Actual source code: ex5f90t.F90

  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: !
 10: !  --------------------------------------------------------------------------
 11: !
 12: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 13: !  the partial differential equation
 14: !
 15: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
 16: !
 17: !  with boundary conditions
 18: !
 19: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
 20: !
 21: !  A finite difference approximation with the usual 5-point stencil
 22: !  is used to discretize the boundary value problem to obtain a nonlinear
 23: !  system of equations.
 24: !
 25: !  The uniprocessor version of this code is snes/tutorials/ex4f.F
 26: !
 27: !  --------------------------------------------------------------------------
 28: !  The following define must be used before including any PETSc include files
 29: !  into a module or interface. This is because they can't handle declarations
 30: !  in them
 31: !

 33:       module f90modulet
 34: #include <petsc/finclude/petscdm.h>
 35:       use petscdmdef
 36:       type userctx
 37:         type(tDM) da
 38:         PetscInt xs,xe,xm,gxs,gxe,gxm
 39:         PetscInt ys,ye,ym,gys,gye,gym
 40:         PetscInt mx,my
 41:         PetscMPIInt rank
 42:         PetscReal lambda
 43:       end type userctx

 45:       contains
 46: ! ---------------------------------------------------------------------
 47: !
 48: !  FormFunction - Evaluates nonlinear function, F(x).
 49: !
 50: !  Input Parameters:
 51: !  snes - the SNES context
 52: !  X - input vector
 53: !  dummy - optional user-defined context, as set by SNESSetFunction()
 54: !          (not used here)
 55: !
 56: !  Output Parameter:
 57: !  F - function vector
 58: !
 59: !  Notes:
 60: !  This routine serves as a wrapper for the lower-level routine
 61: !  "FormFunctionLocal", where the actual computations are
 62: !  done using the standard Fortran style of treating the local
 63: !  vector data as a multidimensional array over the local mesh.
 64: !  This routine merely handles ghost point scatters and accesses
 65: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
 66: !
 67:       subroutine FormFunction(snesIn,X,F,user,ierr)
 68: #include <petsc/finclude/petscsnes.h>
 69:       use petscsnes

 71: !  Input/output variables:
 72:       type(tSNES)     snesIn
 73:       type(tVec)      X,F
 74:       PetscErrorCode ierr
 75:       type (userctx) user

 77: !  Declarations for use with local arrays:
 78:       PetscScalar,pointer :: lx_v(:),lf_v(:)
 79:       type(tVec)              localX

 81: !  Scatter ghost points to local vector, using the 2-step process
 82: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
 83: !  By placing code between these two statements, computations can
 84: !  be done while messages are in transition.
 85:       call DMGetLocalVector(user%da,localX,ierr);CHKERRQ(ierr)
 86:       call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
 87:       call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)

 89: !  Get a pointer to vector data.
 90: !    - For default PETSc vectors, VecGetArray90() returns a pointer to
 91: !      the data array. Otherwise, the routine is implementation dependent.
 92: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
 93: !      the array.
 94: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
 95: !      and is useable from Fortran-90 Only.

 97:       call VecGetArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
 98:       call VecGetArrayF90(F,lf_v,ierr);CHKERRQ(ierr)

100: !  Compute function over the locally owned part of the grid
101:       call FormFunctionLocal(lx_v,lf_v,user,ierr);CHKERRQ(ierr)

103: !  Restore vectors
104:       call VecRestoreArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
105:       call VecRestoreArrayF90(F,lf_v,ierr);CHKERRQ(ierr)

107: !  Insert values into global vector

109:       call DMRestoreLocalVector(user%da,localX,ierr);CHKERRQ(ierr)
110:       call PetscLogFlops(11.0d0*user%ym*user%xm,ierr)

112: !      call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
113: !      call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
114:       return
115:       end subroutine formfunction
116:       end module f90modulet

