Actual source code: ex39f90.F

petsc-3.3-p7 2013-05-11
  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:         integer xs,xe,xm,gxs,gxe,gxm
 42:         integer ys,ye,ym,gys,gye,gym
 43:         integer mx,my,rank
 44:         double precision lambda
 45:       end type userctx
 46:       contains
 47: ! ---------------------------------------------------------------------
 48: !
 49: !  FormFunction - Evaluates nonlinear function, F(x).
 50: !
 51: !  Input Parameters:
 52: !  snes - the SNES context
 53: !  X - input vector
 54: !  dummy - optional user-defined context, as set by SNESSetFunction()
 55: !          (not used here)
 56: !
 57: !  Output Parameter:
 58: !  F - function vector
 59: !
 60: !  Notes:
 61: !  This routine serves as a wrapper for the lower-level routine
 62: !  "FormFunctionLocal", where the actual computations are
 63: !  done using the standard Fortran style of treating the local
 64: !  vector data as a multidimensional array over the local mesh.
 65: !  This routine merely handles ghost point scatters and accesses
 66: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
 67: !
 68:       subroutine FormFunction(snes,X,F,user,ierr)
 69:       implicit none

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

 80: #include <finclude/petscvec.h90>


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

 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 SNESGetDM(snes,da,ierr)
102:       call DMGetLocalVector(da,localX,ierr)
103:       call DMGlobalToLocalBegin(da,X,INSERT_VALUES,                     &
104:      &     localX,ierr)
105:       call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr)

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

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

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

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

122: !  Restore vectors

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

127: !  Insert values into global vector

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

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

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



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

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

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

183:       external FormInitialGuess,FormJacobian,FormLineSearch
184:       external FormPostCheck,FormPreCheck

186: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187: !  Initialize program
188: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

190:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
191:       call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)

193: !  Initialize problem parameters

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


207: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208: !  Create nonlinear solver context
209: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

211:       call SNESCreate(PETSC_COMM_WORLD,snes,ierr)

213: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214: !  Create vector data structures; set function evaluation routine
215: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

219: ! This really needs only the star-type stencil, but we use the box
220: ! stencil temporarily.
221:       call DMDACreate2d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,            &
222:      &     DMDA_BOUNDARY_NONE,DMDA_STENCIL_BOX,                            &
223:      &     -4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1,                         &
224:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
225:       call DMDAGetInfo(da,PETSC_NULL_INTEGER,user%mx,user%my,           &
226:      &               PETSC_NULL_INTEGER,                                &
227:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
228:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
229:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
230:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
231:      &               PETSC_NULL_INTEGER,ierr)
232: 
233: !
234: !   Visualize the distribution of the array across the processors
235: !
236: !     call DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr)

238: !  Extract global and local vectors from DMDA; then duplicate for remaining
239: !  vectors that are the same types
240:       call SNESSetDM(snes,da,ierr)
241:       call DMCreateGlobalVector(da,x,ierr)
242:       call VecDuplicate(x,r,ierr)

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

246:       call DMDAGetCorners(da,user%xs,user%ys,PETSC_NULL_INTEGER,        &
247:      &     user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
248:       call DMDAGetGhostCorners(da,user%gxs,user%gys,                    &
249:      &     PETSC_NULL_INTEGER,user%gxm,user%gym,                        &
250:      &     PETSC_NULL_INTEGER,ierr)

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

255:       user%xs  = user%xs+1
256:       user%ys  = user%ys+1
257:       user%gxs = user%gxs+1
258:       user%gys = user%gys+1

260:       user%ye  = user%ys+user%ym-1
261:       user%xe  = user%xs+user%xm-1
262:       user%gye = user%gys+user%gym-1
263:       user%gxe = user%gxs+user%gxm-1

265: !  Set function evaluation routine and vector

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

269: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
270: !  Create matrix data structure; set Jacobian evaluation routine
271: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

300: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
301: !  Customize nonlinear solver; set runtime options
302: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

