159: !     for preallocating matrix memory.
160: !
161:       call VecGetLocalSize(X,m,ierr)
162:       call MatCreateAIJ(comm,m,m,N,N,ifive,PETSC_NULL_INTEGER,ithree,         &
163:      &     PETSC_NULL_INTEGER,B,ierr)

165: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166: !     if usemf is on then matrix vector product is done via matrix free
167: !     approach. Note this is just an example, and not realistic because
168: !     we still use the actual formed matrix, but in reality one would
169: !     provide their own subroutine that would directly do the matrix
170: !     vector product and not call MatMult()
171: !     Note: we put B into a common block so it will be visible to the
172: !     mymult() routine
173:       usemf = .false.
174:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-mf',usemf,ierr)
175:       if (usemf) then
176:          call MatCreateShell(comm,m,m,N,N,PETSC_NULL_INTEGER,J,ierr)
177:          call MatShellSetOperation(J,MATOP_MULT,mymult,ierr)
178:       else
179: !        If not doing matrix free then matrix operator, J,  and matrix used
180: !        to construct preconditioner, B, are the same
181:         J = B
182:       endif

184: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: !     Customize linear solver set runtime options
186: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187: !
188: !     Set runtime options (e.g., -ksp_monitor -ksp_rtol <rtol> -ksp_type <type>)
189: !
190:        call KSPSetFromOptions(ksp,ierr)

192: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: !     Evaluate initial guess
194: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

196:        call FormInitialGuess(X,ierr)
197:        call ComputeFunction(X,F,ierr)
198:        call VecNorm(F,NORM_2,fnorm,ierr)
199:        ttol = fnorm*rtol
200:        if (.not. nooutput) then
201:          print*, 'Initial function norm ',fnorm
202:        endif

204: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205: !     Solve nonlinear system with a user-defined method
206: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

208: !  This solver is a very simplistic inexact Newton method, with no
209: !  no damping strategies or bells and whistles. The intent of this code
210: !  is merely to demonstrate the repeated solution with KSP of linear
211: !  sytems with the same nonzero structure.
212: !
213: !  This is NOT the recommended approach for solving nonlinear problems
214: !  with PETSc!  We urge users to employ the SNES component for solving
215: !  nonlinear problems whenever possible with application codes, as it
216: !  offers many advantages over coding nonlinear solvers independently.

218:        do 10 i=0,max_nonlin_its

220: !  Compute the Jacobian matrix.  See the comments in this routine for
221: !  important information about setting the flag mat_flag.

223:          call ComputeJacobian(X,B,ierr)

225: !  Solve J Y = F, where J is the Jacobian matrix.
226: !    - First, set the KSP linear operators.  Here the matrix that
227: !      defines the linear system also serves as the preconditioning
228: !      matrix.
229: !    - Then solve the Newton system.

231:          call KSPSetOperators(ksp,J,B,ierr)
232:          call KSPSolve(ksp,F,Y,ierr)

234: !  Compute updated iterate

236:          call VecNorm(Y,NORM_2,ynorm,ierr)
237:          call VecAYPX(Y,mone,X,ierr)
238:          call VecCopy(Y,X,ierr)
239:          call VecNorm(X,NORM_2,xnorm,ierr)
240:          call KSPGetIterationNumber(ksp,lin_its,ierr)
241:          if (.not. nooutput) then
242:            print*,'linear solve iterations = ',lin_its,' xnorm = ',     &
243:      &         xnorm,' ynorm = ',ynorm
244:          endif

246: !  Evaluate nonlinear function at new location

248:          call ComputeFunction(X,F,ierr)
249:          call VecNorm(F,NORM_2,fnorm,ierr)
250:          if (.not. nooutput) then
251:            print*, 'Iteration ',i+1,' function norm',fnorm
252:          endif

254: !  Test for convergence

256:        if (fnorm .le. ttol) then
257:          if (.not. nooutput) then
258:            print*,'Converged: function norm ',fnorm,' tolerance ',ttol
259:          endif
260:          goto 20
261:        endif
262:  10   continue
263:  20   continue

265:       write(6,100) i+1
266:  100  format('Number of SNES iterations =',I2)

268: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
269: !     Free work space.  All PETSc objects should be destroyed when they
270: !     are no longer needed.
271: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