118:       module f90moduleinterfacest
119:         use f90modulet

121:       Interface SNESSetApplicationContext
122:         Subroutine SNESSetApplicationContext(snesIn,ctx,ierr)
123: #include <petsc/finclude/petscsnes.h>
124:         use petscsnes
125:         use f90modulet
126:           type(tSNES)    snesIn
127:           type(userctx) ctx
128:           PetscErrorCode ierr
129:         End Subroutine
130:       End Interface SNESSetApplicationContext

132:       Interface SNESGetApplicationContext
133:         Subroutine SNESGetApplicationContext(snesIn,ctx,ierr)
134: #include <petsc/finclude/petscsnes.h>
135:         use petscsnes
136:         use f90modulet
137:           type(tSNES)     snesIn
138:           type(userctx), pointer :: ctx
139:           PetscErrorCode ierr
140:         End Subroutine
141:       End Interface SNESGetApplicationContext
142:       end module f90moduleinterfacest

144:       program main
145: #include <petsc/finclude/petscdm.h>
146: #include <petsc/finclude/petscsnes.h>
147:       use petscdmda
148:       use petscdm
149:       use petscsnes
150:       use f90modulet
151:       use f90moduleinterfacest
152:       implicit none
153: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
154: !                   Variable declarations
155: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: !
157: !  Variables:
158: !     mysnes      - nonlinear solver
159: !     x, r        - solution, residual vectors
160: !     J           - Jacobian matrix
161: !     its         - iterations for convergence
162: !     Nx, Ny      - number of preocessors in x- and y- directions
163: !     matrix_free - flag - 1 indicates matrix-free version
164: !
165:       type(tSNES)       mysnes
166:       type(tVec)        x,r
167:       type(tMat)        J
168:       PetscErrorCode   ierr
169:       PetscInt         its
170:       PetscBool        flg,matrix_free,set
171:       PetscInt         ione,nfour
172:       PetscReal lambda_max,lambda_min
173:       type(userctx)    user
174:       type(userctx), pointer:: puser
175:       type(tPetscOptions) :: options

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

181: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182: !  Initialize program
183: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
185:       if (ierr .ne. 0) then
186:         print*,'Unable to initialize PETSc'
187:         stop
188:       endif
189:       call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)

191: !  Initialize problem parameters
192:       options%v = 0
193:       lambda_max  = 6.81
194:       lambda_min  = 0.0
195:       user%lambda = 6.0
196:       ione = 1
197:       nfour = 4
198:       call PetscOptionsGetReal(options,PETSC_NULL_CHARACTER,'-par',user%lambda,flg,ierr);CHKERRA(ierr)
199:       if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) then; SETERRA(PETSC_COMM_SELF,PETSC_ERR_USER,'Lambda provided with -par is out of range '); endif

201: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202: !  Create nonlinear solver context
203: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204:       call SNESCreate(PETSC_COMM_WORLD,mysnes,ierr);CHKERRA(ierr)

206: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
207: !  Create vector data structures; set function evaluation routine
208: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

212: ! This really needs only the star-type stencil, but we use the box
213: ! stencil temporarily.
214:       call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,ione,ione, &
215:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr);CHKERRA(ierr)
216:       call DMSetFromOptions(user%da,ierr);CHKERRA(ierr)
217:       call DMSetUp(user%da,ierr);CHKERRA(ierr)
218:       call DMDAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
219:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)

221: !
222: !   Visualize the distribution of the array across the processors
223: !
224: !     call DMView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)

226: !  Extract global and local vectors from DMDA; then duplicate for remaining
227: !  vectors that are the same types
228:       call DMCreateGlobalVector(user%da,x,ierr);CHKERRA(ierr)
229:       call VecDuplicate(x,r,ierr);CHKERRA(ierr)

231: !  Get local grid boundaries (for 2-dimensional DMDA)
232:       call DMDAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER,user%xm,user%ym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
233:       call DMDAGetGhostCorners(user%da,user%gxs,user%gys,PETSC_NULL_INTEGER,user%gxm,user%gym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)

235: !  Here we shift the starting indices up by one so that we can easily
236: !  use the Fortran convention of 1-based indices (rather 0-based indices).
237:       user%xs  = user%xs+1
238:       user%ys  = user%ys+1
239:       user%gxs = user%gxs+1
240:       user%gys = user%gys+1