306:       test_linesearch = PETSC_FALSE
307:       test_check      = PETSC_FALSE
308:       call PetscOptionsGetBool(PETSC_NULL_CHARACTER,'-test_check',
309:      &                          test_check,PETSC_NULL_INTEGER,ierr)
310:       call SNESGetSNESLineSearch(snes, linesearch, ierr)
311:       if (test_check.eqv.PETSC_TRUE) then
312:          call SNESLineSearchSetPreCheck(linesearch,FormPreCheck,user,   &
313:      &    ierr)
314:          call SNESLineSearchSetPostCheck(linesearch,FormPostCheck,user, &
315:      &    ierr)
316:       else
317:          call PetscOptionsGetBool(PETSC_NULL_CHARACTER,
318:      &       '-test_linesearch',test_linesearch,PETSC_NULL_INTEGER,ierr)
319:          if (test_linesearch.eqv.PETSC_TRUE) then
320:             call SNESLineSearchSetType(linesearch,"shell", ierr)
321:             call SNESLineSearchShellSetUserFunc(linesearch,              &
322:      &           FormLineSearch, user, ierr)
323:         end if
324:       end if
325:       call SNESSetFromOptions(snes,ierr)


328: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
329: !  Evaluate initial guess; then solve nonlinear system.
330: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

337:       call FormInitialGuess(snes,x,ierr)
338:         write(*,*)"Before SNESSolve"
339:         write(*,*)"user%xm=",user%xm
340:       call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
341:       call SNESGetIterationNumber(snes,its,ierr);
342:       if (user%rank .eq. 0) then
343:          write(6,100) its
344:       endif
345:   100 format('Number of SNES iterations = ',i5)

347: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
348: !  Free work space.  All PETSc objects should be destroyed when they
349: !  are no longer needed.
350: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

352:       if (matrix_free .eq. 0) call MatDestroy(J,ierr)
353:       call VecDestroy(x,ierr)
354:       call VecDestroy(r,ierr)
355:       call SNESDestroy(snes,ierr)
356:       call DMDestroy(da,ierr)
357:       call PetscFinalize(ierr)
358:       end

360: ! ---------------------------------------------------------------------
361: !
362: !  FormLineSearch - Applies the line search to the step size
363: !
364:       subroutine FormLineSearch(linesearch, user, ierr)

366:       use f90module

368: #include <finclude/petscsys.h>
369: #include <finclude/petscvec.h>
370: #include <finclude/petscvec.h90>
371: #include <finclude/petscmat.h>
372: #include <finclude/petscmat.h90>
373: #include <finclude/petscksp.h>
374: #include <finclude/petscpc.h>
375: #include <finclude/petscsnes.h>

377:       SNES              snes
378:       type (userctx)    user
379:       Vec               x,f,g,y,w
380:       PetscReal fnorm,ynorm,gnorm,xnorm
381:       PetscBool            flag
382:       PetscErrorCode ierr

384:       PetscScalar       mone

386:         write(*,*)"Inside FormLineSearch, user%xm=",user%xm
387:       mone = -1.0d0
388:       call SNESLineSearchGetSNES(linesearch, snes, ierr)
389:       call SNESLineSearchGetVecs(linesearch, x, f, y, w, g, ierr)
390:       call VecNorm(y,NORM_2,ynorm,ierr)
391:       call VecAXPY(x,mone,y,ierr)
392:       call SNESComputeFunction(snes,x,f,ierr)
393:       call VecNorm(f,NORM_2,gnorm,ierr)
394:       call VecNorm(x,NORM_2,xnorm,ierr)
395:       call SNESLineSearchSetNorms(linesearch,xnorm,gnorm,ynorm,ierr)
396:       return
397:       end

399: ! ---------------------------------------------------------------------
400: !
401: !  FormInitialGuess - Forms initial approximation.
402: !
403: !  Input Parameters:
404: !  X - vector
405: !
406: !  Output Parameter:
407: !  X - vector
408: !
409: !  Notes:
410: !  This routine serves as a wrapper for the lower-level routine
411: !  "InitialGuessLocal", where the actual computations are
412: !  done using the standard Fortran style of treating the local
413: !  vector data as a multidimensional array over the local mesh.
414: !  This routine merely handles ghost point scatters and accesses
415: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
416: !
417:       subroutine FormInitialGuess(snes,X,ierr)
418:       use f90module
419:       implicit none

421: #include <finclude/petscvec.h90>
422: #include <finclude/petscsys.h>
423: #include <finclude/petscvec.h>
424: #include <finclude/petscdmda.h>
425: #include <finclude/petscis.h>
426: #include <finclude/petscmat.h>
427: #include <finclude/petscksp.h>
428: #include <finclude/petscpc.h>
429: #include <finclude/petscsnes.h>

431: !  Input/output variables:
432:       SNES     snes
433:       Vec      X
434:       integer  ierr
435:       DM       da

437: !  Declarations for use with local arrays:
438:       PetscScalar,pointer :: lx_v(:)
439:       Vec               localX
440:       type (userctx)         user

442:       0

444: !  Get a pointer to vector data.
445: !    - For default PETSc vectors, VecGetArray90() returns a pointer to
446: !      the data array. Otherwise, the routine is implementation dependent.
447: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
448: !      the array.
449: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
450: !      and is useable from Fortran-90 Only.