273:        call MatDestroy(B,ierr)
274:        if (usemf) then
275:          call MatDestroy(J,ierr)
276:        endif
277:        call VecDestroy(localX,ierr)
278:        call VecDestroy(X,ierr)
279:        call VecDestroy(Y,ierr)
280:        call VecDestroy(F,ierr)
281:        call KSPDestroy(ksp,ierr)
282:        call DMDestroy(da,ierr)
283:        call PetscFinalize(ierr)
284:        end

286: ! -------------------------------------------------------------------
287: !
288: !   FormInitialGuess - Forms initial approximation.
289: !
290: !   Input Parameters:
291: !   X - vector
292: !
293: !   Output Parameter:
294: !   X - vector
295: !
296:       subroutine FormInitialGuess(X,ierr)
297:       implicit none

299: !     petscsys.h       - base PETSc routines   petscvec.h - vectors
300: !     petscmat.h - matrices
301: !     petscis.h     - index sets            petscksp.h - Krylov subspace methods
302: !     petscviewer.h - viewers               petscpc.h  - preconditioners

304: #include <finclude/petscsys.h>
305: #include <finclude/petscis.h>
306: #include <finclude/petscvec.h>
307: #include <finclude/petscmat.h>
308: #include <finclude/petscpc.h>
309: #include <finclude/petscksp.h>
310: #include <finclude/petscdm.h>
311: #include <finclude/petscdmda.h>
312:       PetscErrorCode    ierr
313:       PetscOffset      idx
314:       Vec       X,localX
315:       PetscInt  i,j,row,mx
316:       PetscInt  my, xs,ys,xm
317:       PetscInt  ym
318:       PetscReal one,lambda,temp1,temp,hx,hy
319:       PetscScalar      xx(1)
320:       DM               da
321:       Mat              B
322:       common   /mycommon/ mx,my,B,localX,da

324:       one    = 1.d0
325:       lambda = 6.d0
326:       hx     = one/(mx-1)
327:       hy     = one/(my-1)
328:       temp1  = lambda/(lambda + one)

330: !  Get a pointer to vector data.
331: !    - VecGetArray() returns a pointer to the data array.
332: !    - You MUST call VecRestoreArray() when you no longer need access to
333: !      the array.
334:        call VecGetArray(X,xx,idx,ierr)

336: !  Get local grid boundaries (for 2-dimensional DMDA):
337: !    xs, ys   - starting grid indices (no ghost points)
338: !    xm, ym   - widths of local grid (no ghost points)

340:        call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,             &
341:      &      PETSC_NULL_INTEGER,ierr)

343: !  Compute initial guess over the locally owned part of the grid

345:       do 30 j=ys,ys+ym-1
346:         temp = (min(j,my-j-1))*hy
347:         do 40 i=xs,xs+xm-1
348:           row = i - xs + (j - ys)*xm + 1
349:           if (i .eq. 0 .or. j .eq. 0 .or. i .eq. mx-1 .or.              &
350:      &        j .eq. my-1) then
351:             xx(idx+row) = 0.d0
352:             continue
353:           endif
354:           xx(idx+row) = temp1*sqrt(min((min(i,mx-i-1))*hx,temp))
355:  40     continue
356:  30   continue

358: !     Restore vector

360:        call VecRestoreArray(X,xx,idx,ierr)
361:        return
362:        end

364: ! -------------------------------------------------------------------
365: !
366: !   ComputeFunction - Evaluates nonlinear function, F(x).
367: !
368: !   Input Parameters:
369: !.  X - input vector
370: !
371: !   Output Parameter:
372: !.  F - function vector
373: !
374:       subroutine  ComputeFunction(X,F,ierr)
375:       implicit none

377: !     petscsys.h       - base PETSc routines   petscvec.h - vectors
378: !     petscmat.h - matrices
379: !     petscis.h     - index sets            petscksp.h - Krylov subspace methods
380: !     petscviewer.h - viewers               petscpc.h  - preconditioners

382: #include <finclude/petscsys.h>
383: #include <finclude/petscis.h>
384: #include <finclude/petscvec.h>
385: #include <finclude/petscmat.h>
386: #include <finclude/petscpc.h>
387: #include <finclude/petscksp.h>
388: #include <finclude/petscdm.h>
389: #include <finclude/petscdmda.h>