242:       user%ye  = user%ys+user%ym-1
243:       user%xe  = user%xs+user%xm-1
244:       user%gye = user%gys+user%gym-1
245:       user%gxe = user%gxs+user%gxm-1

247:       call SNESSetApplicationContext(mysnes,user,ierr);CHKERRA(ierr)

249: !  Set function evaluation routine and vector
250:       call SNESSetFunction(mysnes,r,FormFunction,user,ierr);CHKERRA(ierr)

252: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
253: !  Create matrix data structure; set Jacobian evaluation routine
254: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

256: !  Set Jacobian matrix data structure and default Jacobian evaluation
257: !  routine. User can override with:
258: !     -snes_fd : default finite differencing approximation of Jacobian
259: !     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
260: !                (unless user explicitly sets preconditioner)
261: !     -snes_mf_operator : form preconditioning matrix as set by the user,
262: !                         but use matrix-free approx for Jacobian-vector
263: !                         products within Newton-Krylov method
264: !
265: !  Note:  For the parallel case, vectors and matrices MUST be partitioned
266: !     accordingly.  When using distributed arrays (DMDAs) to create vectors,
267: !     the DMDAs determine the problem partitioning.  We must explicitly
268: !     specify the local matrix dimensions upon its creation for compatibility
269: !     with the vector distribution.  Thus, the generic MatCreate() routine
270: !     is NOT sufficient when working with distributed arrays.
271: !
272: !     Note: Here we only approximately preallocate storage space for the
273: !     Jacobian.  See the users manual for a discussion of better techniques
274: !     for preallocating matrix memory.

276:       call PetscOptionsHasName(options,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr);CHKERRA(ierr)
277:       if (.not. matrix_free) then
278:         call DMSetMatType(user%da,MATAIJ,ierr);CHKERRA(ierr)
279:         call DMCreateMatrix(user%da,J,ierr);CHKERRA(ierr)
280:         call SNESSetJacobian(mysnes,J,J,FormJacobian,user,ierr);CHKERRA(ierr)
281:       endif

283: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
284: !  Customize nonlinear solver; set runtime options
285: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
286: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
287:       call SNESSetFromOptions(mysnes,ierr);CHKERRA(ierr)

289: !     Test Fortran90 wrapper for SNESSet/Get ApplicationContext()
290:       call PetscOptionsGetBool(options,PETSC_NULL_CHARACTER,'-test_appctx',flg,set,ierr);CHKERRA(ierr)
291:       if (flg) then
292:         call SNESGetApplicationContext(mysnes,puser,ierr);CHKERRA(ierr)
293:       endif

295: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
296: !  Evaluate initial guess; then solve nonlinear system.
297: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
298: !  Note: The user should initialize the vector, x, with the initial guess
299: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
300: !  to employ an initial guess of zero, the user should explicitly set
301: !  this vector to zero by calling VecSet().

303:       call FormInitialGuess(mysnes,x,ierr);CHKERRA(ierr)
304:       call SNESSolve(mysnes,PETSC_NULL_VEC,x,ierr);CHKERRA(ierr)
305:       call SNESGetIterationNumber(mysnes,its,ierr);CHKERRA(ierr)
306:       if (user%rank .eq. 0) then
307:          write(6,100) its
308:       endif
309:   100 format('Number of SNES iterations = ',i5)

311: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
312: !  Free work space.  All PETSc objects should be destroyed when they
313: !  are no longer needed.
314: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
315:       if (.not. matrix_free) call MatDestroy(J,ierr);CHKERRA(ierr)
316:       call VecDestroy(x,ierr);CHKERRA(ierr)
317:       call VecDestroy(r,ierr);CHKERRA(ierr)
318:       call SNESDestroy(mysnes,ierr);CHKERRA(ierr)
319:       call DMDestroy(user%da,ierr);CHKERRA(ierr)

