Actual source code: ex39f90.F

  1: !
  2: !  Description: Solves a nonlinear system in parallel with SNES.
  3: !  We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
  4: !  domain, using distributed arrays (DMDAs) to partition the parallel grid.
  5: !  The command line options include:
  6: !    -par <parameter>, where <parameter> indicates the nonlinearity of the problem
  7: !       problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)
  8: !
  9: !   Modified from ex5f90.F by Mike McCourt <mccomic@iit.edu>
 10: !   for testing Fortran interface on
 11: !   SNESLineSearchSet(), SNESLineSearchSetPreCheck(), SNESLineSearchSetPostCheck()
 12: !
 13: !  --------------------------------------------------------------------------
 14: !
 15: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 16: !  the partial differential equation
 17: !
 18: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
 19: !
 20: !  with boundary conditions
 21: !
 22: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
 23: !
 24: !  A finite difference approximation with the usual 5-point stencil
 25: !  is used to discretize the boundary value problem to obtain a nonlinear
 26: !  system of equations.
 27: !
 28: !  The uniprocessor version of this code is snes/examples/tutorials/ex4f.F
 29: !
 30: !  --------------------------------------------------------------------------
 31: !  The following define must be used before including any PETSc include files
 32: !  into a module or interface. This is because they can't handle declarations
 33: !  in them
 34: !

 36:       module f90module
 37:       type userctx
 38: #include <finclude/petscsysdef.h>
 39: #include <finclude/petscvecdef.h>
 40: #include <finclude/petscdmdef.h>
 41:         DM      da
 42:         integer xs,xe,xm,gxs,gxe,gxm
 43:         integer ys,ye,ym,gys,gye,gym
 44:         integer mx,my,rank
 45:         double precision lambda
 46:       end type userctx
 47:       contains
 48: ! ---------------------------------------------------------------------
 49: !
 50: !  FormFunction - Evaluates nonlinear function, F(x).
 51: !
 52: !  Input Parameters:
 53: !  snes - the SNES context
 54: !  X - input vector
 55: !  dummy - optional user-defined context, as set by SNESSetFunction()
 56: !          (not used here)
 57: !
 58: !  Output Parameter:
 59: !  F - function vector
 60: !
 61: !  Notes:
 62: !  This routine serves as a wrapper for the lower-level routine
 63: !  "FormFunctionLocal", where the actual computations are
 64: !  done using the standard Fortran style of treating the local
 65: !  vector data as a multidimensional array over the local mesh.
 66: !  This routine merely handles ghost point scatters and accesses
 67: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
 68: !
 69:       subroutine FormFunction(snes,X,F,user,ierr)
 70:       implicit none

 72: #include <finclude/petscsys.h>
 73: #include <finclude/petscvec.h>
 74: #include <finclude/petscdmda.h>
 75: #include <finclude/petscis.h>
 76: #include <finclude/petscmat.h>
 77: #include <finclude/petscksp.h>
 78: #include <finclude/petscpc.h>
 79: #include <finclude/petscsnes.h>

 81: #include <finclude/petscvec.h90>


 84: !  Input/output variables:
 85:       SNES           snes
 86:       Vec            X,F
 87:       integer        ierr
 88:       type (userctx) user

 90: !  Declarations for use with local arrays:
 91:       PetscScalar,pointer :: lx_v(:),lf_v(:)
 92:       Vec            localX

 94:       write(*,*)"Inside FormFunction, user%xm=",user%xm

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

101:       call DMGetLocalVector(user%da,localX,ierr)
102:       call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,                &
103:      &     localX,ierr)
104:       call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)

106: !  Get a pointer to vector data.
107: !    - For default PETSc vectors, VecGetArray90() returns a pointer to
108: !      the data array. Otherwise, the routine is implementation dependent.
109: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
110: !      the array.
111: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
112: !      and is useable from Fortran-90 Only.