391:       Vec              X,F,localX
392:       PetscInt         gys,gxm,gym
393:       PetscOffset      idx,idf
394:       PetscErrorCode ierr
395:       PetscInt i,j,row,mx,my,xs,ys,xm,ym,gxs
396:       PetscInt rowf
397:       PetscReal two,one,lambda,hx
398:       PetscReal hy,hxdhy,hydhx,sc
399:       PetscScalar      u,uxx,uyy,xx(1),ff(1)
400:       DM               da
401:       Mat              B
402:       common   /mycommon/ mx,my,B,localX,da

404:       two    = 2.d0
405:       one    = 1.d0
406:       lambda = 6.d0

408:       hx     = one/(mx-1)
409:       hy     = one/(my-1)
410:       sc     = hx*hy*lambda
411:       hxdhy  = hx/hy
412:       hydhx  = hy/hx

414: !  Scatter ghost points to local vector, using the 2-step process
415: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
416: !  By placing code between these two statements, computations can be
417: !  done while messages are in transition.
418: !
419:       call DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr)
420:       call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr)

422: !  Get pointers to vector data

424:       call VecGetArray(localX,xx,idx,ierr)
425:       call VecGetArray(F,ff,idf,ierr)

427: !  Get local grid boundaries

429:       call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
430:      &     PETSC_NULL_INTEGER,ierr)
431:       call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,     &
432:      &     PETSC_NULL_INTEGER,ierr)

434: !  Compute function over the locally owned part of the grid
435:       rowf = 0
436:       do 50 j=ys,ys+ym-1

438:         row  = (j - gys)*gxm + xs - gxs
439:         do 60 i=xs,xs+xm-1
440:           row  = row + 1
441:           rowf = rowf + 1

443:           if (i .eq. 0 .or. j .eq. 0 .or. i .eq. mx-1 .or.              &
444:      &        j .eq. my-1) then
445:             ff(idf+rowf) = xx(idx+row)
446:             goto 60
447:           endif
448:           u   = xx(idx+row)
449:           uxx = (two*u - xx(idx+row-1) - xx(idx+row+1))*hydhx
450:           uyy = (two*u - xx(idx+row-gxm) - xx(idx+row+gxm))*hxdhy
451:           ff(idf+rowf) = uxx + uyy - sc*exp(u)
452:  60     continue
453:  50   continue

455: !  Restore vectors

457:        call VecRestoreArray(localX,xx,idx,ierr)
458:        call VecRestoreArray(F,ff,idf,ierr)
459:        return
460:        end

462: ! -------------------------------------------------------------------
463: !
464: !   ComputeJacobian - Evaluates Jacobian matrix.
465: !
466: !   Input Parameters:
467: !   x - input vector
468: !
469: !   Output Parameters:
470: !   jac - Jacobian matrix
471: !   flag - flag indicating matrix structure
472: !
473: !   Notes:
474: !   Due to grid point reordering with DMDAs, we must always work
475: !   with the local grid points, and then transform them to the new
476: !   global numbering with the 'ltog' mapping
477: !   We cannot work directly with the global numbers for the original
478: !   uniprocessor grid!
479: !
480:       subroutine ComputeJacobian(X,jac,ierr)
481:       implicit none

483: !     petscsys.h  - base PETSc routines   petscvec.h - vectors
484: !     petscmat.h - matrices
485: !     petscis.h     - index sets            petscksp.h - Krylov subspace methods
486: !     petscviewer.h - viewers               petscpc.h  - preconditioners

488: #include <finclude/petscsys.h>
489: #include <finclude/petscis.h>
490: #include <finclude/petscvec.h>
491: #include <finclude/petscmat.h>
492: #include <finclude/petscpc.h>
493: #include <finclude/petscksp.h>
494: #include <finclude/petscdm.h>
495: #include <finclude/petscdmda.h>

497:       Vec         X
498:       Mat         jac
499:       Vec         localX
500:       DM          da
501:       PetscInt     ltog(1)
502:       PetscOffset idltog,idx
503:       PetscErrorCode ierr
504:       PetscInt xs,ys,xm,ym
505:       PetscInt gxs,gys,gxm,gym
506:       PetscInt grow(1),i,j
507:       PetscInt row,mx,my,ione
508:       PetscInt col(5),ifive
509:       PetscScalar two,one,lambda
510:       PetscScalar v(5),hx,hy,hxdhy
511:       PetscScalar hydhx,sc,xx(1)
512:       Mat         B
513:       ISLocalToGlobalMapping ltogm
514:       common   /mycommon/ mx,my,B,localX,da