321:       call PetscFinalize(ierr)
322:       end

324: ! ---------------------------------------------------------------------
325: !
326: !  FormInitialGuess - Forms initial approximation.
327: !
328: !  Input Parameters:
329: !  X - vector
330: !
331: !  Output Parameter:
332: !  X - vector
333: !
334: !  Notes:
335: !  This routine serves as a wrapper for the lower-level routine
336: !  "InitialGuessLocal", where the actual computations are
337: !  done using the standard Fortran style of treating the local
338: !  vector data as a multidimensional array over the local mesh.
339: !  This routine merely handles ghost point scatters and accesses
340: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
341: !
342:       subroutine FormInitialGuess(mysnes,X,ierr)
343: #include <petsc/finclude/petscsnes.h>
344:       use petscsnes
345:       use f90modulet
346:       use f90moduleinterfacest
347: !  Input/output variables:
348:       type(tSNES)     mysnes
349:       type(userctx), pointer:: puser
350:       type(tVec)      X
351:       PetscErrorCode ierr

353: !  Declarations for use with local arrays:
354:       PetscScalar,pointer :: lx_v(:)

356:       0
357:       call SNESGetApplicationContext(mysnes,puser,ierr)
358: !  Get a pointer to vector data.
359: !    - For default PETSc vectors, VecGetArray90() returns a pointer to
360: !      the data array. Otherwise, the routine is implementation dependent.
361: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
362: !      the array.
363: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
364: !      and is useable from Fortran-90 Only.

366:       call VecGetArrayF90(X,lx_v,ierr)

368: !  Compute initial guess over the locally owned part of the grid
369:       call InitialGuessLocal(puser,lx_v,ierr)

371: !  Restore vector
372:       call VecRestoreArrayF90(X,lx_v,ierr)

374: !  Insert values into global vector

376:       return
377:       end

379: ! ---------------------------------------------------------------------
380: !
381: !  InitialGuessLocal - Computes initial approximation, called by
382: !  the higher level routine FormInitialGuess().
383: !
384: !  Input Parameter:
385: !  x - local vector data
386: !
387: !  Output Parameters:
388: !  x - local vector data
389: !  ierr - error code
390: !
391: !  Notes:
392: !  This routine uses standard Fortran-style computations over a 2-dim array.
393: !
394:       subroutine InitialGuessLocal(user,x,ierr)
395: #include <petsc/finclude/petscsys.h>
396:       use petscsys
397:       use f90modulet
398: !  Input/output variables:
399:       type (userctx)         user
400:       PetscScalar  x(user%xs:user%xe,user%ys:user%ye)
401:       PetscErrorCode ierr

403: !  Local variables:
404:       PetscInt  i,j
405:       PetscScalar   temp1,temp,hx,hy
406:       PetscScalar   one

408: !  Set parameters

410:       0
411:       one    = 1.0
412:       hx     = one/(PetscIntToReal(user%mx-1))
413:       hy     = one/(PetscIntToReal(user%my-1))
414:       temp1  = user%lambda/(user%lambda + one)

416:       do 20 j=user%ys,user%ye
417:          temp = PetscIntToReal(min(j-1,user%my-j))*hy
418:          do 10 i=user%xs,user%xe
419:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
420:               x(i,j) = 0.0
421:             else
422:               x(i,j) = temp1 * sqrt(min(PetscIntToReal(min(i-1,user%mx-i)*hx),PetscIntToReal(temp)))
423:             endif
424:  10      continue
425:  20   continue

427:       return
428:       end

430: ! ---------------------------------------------------------------------
431: !
432: !  FormFunctionLocal - Computes nonlinear function, called by
433: !  the higher level routine FormFunction().
434: !
435: !  Input Parameter:
436: !  x - local vector data
437: !
438: !  Output Parameters:
439: !  f - local vector data, f(x)
440: !  ierr - error code
441: !
442: !  Notes:
443: !  This routine uses standard Fortran-style computations over a 2-dim array.
444: !
445:       subroutine FormFunctionLocal(x,f,user,ierr)
446: #include <petsc/finclude/petscsys.h>
447:       use petscsys
448:       use f90modulet
449: !  Input/output variables:
450:       type (userctx) user
451:       PetscScalar  x(user%gxs:user%gxe,user%gys:user%gye)
452:       PetscScalar  f(user%xs:user%xe,user%ys:user%ye)
453:       PetscErrorCode ierr