452:       call SNESGetApplicationContext(snes,user,ierr)
453:       call SNESGetDM(snes,da,ierr)
454:       call DMGetLocalVector(da,localX,ierr)
455:       call VecGetArrayF90(localX,lx_v,ierr)

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

459:       call InitialGuessLocal(user,lx_v,ierr)

461: !  Restore vector

463:       call VecRestoreArrayF90(localX,lx_v,ierr)

465: !  Insert values into global vector

467:       call DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X,ierr)
468:       call DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X,ierr)
469:       call DMRestoreLocalVector(da,localX,ierr)

471:       return
472:       end

474: ! ---------------------------------------------------------------------
475: !
476: !  InitialGuessLocal - Computes initial approximation, called by
477: !  the higher level routine FormInitialGuess().
478: !
479: !  Input Parameter:
480: !  x - local vector data
481: !
482: !  Output Parameters:
483: !  x - local vector data
484: !  ierr - error code
485: !
486: !  Notes:
487: !  This routine uses standard Fortran-style computations over a 2-dim array.
488: !
489:       subroutine InitialGuessLocal(user,x,ierr)
490:       use f90module
491:       implicit none

493: #include <finclude/petscsys.h>
494: #include <finclude/petscvec.h>
495: #include <finclude/petscdmda.h>
496: #include <finclude/petscis.h>
497: #include <finclude/petscmat.h>
498: #include <finclude/petscksp.h>
499: #include <finclude/petscpc.h>
500: #include <finclude/petscsnes.h>

502: !  Input/output variables:
503:       type (userctx) user
504:       PetscScalar  x(user%gxs:user%gxe,                                         &
505:      &              user%gys:user%gye)
506:       integer ierr

508: !  Local variables:
509:       integer  i,j
510:       PetscScalar   temp1,temp,hx,hy
511:       PetscScalar   one

513: !  Set parameters

515:       0
516:       one    = 1.0
517:       hx     = one/(dble(user%mx-1))
518:       hy     = one/(dble(user%my-1))
519:       temp1  = user%lambda/(user%lambda + one)

521:       do 20 j=user%ys,user%ye
522:          temp = dble(min(j-1,user%my-j))*hy
523:          do 10 i=user%xs,user%xe
524:             if (i .eq. 1 .or. j .eq. 1                                  &
525:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
526:               x(i,j) = 0.0
527:             else
528:               x(i,j) = temp1 *                                          &
529:      &          sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
530:             endif
531:  10      continue
532:  20   continue

534:       return
535:       end

537: ! ---------------------------------------------------------------------
538: !
539: !  FormFunctionLocal - Computes nonlinear function, called by
540: !  the higher level routine FormFunction().
541: !
542: !  Input Parameter:
543: !  x - local vector data
544: !
545: !  Output Parameters:
546: !  f - local vector data, f(x)
547: !  ierr - error code
548: !
549: !  Notes:
550: !  This routine uses standard Fortran-style computations over a 2-dim array.
551: !
552:       subroutine FormFunctionLocal(x,f,user,ierr)
553:       use f90module

555:       implicit none

557: !  Input/output variables:
558:       type (userctx) user
559:       PetscScalar  x(user%gxs:user%gxe,                                         &
560:      &              user%gys:user%gye)
561:       PetscScalar  f(user%xs:user%xe,                                           &
562:      &              user%ys:user%ye)
563:       integer  ierr

565: !  Local variables:
566:       PetscScalar   two,one,hx,hy,hxdhy,hydhx,sc
567:       PetscScalar   u,uxx,uyy
568:       integer  i,j

570:       one    = 1.0
571:       two    = 2.0
572:       hx     = one/dble(user%mx-1)
573:       hy     = one/dble(user%my-1)
574:       sc     = hx*hy*user%lambda
575:       hxdhy  = hx/hy
576:       hydhx  = hy/hx

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

580:       do 20 j=user%ys,user%ye
581:          do 10 i=user%xs,user%xe
582:             if (i .eq. 1 .or. j .eq. 1                                  &
583:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
584:                f(i,j) = x(i,j)
585:             else
586:                u = x(i,j)
587:                uxx = hydhx * (two*u                                     &
588:      &                - x(i-1,j) - x(i+1,j))
589:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
590:                f(i,j) = uxx + uyy - sc*exp(u)
591:             endif
592:  10      continue
593:  20   continue