114:       call VecGetArrayF90(localX,lx_v,ierr)
115:       call VecGetArrayF90(F,lf_v,ierr)

117: !  Compute function over the locally owned part of the grid

119:       call FormFunctionLocal(lx_v,lf_v,user,ierr)

121: !  Restore vectors

123:       call VecRestoreArrayF90(localX,lx_v,ierr)
124:       call VecRestoreArrayF90(F,lf_v,ierr)

126: !  Insert values into global vector

128:       call DMRestoreLocalVector(user%da,localX,ierr)
129:       call PetscLogFlops(11.0d0*user%ym*user%xm,ierr)

131: !      call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
132: !      call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)

134:       return
135:       end subroutine formfunction
136:       end module f90module



140:       program main
141:       use f90module
142:       implicit none
143: !
144: !
145: #include <finclude/petscsys.h>
146: #include <finclude/petscvec.h>
147: #include <finclude/petscdmda.h>
148: #include <finclude/petscis.h>
149: #include <finclude/petscmat.h>
150: #include <finclude/petscksp.h>
151: #include <finclude/petscpc.h>
152: #include <finclude/petscsnes.h>
153: #include <finclude/petscvec.h90>
154: #include <finclude/petscdmda.h90>

156: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: !                   Variable declarations
158: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
159: !
160: !  Variables:
161: !     snes        - nonlinear solver
162: !     x, r        - solution, residual vectors
163: !     J           - Jacobian matrix
164: !     its         - iterations for convergence
165: !     Nx, Ny      - number of preocessors in x- and y- directions
166: !     matrix_free - flag - 1 indicates matrix-free version
167: !
168: !
169:       SNES                snes
170:       Vec                 x,r
171:       Mat                 J
172:       integer             its,matrix_free,flg,ierr
173:       double precision    lambda_max,lambda_min
174:       type (userctx)      user
175:       PetscBool           test_linesearch,test_check

177: !  Note: Any user-defined Fortran routines (such as FormJacobian)
178: !  MUST be declared as external.

180:       external FormInitialGuess,FormJacobian,FormLineSearch
181:       external FormPostCheck,FormPreCheck

183: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184: !  Initialize program
185: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

187:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
188:       call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)

190: !  Initialize problem parameters

192:       lambda_max  = 6.81
193:       lambda_min  = 0.0
194:       user%lambda = 6.0
195:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par',             &
196:      &     user%lambda,flg,ierr)
197:       if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) &
198:      &     then
199:          if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
200:          SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
201:       endif


204: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205: !  Create nonlinear solver context
206: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

208:       call SNESCreate(PETSC_COMM_WORLD,snes,ierr)

210: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211: !  Create vector data structures; set function evaluation routine
212: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

214: !  Create distributed array (DMDA) to manage parallel grid and vectors

216: ! This really needs only the star-type stencil, but we use the box
217: ! stencil temporarily.
218:       call DMDACreate2d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,            &
219:      &     DMDA_BOUNDARY_NONE,DMDA_STENCIL_BOX,                            &
220:      &     -4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1,                         &
221:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr)
222:       call DMDAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my,        &
223:      &               PETSC_NULL_INTEGER,                                &
224:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
225:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
226:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
227:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
228:      &               PETSC_NULL_INTEGER,ierr)
229: 
230: !
231: !   Visualize the distribution of the array across the processors
232: !
233: !     call DMView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)

235: !  Extract global and local vectors from DMDA; then duplicate for remaining
236: !  vectors that are the same types

238:       call DMCreateGlobalVector(user%da,x,ierr)
239:       call VecDuplicate(x,r,ierr)

241: !  Get local grid boundaries (for 2-dimensional DMDA)

243:       call DMDAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER,     &
244:      &     user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
245:       call DMDAGetGhostCorners(user%da,user%gxs,user%gys,                 &
246:      &     PETSC_NULL_INTEGER,user%gxm,user%gym,                        &
247:      &     PETSC_NULL_INTEGER,ierr)

249: !  Here we shift the starting indices up by one so that we can easily
250: !  use the Fortran convention of 1-based indices (rather 0-based indices).