455: !  Local variables:
456:       PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
457:       PetscScalar u,uxx,uyy
458:       PetscInt  i,j

460:       one    = 1.0
461:       two    = 2.0
462:       hx     = one/PetscIntToReal(user%mx-1)
463:       hy     = one/PetscIntToReal(user%my-1)
464:       sc     = hx*hy*user%lambda
465:       hxdhy  = hx/hy
466:       hydhx  = hy/hx

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

470:       do 20 j=user%ys,user%ye
471:          do 10 i=user%xs,user%xe
472:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
473:                f(i,j) = x(i,j)
474:             else
475:                u = x(i,j)
476:                uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
477:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
478:                f(i,j) = uxx + uyy - sc*exp(u)
479:             endif
480:  10      continue
481:  20   continue
482:       0
483:       return
484:       end

486: ! ---------------------------------------------------------------------
487: !
488: !  FormJacobian - Evaluates Jacobian matrix.
489: !
490: !  Input Parameters:
491: !  snes     - the SNES context
492: !  x        - input vector
493: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
494: !             (not used here)
495: !
496: !  Output Parameters:
497: !  jac      - Jacobian matrix
498: !  jac_prec - optionally different preconditioning matrix (not used here)
499: !  flag     - flag indicating matrix structure
500: !
501: !  Notes:
502: !  This routine serves as a wrapper for the lower-level routine
503: !  "FormJacobianLocal", where the actual computations are
504: !  done using the standard Fortran style of treating the local
505: !  vector data as a multidimensional array over the local mesh.
506: !  This routine merely accesses the local vector data via
507: !  VecGetArrayF90() and VecRestoreArrayF90().
508: !
509: !  Notes:
510: !  Due to grid point reordering with DMDAs, we must always work
511: !  with the local grid points, and then transform them to the new
512: !  global numbering with the "ltog" mapping
513: !  We cannot work directly with the global numbers for the original
514: !  uniprocessor grid!
515: !
516: !  Two methods are available for imposing this transformation
517: !  when setting matrix entries:
518: !    (A) MatSetValuesLocal(), using the local ordering (including
519: !        ghost points!)
520: !        - Set matrix entries using the local ordering
521: !          by calling MatSetValuesLocal()
522: !    (B) MatSetValues(), using the global ordering
523: !        - Use DMGetLocalToGlobalMapping() then
524: !          ISLocalToGlobalMappingGetIndicesF90() to extract the local-to-global map
525: !        - Then apply this map explicitly yourself
526: !        - Set matrix entries using the global ordering by calling
527: !          MatSetValues()
528: !  Option (A) seems cleaner/easier in many cases, and is the procedure
529: !  used in this example.
530: !
531:       subroutine FormJacobian(mysnes,X,jac,jac_prec,user,ierr)
532: #include <petsc/finclude/petscsnes.h>
533:       use petscsnes
534:       use f90modulet
535: !  Input/output variables:
536:       type(tSNES)     mysnes
537:       type(tVec)      X
538:       type(tMat)      jac,jac_prec
539:       type(userctx)  user
540:       PetscErrorCode ierr

542: !  Declarations for use with local arrays:
543:       PetscScalar,pointer :: lx_v(:)
544:       type(tVec)      localX

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

551:       call DMGetLocalVector(user%da,localX,ierr)
552:       call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,ierr)
553:       call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)

555: !  Get a pointer to vector data
556:       call VecGetArrayF90(localX,lx_v,ierr)

558: !  Compute entries for the locally owned part of the Jacobian preconditioner.
559:       call FormJacobianLocal(lx_v,jac_prec,user,ierr)

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

566:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
567: !      if (jac .ne. jac_prec) then
568:          call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
569: !      endif
570:       call VecRestoreArrayF90(localX,lx_v,ierr)
571:       call DMRestoreLocalVector(user%da,localX,ierr)
572:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
573: !      if (jac .ne. jac_prec) then
574:         call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
575: !      endif

