Actual source code: ex5f90.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: !

 10: !
 11: !  --------------------------------------------------------------------------
 12: !
 13: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
 14: !  the partial differential equation
 15: !
 16: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
 17: !
 18: !  with boundary conditions
 19: !
 20: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
 21: !
 22: !  A finite difference approximation with the usual 5-point stencil
 23: !  is used to discretize the boundary value problem to obtain a nonlinear
 24: !  system of equations.
 25: !
 26: !  The uniprocessor version of this code is snes/tutorials/ex4f.F
 27: !
 28: !  --------------------------------------------------------------------------
 29: !  The following define must be used before including any PETSc include files
 30: !  into a module or interface. This is because they can't handle declarations
 31: !  in them
 32: !

 34: module ex5f90module
 35: #include <petsc/finclude/petscsnes.h>
 36: #include <petsc/finclude/petscdmda.h>
 37:   use petscsnes
 38:   use petscdmda
 39:   type userctx
 40:     PetscInt xs, xe, xm, gxs, gxe, gxm
 41:     PetscInt ys, ye, ym, gys, gye, gym
 42:     PetscInt mx, my
 43:     PetscMPIInt rank
 44:     PetscReal lambda
 45:   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 VecGetArray() and VecRestoreArray().
 68: !
 69:   subroutine FormFunction(snes, X, F, user, ierr)
 70:     implicit none

 72: !  Input/output variables:
 73:     SNES snes
 74:     Vec X, F
 75:     PetscErrorCode ierr
 76:     type(userctx) user
 77:     DM da

 79: !  Declarations for use with local arrays:
 80:     PetscScalar, pointer :: lx_v(:), lf_v(:)
 81:     Vec localX

 83: !  Scatter ghost points to local vector, using the 2-step process
 84: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
 85: !  By placing code between these two statements, computations can
 86: !  be done while messages are in transition.
 87:     PetscCall(SNESGetDM(snes, da, ierr))
 88:     PetscCall(DMGetLocalVector(da, localX, ierr))
 89:     PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX, ierr))
 90:     PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX, ierr))

 92: !  Get a pointer to vector data.
 93: !    - For default PETSc vectors, VecGetArray() returns a pointer to
 94: !      the data array. Otherwise, the routine is implementation dependent.
 95: !    - You MUST call VecRestoreArray() when you no longer need access to
 96: !      the array.
 97: !    - Note that the interface to VecGetArray() differs from VecGetArray().

 99:     PetscCall(VecGetArray(localX, lx_v, ierr))
100:     PetscCall(VecGetArray(F, lf_v, ierr))

102: !  Compute function over the locally owned part of the grid
103:     PetscCall(FormFunctionLocal(lx_v, lf_v, user, ierr))

105: !  Restore vectors
106:     PetscCall(VecRestoreArray(localX, lx_v, ierr))
107:     PetscCall(VecRestoreArray(F, lf_v, ierr))

109: !  Insert values into global vector

111:     PetscCall(DMRestoreLocalVector(da, localX, ierr))
112:     PetscCall(PetscLogFlops(11.0d0*user%ym*user%xm, ierr))

114: !      PetscCallA(VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr))
115: !      PetscCallA(VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr))
116:   end subroutine formfunction
117: end module ex5f90module

119: module ex5f90moduleinterfaces
120:   use ex5f90module

122:   Interface SNESSetApplicationContext
123:     Subroutine SNESSetApplicationContext(snes, ctx, ierr)
124:       use ex5f90module
125:       SNES snes
126:       type(userctx) ctx
127:       PetscErrorCode ierr
128:     End Subroutine
129:   End Interface SNESSetApplicationContext

131:   Interface SNESGetApplicationContext
132:     Subroutine SNESGetApplicationContext(snes, ctx, ierr)
133:       use ex5f90module
134:       SNES snes
135:       type(userctx), pointer :: ctx
136:       PetscErrorCode ierr
137:     End Subroutine
138:   End Interface SNESGetApplicationContext
139: end module ex5f90moduleinterfaces

141: program main
142:   use ex5f90module
143:   use ex5f90moduleinterfaces
144:   implicit none
145: !

147: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: !                   Variable declarations
149: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: !
151: !  Variables:
152: !     snes        - nonlinear solver
153: !     x, r        - solution, residual vectors
154: !     J           - Jacobian matrix
155: !     its         - iterations for convergence
156: !     Nx, Ny      - number of preocessors in x- and y- directions
157: !     matrix_free - flag - 1 indicates matrix-free version
158: !
159:   SNES snes
160:   Vec x, r
161:   Mat J
162:   PetscErrorCode ierr
163:   PetscInt its
164:   PetscBool flg, matrix_free
165:   PetscInt ione, nfour
166:   PetscReal lambda_max, lambda_min
167:   type(userctx) user
168:   DM da

170: !  Note: Any user-defined Fortran routines (such as FormJacobian)
171: !  MUST be declared as external.
172:   external FormInitialGuess, FormJacobian

174: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: !  Initialize program
176: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177:   PetscCallA(PetscInitialize(ierr))
178:   PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD, user%rank, ierr))

180: !  Initialize problem parameters
181:   lambda_max = 6.81
182:   lambda_min = 0.0
183:   user%lambda = 6.0
184:   ione = 1
185:   nfour = 4
186:   PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS, PETSC_NULL_CHARACTER, '-par', user%lambda, flg, ierr))
187:   PetscCheckA(user%lambda < lambda_max .and. user%lambda > lambda_min, PETSC_COMM_SELF, PETSC_ERR_USER, 'Lambda provided with -par is out of range')

189: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: !  Create nonlinear solver context
191: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
192:   PetscCallA(SNESCreate(PETSC_COMM_WORLD, snes, ierr))