252:       user%xs  = user%xs+1
253:       user%ys  = user%ys+1
254:       user%gxs = user%gxs+1
255:       user%gys = user%gys+1

257:       user%ye  = user%ys+user%ym-1
258:       user%xe  = user%xs+user%xm-1
259:       user%gye = user%gys+user%gym-1
260:       user%gxe = user%gxs+user%gxm-1

262: !  Set function evaluation routine and vector

264:       call SNESSetFunction(snes,r,FormFunction,user,ierr)

266: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
267: !  Create matrix data structure; set Jacobian evaluation routine
268: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

270: !  Set Jacobian matrix data structure and default Jacobian evaluation
271: !  routine. User can override with:
272: !     -snes_fd : default finite differencing approximation of Jacobian
273: !     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
274: !                (unless user explicitly sets preconditioner)
275: !     -snes_mf_operator : form preconditioning matrix as set by the user,
276: !                         but use matrix-free approx for Jacobian-vector
277: !                         products within Newton-Krylov method
278: !
279: !  Note:  For the parallel case, vectors and matrices MUST be partitioned
280: !     accordingly.  When using distributed arrays (DMDAs) to create vectors,
281: !     the DMDAs determine the problem partitioning.  We must explicitly
282: !     specify the local matrix dimensions upon its creation for compatibility
283: !     with the vector distribution.  Thus, the generic MatCreate() routine
284: !     is NOT sufficient when working with distributed arrays.
285: !
286: !     Note: Here we only approximately preallocate storage space for the
287: !     Jacobian.  See the users manual for a discussion of better techniques
288: !     for preallocating matrix memory.

290:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf',         &
291:      &     matrix_free,ierr)
292:       if (matrix_free .eq. 0) then
293:         call DMCreateMatrix(user%da,MATAIJ,J,ierr)
294:         call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)
295:       endif

297: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
298: !  Customize nonlinear solver; set runtime options
299: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

301: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)

303:       call SNESSetFromOptions(snes,ierr)
304:       test_linesearch = 0
305:       test_check      = 0
306:       call PetscOptionsGetBool(PETSC_NULL_CHARACTER,'-test_check',
307:      &                          test_check,PETSC_NULL_INTEGER,ierr)
308:       if (test_check.eq.1) then
309:         call SNESLineSearchSetPreCheck(snes,FormPreCheck,user,ierr)
310:         call SNESLineSearchSetPostCheck(snes,FormPostCheck,user,ierr)
311:       else
312:         call PetscOptionsGetBool(PETSC_NULL_CHARACTER,
313:      &       '-test_linesearch',test_linesearch,PETSC_NULL_INTEGER,ierr)
314:         if (test_linesearch.eq.1) then
315:           call SNESLineSearchSet(snes,FormLineSearch,user,ierr)
316:         end if
317:       end if
318: 
319: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
320: !  Evaluate initial guess; then solve nonlinear system.
321: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

323: !  Note: The user should initialize the vector, x, with the initial guess
324: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
325: !  to employ an initial guess of zero, the user should explicitly set
326: !  this vector to zero by calling VecSet().

328:       call FormInitialGuess(user,x,ierr)
329:         write(*,*)"Before SNESSolve"
330:         write(*,*)"user%xm=",user%xm
331:       call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
332:       call SNESGetIterationNumber(snes,its,ierr);
333:       if (user%rank .eq. 0) then
334:          write(6,100) its
335:       endif
336:   100 format('Number of SNES iterations = ',i5)

338: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
339: !  Free work space.  All PETSc objects should be destroyed when they
340: !  are no longer needed.
341: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

343:       if (matrix_free .eq. 0) call MatDestroy(J,ierr)
344:       call VecDestroy(x,ierr)
345:       call VecDestroy(r,ierr)
346:       call SNESDestroy(snes,ierr)
347:       call DMDestroy(user%da,ierr)
348:       call PetscFinalize(ierr)
349:       end

351: ! ---------------------------------------------------------------------
352: !
353: !  FormLineSearch - Applies the line search to the step size
354: !
355:       subroutine FormLineSearch(snes,user,x,f,g,y,w,fnorm,ynorm,gnorm,
356:      & flag,ierr)

358:       use f90module

360: #include <finclude/petscsys.h>
361: #include <finclude/petscvec.h>
362: #include <finclude/petscvec.h90>
363: #include <finclude/petscmat.h>
364: #include <finclude/petscmat.h90>
365: #include <finclude/petscksp.h>
366: #include <finclude/petscpc.h>
367: #include <finclude/petscsnes.h>