595:       return
596:       end

598: ! ---------------------------------------------------------------------
599: !
600: !  FormJacobian - Evaluates Jacobian matrix.
601: !
602: !  Input Parameters:
603: !  snes     - the SNES context
604: !  x        - input vector
605: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
606: !             (not used here)
607: !
608: !  Output Parameters:
609: !  jac      - Jacobian matrix
610: !  jac_prec - optionally different preconditioning matrix (not used here)
611: !  flag     - flag indicating matrix structure
612: !
613: !  Notes:
614: !  This routine serves as a wrapper for the lower-level routine
615: !  "FormJacobianLocal", where the actual computations are
616: !  done using the standard Fortran style of treating the local
617: !  vector data as a multidimensional array over the local mesh.
618: !  This routine merely accesses the local vector data via
619: !  VecGetArrayF90() and VecRestoreArrayF90().
620: !
621: !  Notes:
622: !  Due to grid point reordering with DMDAs, we must always work
623: !  with the local grid points, and then transform them to the new
624: !  global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
625: !  We cannot work directly with the global numbers for the original
626: !  uniprocessor grid!
627: !
628: !  Two methods are available for imposing this transformation
629: !  when setting matrix entries:
630: !    (A) MatSetValuesLocal(), using the local ordering (including
631: !        ghost points!)
632: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
633: !        - Associate this map with the matrix by calling
634: !          MatSetLocalToGlobalMapping() once
635: !        - Set matrix entries using the local ordering
636: !          by calling MatSetValuesLocal()
637: !    (B) MatSetValues(), using the global ordering
638: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
639: !        - Then apply this map explicitly yourself
640: !        - Set matrix entries using the global ordering by calling
641: !          MatSetValues()
642: !  Option (A) seems cleaner/easier in many cases, and is the procedure
643: !  used in this example.
644: !
645:       subroutine FormJacobian(snes,X,jac,jac_prec,flag,user,ierr)
646:       use f90module
647:       implicit none

649: #include <finclude/petscsys.h>
650: #include <finclude/petscvec.h>
651: #include <finclude/petscdmda.h>
652: #include <finclude/petscis.h>
653: #include <finclude/petscmat.h>
654: #include <finclude/petscksp.h>
655: #include <finclude/petscpc.h>
656: #include <finclude/petscsnes.h>

658: #include <finclude/petscvec.h90>

660: !  Input/output variables:
661:       SNES         snes
662:       Vec          X
663:       Mat          jac,jac_prec
664:       MatStructure flag
665:       type(userctx) user
666:       integer      ierr
667:       DM           da

669: !  Declarations for use with local arrays:
670:       PetscScalar,pointer :: lx_v(:)
671:       Vec            localX

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

678:       call SNESGetDM(snes,da,ierr)
679:       call DMGetLocalVector(da,localX,ierr)
680:       call DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,              &
681:      &     ierr)
682:       call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr)

684: !  Get a pointer to vector data

686:       call VecGetArrayF90(localX,lx_v,ierr)

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

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

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

697:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
698:       call VecRestoreArrayF90(localX,lx_v,ierr)
699:       call DMRestoreLocalVector(da,localX,ierr)
700:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)

702: !  Set flag to indicate that the Jacobian matrix retains an identical
703: !  nonzero structure throughout all nonlinear iterations (although the
704: !  values of the entries change). Thus, we can save some work in setting
705: !  up the preconditioner (e.g., no need to redo symbolic factorization for
706: !  ILU/ICC preconditioners).
707: !   - If the nonzero structure of the matrix is different during
708: !     successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
709: !     must be used instead.  If you are unsure whether the matrix
710: !     structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
711: !   - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
712: !     believes your assertion and does not check the structure
713: !     of the matrix.  If you erroneously claim that the structure
714: !     is the same when it actually is not, the new preconditioner
715: !     will not function correctly.  Thus, use this optimization
716: !     feature with caution!