516:       ione   = 1
517:       ifive  = 5
518:       one    = 1.d0
519:       two    = 2.d0
520:       hx     = one/(mx-1)
521:       hy     = one/(my-1)
522:       sc     = hx*hy
523:       hxdhy  = hx/hy
524:       hydhx  = hy/hx
525:       lambda = 6.d0

527: !  Scatter ghost points to local vector, using the 2-step process
528: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
529: !  By placing code between these two statements, computations can be
530: !  done while messages are in transition.

532:       call DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr)
533:       call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr)

535: !  Get pointer to vector data

537:       call VecGetArray(localX,xx,idx,ierr)

539: !  Get local grid boundaries

541:       call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,              &
542:      &     PETSC_NULL_INTEGER,ierr)
543:       call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,     &
544:      &                        PETSC_NULL_INTEGER,ierr)

546: !  Get the global node numbers for all local nodes, including ghost points

548:       call DMGetLocalToGlobalMapping(da,ltogm,ierr)
549:       call ISLocalToGlobalMappingGetIndices(ltogm,ltog,idltog,ierr)

551: !  Compute entries for the locally owned part of the Jacobian.
552: !   - Currently, all PETSc parallel matrix formats are partitioned by
553: !     contiguous chunks of rows across the processors. The 'grow'
554: !     parameter computed below specifies the global row number
555: !     corresponding to each local grid point.
556: !   - Each processor needs to insert only elements that it owns
557: !     locally (but any non-local elements will be sent to the
558: !     appropriate processor during matrix assembly).
559: !   - Always specify global row and columns of matrix entries.
560: !   - Here, we set all entries for a particular row at once.

562:       do 10 j=ys,ys+ym-1
563:         row = (j - gys)*gxm + xs - gxs
564:         do 20 i=xs,xs+xm-1
565:           row = row + 1
566:           grow(1) = ltog(idltog+row)
567:           if (i .eq. 0 .or. j .eq. 0 .or. i .eq. (mx-1) .or.            &
568:      &        j .eq. (my-1)) then
569:              call MatSetValues(jac,ione,grow,ione,grow,one,             &
570:      &                         INSERT_VALUES,ierr)
571:              go to 20
572:           endif
573:           v(1)   = -hxdhy
574:           col(1) = ltog(idltog+row - gxm)
575:           v(2)   = -hydhx
576:           col(2) = ltog(idltog+row - 1)
577:           v(3)   = two*(hydhx + hxdhy) - sc*lambda*exp(xx(idx+row))
578:           col(3) = grow(1)
579:           v(4)   = -hydhx
580:           col(4) = ltog(idltog+row + 1)
581:           v(5)   = -hxdhy
582:           col(5) = ltog(idltog+row + gxm)
583:           call MatSetValues(jac,ione,grow,ifive,col,v,INSERT_VALUES,       &
584:      &                      ierr)
585:  20     continue
586:  10   continue

588:       call ISLocalToGlobalMappingRestoreIndices(ltogm,ltog,idltog,ierr)

590: !  Assemble matrix, using the 2-step process:
591: !    MatAssemblyBegin(), MatAssemblyEnd().
592: !  By placing code between these two statements, computations can be
593: !  done while messages are in transition.

595:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
596:       call VecRestoreArray(localX,xx,idx,ierr)
597:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
598:       return
599:       end


602: ! -------------------------------------------------------------------
603: !
604: !   MyMult - user provided matrix multiply
605: !
606: !   Input Parameters:
607: !.  X - input vector
608: !
609: !   Output Parameter:
610: !.  F - function vector
611: !
612:       subroutine  MyMult(J,X,F,ierr)
613:       implicit none
614:       Mat     J,B
615:       Vec     X,F
616:       PetscErrorCode ierr
617:       PetscInt mx,my
618:       DM      da
619:       Vec     localX

621:       common   /mycommon/ mx,my,B,localX,da
622: !
623: !       Here we use the actual formed matrix B; users would
624: !     instead write their own matrix vector product routine
625: !
626:       call MatMult(B,X,F,ierr)
627:       return
628:       end