369:       SNES              snes
370:       type (userctx)    user
371:       Vec               x,f,g,y,w
372:       PetscReal fnorm,ynorm,gnorm
373:       PetscBool            flag
374:       PetscErrorCode ierr

376:       PetscScalar       mone

378:         write(*,*)"Inside FormLineSearch, user%xm=",user%xm
379:       mone = -1.0d0
380:       flag = 0
381:       call VecNorm(y,NORM_2,ynorm,ierr)
382:       call VecAYPX(y,mone,x,ierr)
383:       call SNESComputeFunction(snes,y,g,ierr)
384:       call VecNorm(g,NORM_2,gnorm,ierr)
385:       return
386:       end

388: ! ---------------------------------------------------------------------
389: !
390: !  FormInitialGuess - Forms initial approximation.
391: !
392: !  Input Parameters:
393: !  X - vector
394: !
395: !  Output Parameter:
396: !  X - vector
397: !
398: !  Notes:
399: !  This routine serves as a wrapper for the lower-level routine
400: !  "InitialGuessLocal", where the actual computations are
401: !  done using the standard Fortran style of treating the local
402: !  vector data as a multidimensional array over the local mesh.
403: !  This routine merely handles ghost point scatters and accesses
404: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
405: !
406:       subroutine FormInitialGuess(user,X,ierr)
407:       use f90module
408:       implicit none

410: #include <finclude/petscvec.h90>
411: #include <finclude/petscsys.h>
412: #include <finclude/petscvec.h>
413: #include <finclude/petscdmda.h>
414: #include <finclude/petscis.h>
415: #include <finclude/petscmat.h>
416: #include <finclude/petscksp.h>
417: #include <finclude/petscpc.h>
418: #include <finclude/petscsnes.h>

420: !  Input/output variables:
421:       type (userctx)         user
422:       Vec      X
423:       integer  ierr
424: 
425: !  Declarations for use with local arrays:
426:       PetscScalar,pointer :: lx_v(:)
427:       Vec               localX

429:       0

431: !  Get a pointer to vector data.
432: !    - For default PETSc vectors, VecGetArray90() returns a pointer to
433: !      the data array. Otherwise, the routine is implementation dependent.
434: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
435: !      the array.
436: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
437: !      and is useable from Fortran-90 Only.

439:       call DMGetLocalVector(user%da,localX,ierr)
440:       call VecGetArrayF90(localX,lx_v,ierr)

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

444:       call InitialGuessLocal(user,lx_v,ierr)

446: !  Restore vector

448:       call VecRestoreArrayF90(localX,lx_v,ierr)

450: !  Insert values into global vector

452:       call DMLocalToGlobalBegin(user%da,localX,INSERT_VALUES,X,ierr)
453:       call DMLocalToGlobalEnd(user%da,localX,INSERT_VALUES,X,ierr)
454:       call DMRestoreLocalVector(user%da,localX,ierr)

456:       return
457:       end

459: ! ---------------------------------------------------------------------
460: !
461: !  InitialGuessLocal - Computes initial approximation, called by
462: !  the higher level routine FormInitialGuess().
463: !
464: !  Input Parameter:
465: !  x - local vector data
466: !
467: !  Output Parameters:
468: !  x - local vector data
469: !  ierr - error code
470: !
471: !  Notes:
472: !  This routine uses standard Fortran-style computations over a 2-dim array.
473: !
474:       subroutine InitialGuessLocal(user,x,ierr)
475:       use f90module
476:       implicit none

478: #include <finclude/petscsys.h>
479: #include <finclude/petscvec.h>
480: #include <finclude/petscdmda.h>
481: #include <finclude/petscis.h>
482: #include <finclude/petscmat.h>
483: #include <finclude/petscksp.h>
484: #include <finclude/petscpc.h>
485: #include <finclude/petscsnes.h>

487: !  Input/output variables:
488:       type (userctx)         user
489:       PetscScalar  x(user%gxs:user%gxe,                                         &
490:      &              user%gys:user%gye)
491:       integer ierr