718:       flag = SAME_NONZERO_PATTERN

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

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

725:       return
726:       end

728: ! ---------------------------------------------------------------------
729: !
730: !  FormJacobianLocal - Computes Jacobian matrix, called by
731: !  the higher level routine FormJacobian().
732: !
733: !  Input Parameters:
734: !  x        - local vector data
735: !
736: !  Output Parameters:
737: !  jac      - Jacobian matrix
738: !  jac_prec - optionally different preconditioning matrix (not used here)
739: !  ierr     - error code
740: !
741: !  Notes:
742: !  This routine uses standard Fortran-style computations over a 2-dim array.
743: !
744: !  Notes:
745: !  Due to grid point reordering with DMDAs, we must always work
746: !  with the local grid points, and then transform them to the new
747: !  global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
748: !  We cannot work directly with the global numbers for the original
749: !  uniprocessor grid!
750: !
751: !  Two methods are available for imposing this transformation
752: !  when setting matrix entries:
753: !    (A) MatSetValuesLocal(), using the local ordering (including
754: !        ghost points!)
755: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
756: !        - Associate this map with the matrix by calling
757: !          MatSetLocalToGlobalMapping() once
758: !        - Set matrix entries using the local ordering
759: !          by calling MatSetValuesLocal()
760: !    (B) MatSetValues(), using the global ordering
761: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
762: !        - Then apply this map explicitly yourself
763: !        - Set matrix entries using the global ordering by calling
764: !          MatSetValues()
765: !  Option (A) seems cleaner/easier in many cases, and is the procedure
766: !  used in this example.
767: !
768:       subroutine FormJacobianLocal(x,jac,jac_prec,user,ierr)
769:       use f90module
770:       implicit none

772: #include <finclude/petscsys.h>
773: #include <finclude/petscvec.h>
774: #include <finclude/petscdmda.h>
775: #include <finclude/petscis.h>
776: #include <finclude/petscmat.h>
777: #include <finclude/petscksp.h>
778: #include <finclude/petscpc.h>
779: #include <finclude/petscsnes.h>

781: !  Input/output variables:
782:       type (userctx) user
783:       PetscScalar  x(user%gxs:user%gxe,                                         &
784:      &              user%gys:user%gye)
785:       Mat      jac,jac_prec
786:       integer  ierr

788: !  Local variables:
789:       integer  row,col(5),i,j
790:       PetscScalar   two,one,hx,hy,hxdhy
791:       PetscScalar   hydhx,sc,v(5)

793: !  Set parameters

795:       one    = 1.0
796:       two    = 2.0
797:       hx     = one/dble(user%mx-1)
798:       hy     = one/dble(user%my-1)
799:       sc     = hx*hy
800:       hxdhy  = hx/hy
801:       hydhx  = hy/hx


804: !     Compute entries for the locally owned part of the Jacobian.
805: !   - Currently, all PETSc parallel matrix formats are partitioned by
806: !     contiguous chunks of rows across the processors.
807: !   - Each processor needs to insert only elements that it owns
808: !     locally (but any non-local elements will be sent to the
809: !     appropriate processor during matrix assembly).
810: !   - Here, we set all entries for a particular row at once.
811: !   - We can set matrix entries either using either
812: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
813: !   - Note that MatSetValues() uses 0-based row and column numbers
814: !     in Fortran as well as in C.

816:       do 20 j=user%ys,user%ye
817:          row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
818:          do 10 i=user%xs,user%xe
819:             row = row + 1
820: !           boundary points
821:             if (i .eq. 1 .or. j .eq. 1                                  &
822:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
823:                col(1) = row
824:                v(1)   = one
825:                call MatSetValuesLocal(jac,1,row,1,col,v,                &
826:      &                           INSERT_VALUES,ierr)
827: !           interior grid points
828:             else
829:                v(1) = -hxdhy
830:                v(2) = -hydhx
831:                v(3) = two*(hydhx + hxdhy)                               &
832:      &                  - sc*user%lambda*exp(x(i,j))
833:                v(4) = -hydhx
834:                v(5) = -hxdhy
835:                col(1) = row - user%gxm
836:                col(2) = row - 1
837:                col(3) = row
838:                col(4) = row + 1
839:                col(5) = row + user%gxm
840:                call MatSetValuesLocal(jac,1,row,5,col,v,                &
841:      &                                INSERT_VALUES,ierr)
842:             endif
843:  10      continue
844:  20   continue

846:       return
847:       end

849:       subroutine FormPreCheck(snes,X,Y,changed_Y,user,ierr)
850:       use f90module

852:       SNES           snes
853:       Vec            X,Y
854:       type (userctx) user
855:       PetscBool      changed_Y
856:       PetscErrorCode ierr

858:              write(*,*)"Inside formPreCheck, user%xm=",user%xm
859:       end subroutine formPreCheck

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

864:       SNES           snes
865:       Vec            X,Y,W
866:       type (userctx) user
867:       PetscBool      changed_Y,changed_W
868:       PetscErrorCode ierr

870:              write(*,*)"Inside formPostCheck, user%xm=",user%xm
871:       end subroutine formPostCheck