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

580:       call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr)

582:       return
583:       end

585: ! ---------------------------------------------------------------------
586: !
587: !  FormJacobianLocal - Computes Jacobian preconditioner matrix,
588: !  called by the higher level routine FormJacobian().
589: !
590: !  Input Parameters:
591: !  x        - local vector data
592: !
593: !  Output Parameters:
594: !  jac_prec - Jacobian preconditioner matrix
595: !  ierr     - error code
596: !
597: !  Notes:
598: !  This routine uses standard Fortran-style computations over a 2-dim array.
599: !
600: !  Notes:
601: !  Due to grid point reordering with DMDAs, we must always work
602: !  with the local grid points, and then transform them to the new
603: !  global numbering with the "ltog" mapping
604: !  We cannot work directly with the global numbers for the original
605: !  uniprocessor grid!
606: !
607: !  Two methods are available for imposing this transformation
608: !  when setting matrix entries:
609: !    (A) MatSetValuesLocal(), using the local ordering (including
610: !        ghost points!)
611: !        - Set matrix entries using the local ordering
612: !          by calling MatSetValuesLocal()
613: !    (B) MatSetValues(), using the global ordering
614: !        - Set matrix entries using the global ordering by calling
615: !          MatSetValues()
616: !  Option (A) seems cleaner/easier in many cases, and is the procedure
617: !  used in this example.
618: !
619:       subroutine FormJacobianLocal(x,jac_prec,user,ierr)
620: #include <petsc/finclude/petscmat.h>
621:       use petscmat
622:       use f90modulet
623: !  Input/output variables:
624:       type (userctx) user
625:       PetscScalar    x(user%gxs:user%gxe,user%gys:user%gye)
626:       type(tMat)      jac_prec
627:       PetscErrorCode ierr

629: !  Local variables:
630:       PetscInt    row,col(5),i,j
631:       PetscInt    ione,ifive
632:       PetscScalar two,one,hx,hy,hxdhy
633:       PetscScalar hydhx,sc,v(5)

635: !  Set parameters
636:       ione   = 1
637:       ifive  = 5
638:       one    = 1.0
639:       two    = 2.0
640:       hx     = one/PetscIntToReal(user%mx-1)
641:       hy     = one/PetscIntToReal(user%my-1)
642:       sc     = hx*hy
643:       hxdhy  = hx/hy
644:       hydhx  = hy/hx

646: !  Compute entries for the locally owned part of the Jacobian.
647: !   - Currently, all PETSc parallel matrix formats are partitioned by
648: !     contiguous chunks of rows across the processors.
649: !   - Each processor needs to insert only elements that it owns
650: !     locally (but any non-local elements will be sent to the
651: !     appropriate processor during matrix assembly).
652: !   - Here, we set all entries for a particular row at once.
653: !   - We can set matrix entries either using either
654: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
655: !   - Note that MatSetValues() uses 0-based row and column numbers
656: !     in Fortran as well as in C.

658:       do 20 j=user%ys,user%ye
659:          row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
660:          do 10 i=user%xs,user%xe
661:             row = row + 1
662: !           boundary points
663:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
664:                col(1) = row
665:                v(1)   = one
666:                call MatSetValuesLocal(jac_prec,ione,row,ione,col,v,INSERT_VALUES,ierr)
667: !           interior grid points
668:             else
669:                v(1) = -hxdhy
670:                v(2) = -hydhx
671:                v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i,j))
672:                v(4) = -hydhx
673:                v(5) = -hxdhy
674:                col(1) = row - user%gxm
675:                col(2) = row - 1
676:                col(3) = row
677:                col(4) = row + 1
678:                col(5) = row + user%gxm
679:                call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v,INSERT_VALUES,ierr)
680:             endif
681:  10      continue
682:  20   continue
683:       return
684:       end

686: !/*TEST
687: !
688: !   test:
689: !      nsize: 4
690: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
691: !
692: !TEST*/