493: !  Local variables:
494:       integer  i,j
495:       PetscScalar   temp1,temp,hx,hy
496:       PetscScalar   one

498: !  Set parameters

500:       0
501:       one    = 1.0
502:       hx     = one/(dble(user%mx-1))
503:       hy     = one/(dble(user%my-1))
504:       temp1  = user%lambda/(user%lambda + one)

506:       do 20 j=user%ys,user%ye
507:          temp = dble(min(j-1,user%my-j))*hy
508:          do 10 i=user%xs,user%xe
509:             if (i .eq. 1 .or. j .eq. 1                                  &
510:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
511:               x(i,j) = 0.0
512:             else
513:               x(i,j) = temp1 *                                          &
514:      &          sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
515:             endif
516:  10      continue
517:  20   continue

519:       return
520:       end

522: ! ---------------------------------------------------------------------
523: !
524: !  FormFunctionLocal - Computes nonlinear function, called by
525: !  the higher level routine FormFunction().
526: !
527: !  Input Parameter:
528: !  x - local vector data
529: !
530: !  Output Parameters:
531: !  f - local vector data, f(x)
532: !  ierr - error code
533: !
534: !  Notes:
535: !  This routine uses standard Fortran-style computations over a 2-dim array.
536: !
537:       subroutine FormFunctionLocal(x,f,user,ierr)
538:       use f90module

540:       implicit none

542: !  Input/output variables:
543:       type (userctx) user
544:       PetscScalar  x(user%gxs:user%gxe,                                         &
545:      &              user%gys:user%gye)
546:       PetscScalar  f(user%xs:user%xe,                                           &
547:      &              user%ys:user%ye)
548:       integer  ierr

550: !  Local variables:
551:       PetscScalar   two,one,hx,hy,hxdhy,hydhx,sc
552:       PetscScalar   u,uxx,uyy
553:       integer  i,j

555:       one    = 1.0
556:       two    = 2.0
557:       hx     = one/dble(user%mx-1)
558:       hy     = one/dble(user%my-1)
559:       sc     = hx*hy*user%lambda
560:       hxdhy  = hx/hy
561:       hydhx  = hy/hx

563: !  Compute function over the locally owned part of the grid

565:       do 20 j=user%ys,user%ye
566:          do 10 i=user%xs,user%xe
567:             if (i .eq. 1 .or. j .eq. 1                                  &
568:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
569:                f(i,j) = x(i,j)
570:             else
571:                u = x(i,j)
572:                uxx = hydhx * (two*u                                     &
573:      &                - x(i-1,j) - x(i+1,j))
574:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
575:                f(i,j) = uxx + uyy - sc*exp(u)
576:             endif
577:  10      continue
578:  20   continue

580:       return
581:       end

583: ! ---------------------------------------------------------------------
584: !
585: !  FormJacobian - Evaluates Jacobian matrix.
586: !
587: !  Input Parameters:
588: !  snes     - the SNES context
589: !  x        - input vector
590: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
591: !             (not used here)
592: !
593: !  Output Parameters:
594: !  jac      - Jacobian matrix
595: !  jac_prec - optionally different preconditioning matrix (not used here)
596: !  flag     - flag indicating matrix structure
597: !
598: !  Notes:
599: !  This routine serves as a wrapper for the lower-level routine
600: !  "FormJacobianLocal", where the actual computations are
601: !  done using the standard Fortran style of treating the local
602: !  vector data as a multidimensional array over the local mesh.
603: !  This routine merely accesses the local vector data via
604: !  VecGetArrayF90() and VecRestoreArrayF90().
605: !
606: !  Notes:
607: !  Due to grid point reordering with DMDAs, we must always work
608: !  with the local grid points, and then transform them to the new
609: !  global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
610: !  We cannot work directly with the global numbers for the original
611: !  uniprocessor grid!
612: !
613: !  Two methods are available for imposing this transformation
614: !  when setting matrix entries:
615: !    (A) MatSetValuesLocal(), using the local ordering (including
616: !        ghost points!)
617: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
618: !        - Associate this map with the matrix by calling
619: !          MatSetLocalToGlobalMapping() once
620: !        - Set matrix entries using the local ordering
621: !          by calling MatSetValuesLocal()
622: !    (B) MatSetValues(), using the global ordering
623: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
624: !        - Then apply this map explicitly yourself
625: !        - Set matrix entries using the global ordering by calling
626: !          MatSetValues()
627: !  Option (A) seems cleaner/easier in many cases, and is the procedure
628: !  used in this example.
629: !
630:       subroutine FormJacobian(snes,X,jac,jac_prec,flag,user,ierr)
631:       use f90module
632:       implicit none

634: #include <finclude/petscsys.h>
635: #include <finclude/petscvec.h>
636: #include <finclude/petscdmda.h>
637: #include <finclude/petscis.h>
638: #include <finclude/petscmat.h>
639: #include <finclude/petscksp.h>
640: #include <finclude/petscpc.h>
641: #include <finclude/petscsnes.h>

643: #include <finclude/petscvec.h90>

645: !  Input/output variables:
646:       SNES         snes
647:       Vec          X
648:       Mat          jac,jac_prec
649:       MatStructure flag
650:       type(userctx) user
651:       integer      ierr

653: !  Declarations for use with local arrays:
654:       PetscScalar,pointer :: lx_v(:)
655:       Vec            localX

657: !  Scatter ghost points to local vector, using the 2-step process
658: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
659: !  Computations can be done while messages are in transition,
660: !  by placing code between these two statements.

662:       call DMGetLocalVector(user%da,localX,ierr)
663:       call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,            &
664:      &     ierr)
665:       call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)

667: !  Get a pointer to vector data

669:       call VecGetArrayF90(localX,lx_v,ierr)

671: !  Compute entries for the locally owned part of the Jacobian.

673:       call FormJacobianLocal(lx_v,jac,jac_prec,user,ierr)

675: !  Assemble matrix, using the 2-step process:
676: !     MatAssemblyBegin(), MatAssemblyEnd()
677: !  Computations can be done while messages are in transition,
678: !  by placing code between these two statements.

680:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
681:       call VecRestoreArrayF90(localX,lx_v,ierr)
682:       call DMRestoreLocalVector(user%da,localX,ierr)
683:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)

685: !  Set flag to indicate that the Jacobian matrix retains an identical
686: !  nonzero structure throughout all nonlinear iterations (although the
687: !  values of the entries change). Thus, we can save some work in setting
688: !  up the preconditioner (e.g., no need to redo symbolic factorization for
689: !  ILU/ICC preconditioners).
690: !   - If the nonzero structure of the matrix is different during
691: !     successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
692: !     must be used instead.  If you are unsure whether the matrix
693: !     structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
694: !   - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
695: !     believes your assertion and does not check the structure
696: !     of the matrix.  If you erroneously claim that the structure
697: !     is the same when it actually is not, the new preconditioner
698: !     will not function correctly.  Thus, use this optimization
699: !     feature with caution!

701:       flag = SAME_NONZERO_PATTERN

703: !  Tell the matrix we will never add a new nonzero location to the
704: !  matrix. If we do it will generate an error.

706: !       call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,ierr)

708:       return
709:       end

711: ! ---------------------------------------------------------------------
712: !
713: !  FormJacobianLocal - Computes Jacobian matrix, called by
714: !  the higher level routine FormJacobian().
715: !
716: !  Input Parameters:
717: !  x        - local vector data
718: !
719: !  Output Parameters:
720: !  jac      - Jacobian matrix
721: !  jac_prec - optionally different preconditioning matrix (not used here)
722: !  ierr     - error code
723: !
724: !  Notes:
725: !  This routine uses standard Fortran-style computations over a 2-dim array.
726: !
727: !  Notes:
728: !  Due to grid point reordering with DMDAs, we must always work
729: !  with the local grid points, and then transform them to the new
730: !  global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
731: !  We cannot work directly with the global numbers for the original
732: !  uniprocessor grid!
733: !
734: !  Two methods are available for imposing this transformation
735: !  when setting matrix entries:
736: !    (A) MatSetValuesLocal(), using the local ordering (including
737: !        ghost points!)
738: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
739: !        - Associate this map with the matrix by calling
740: !          MatSetLocalToGlobalMapping() once
741: !        - Set matrix entries using the local ordering
742: !          by calling MatSetValuesLocal()
743: !    (B) MatSetValues(), using the global ordering
744: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
745: !        - Then apply this map explicitly yourself
746: !        - Set matrix entries using the global ordering by calling
747: !          MatSetValues()
748: !  Option (A) seems cleaner/easier in many cases, and is the procedure
749: !  used in this example.
750: !
751:       subroutine FormJacobianLocal(x,jac,jac_prec,user,ierr)
752:       use f90module
753:       implicit none

755: #include <finclude/petscsys.h>
756: #include <finclude/petscvec.h>
757: #include <finclude/petscdmda.h>
758: #include <finclude/petscis.h>
759: #include <finclude/petscmat.h>
760: #include <finclude/petscksp.h>
761: #include <finclude/petscpc.h>
762: #include <finclude/petscsnes.h>

764: !  Input/output variables:
765:       type (userctx) user
766:       PetscScalar  x(user%gxs:user%gxe,                                         &
767:      &              user%gys:user%gye)
768:       Mat      jac,jac_prec
769:       integer  ierr

771: !  Local variables:
772:       integer  row,col(5),i,j
773:       PetscScalar   two,one,hx,hy,hxdhy
774:       PetscScalar   hydhx,sc,v(5)

776: !  Set parameters

778:       one    = 1.0
779:       two    = 2.0
780:       hx     = one/dble(user%mx-1)
781:       hy     = one/dble(user%my-1)
782:       sc     = hx*hy
783:       hxdhy  = hx/hy
784:       hydhx  = hy/hx

786: !  Compute entries for the locally owned part of the Jacobian.
787: !   - Currently, all PETSc parallel matrix formats are partitioned by
788: !     contiguous chunks of rows across the processors.
789: !   - Each processor needs to insert only elements that it owns
790: !     locally (but any non-local elements will be sent to the
791: !     appropriate processor during matrix assembly).
792: !   - Here, we set all entries for a particular row at once.
793: !   - We can set matrix entries either using either
794: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
795: !   - Note that MatSetValues() uses 0-based row and column numbers
796: !     in Fortran as well as in C.

798:       do 20 j=user%ys,user%ye
799:          row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
800:          do 10 i=user%xs,user%xe
801:             row = row + 1
802: !           boundary points
803:             if (i .eq. 1 .or. j .eq. 1                                  &
804:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
805:                col(1) = row
806:                v(1)   = one
807:                call MatSetValuesLocal(jac,1,row,1,col,v,                &
808:      &                           INSERT_VALUES,ierr)
809: !           interior grid points
810:             else
811:                v(1) = -hxdhy
812:                v(2) = -hydhx
813:                v(3) = two*(hydhx + hxdhy)                               &
814:      &                  - sc*user%lambda*exp(x(i,j))
815:                v(4) = -hydhx
816:                v(5) = -hxdhy
817:                col(1) = row - user%gxm
818:                col(2) = row - 1
819:                col(3) = row
820:                col(4) = row + 1
821:                col(5) = row + user%gxm
822:                call MatSetValuesLocal(jac,1,row,5,col,v,                &
823:      &                                INSERT_VALUES,ierr)
824:             endif
825:  10      continue
826:  20   continue

828:       return
829:       end

831:       subroutine FormPreCheck(snes,X,Y,user,changed_Y,ierr)
832:       use f90module

834:       SNES           snes
835:       Vec            X,Y
836:       type (userctx) user
837:       PetscBool      changed_Y
838:       PetscErrorCode ierr

840:              write(*,*)"Inside formPreCheck, user%xm=",user%xm
841:       end subroutine formPreCheck

843:       subroutine FormPostCheck(snes,X,Y,W,user,changed_Y,changed_W,ierr)
844:       use f90module

846:       SNES           snes
847:       Vec            X,Y,W
848:       type (userctx) user
849:       PetscBool      changed_Y,changed_W
850:       PetscErrorCode ierr

852:              write(*,*)"Inside formPostCheck, user%xm=",user%xm
853:       end subroutine formPostCheck