194: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195: !  Create vector data structures; set function evaluation routine
196: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

200: ! This really needs only the star-type stencil, but we use the box
201: ! stencil temporarily.
202:   PetscCallA(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_BOX, nfour, nfour, PETSC_DECIDE, PETSC_DECIDE, ione, ione, PETSC_NULL_INTEGER_ARRAY, PETSC_NULL_INTEGER_ARRAY, da, ierr))
203:   PetscCallA(DMSetFromOptions(da, ierr))
204:   PetscCallA(DMSetUp(da, ierr))

206:   PetscCallA(DMDAGetInfo(da, PETSC_NULL_INTEGER, user%mx, user%my, PETSC_NULL_INTEGER, PETSC_NULL_INTEGER, PETSC_NULL_INTEGER, PETSC_NULL_INTEGER, PETSC_NULL_INTEGER, PETSC_NULL_INTEGER, PETSC_NULL_DMBOUNDARYTYPE, PETSC_NULL_DMBOUNDARYTYPE, PETSC_NULL_DMBOUNDARYTYPE, PETSC_NULL_DMDASTENCILTYPE, ierr))

208: !
209: !   Visualize the distribution of the array across the processors
210: !
211: !     PetscCallA(DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr))

213: !  Extract global and local vectors from DMDA; then duplicate for remaining
214: !  vectors that are the same types
215:   PetscCallA(DMCreateGlobalVector(da, x, ierr))
216:   PetscCallA(VecDuplicate(x, r, ierr))

218: !  Get local grid boundaries (for 2-dimensional DMDA)
219:   PetscCallA(DMDAGetCorners(da, user%xs, user%ys, PETSC_NULL_INTEGER, user%xm, user%ym, PETSC_NULL_INTEGER, ierr))
220:   PetscCallA(DMDAGetGhostCorners(da, user%gxs, user%gys, PETSC_NULL_INTEGER, user%gxm, user%gym, PETSC_NULL_INTEGER, ierr))

222: !  Here we shift the starting indices up by one so that we can easily
223: !  use the Fortran convention of 1-based indices (rather 0-based indices).
224:   user%xs = user%xs + 1
225:   user%ys = user%ys + 1
226:   user%gxs = user%gxs + 1
227:   user%gys = user%gys + 1

229:   user%ye = user%ys + user%ym - 1
230:   user%xe = user%xs + user%xm - 1
231:   user%gye = user%gys + user%gym - 1
232:   user%gxe = user%gxs + user%gxm - 1

234:   PetscCallA(SNESSetApplicationContext(snes, user, ierr))

236: !  Set function evaluation routine and vector
237:   PetscCallA(SNESSetFunction(snes, r, FormFunction, user, ierr))

239: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
240: !  Create matrix data structure; set Jacobian evaluation routine
241: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

243: !  Set Jacobian matrix data structure and default Jacobian evaluation
244: !  routine. User can override with:
245: !     -snes_fd : default finite differencing approximation of Jacobian
246: !     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
247: !                (unless user explicitly sets preconditioner)
248: !     -snes_mf_operator : form matrix used to construct the preconditioner as set by the user,
249: !                         but use matrix-free approx for Jacobian-vector
250: !                         products within Newton-Krylov method
251: !
252: !  Note:  For the parallel case, vectors and matrices MUST be partitioned
253: !     accordingly.  When using distributed arrays (DMDAs) to create vectors,
254: !     the DMDAs determine the problem partitioning.  We must explicitly
255: !     specify the local matrix dimensions upon its creation for compatibility
256: !     with the vector distribution.  Thus, the generic MatCreate() routine
257: !     is NOT sufficient when working with distributed arrays.
258: !
259: !     Note: Here we only approximately preallocate storage space for the
260: !     Jacobian.  See the users manual for a discussion of better techniques
261: !     for preallocating matrix memory.

263:   PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS, PETSC_NULL_CHARACTER, '-snes_mf', matrix_free, ierr))
264:   if (.not. matrix_free) then
265:     PetscCallA(DMSetMatType(da, MATAIJ, ierr))
266:     PetscCallA(DMCreateMatrix(da, J, ierr))
267:     PetscCallA(SNESSetJacobian(snes, J, J, FormJacobian, user, ierr))
268:   end if

270: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
271: !  Customize nonlinear solver; set runtime options
272: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
273: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
274:   PetscCallA(SNESSetDM(snes, da, ierr))
275:   PetscCallA(SNESSetFromOptions(snes, ierr))

277: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
278: !  Evaluate initial guess; then solve nonlinear system.
279: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
280: !  Note: The user should initialize the vector, x, with the initial guess
281: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
282: !  to employ an initial guess of zero, the user should explicitly set
283: !  this vector to zero by calling VecSet().

285:   PetscCallA(FormInitialGuess(snes, x, ierr))
286:   PetscCallA(SNESSolve(snes, PETSC_NULL_VEC, x, ierr))
287:   PetscCallA(SNESGetIterationNumber(snes, its, ierr))
288:   if (user%rank == 0) then
289:     write (6, 100) its
290:   end if
291: 100 format('Number of SNES iterations = ', i5)

293: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
294: !  Free work space.  All PETSc objects should be destroyed when they
295: !  are no longer needed.
296: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
297:   if (.not. matrix_free) PetscCallA(MatDestroy(J, ierr))
298:   PetscCallA(VecDestroy(x, ierr))
299:   PetscCallA(VecDestroy(r, ierr))
300:   PetscCallA(SNESDestroy(snes, ierr))
301:   PetscCallA(DMDestroy(da, ierr))

303:   PetscCallA(PetscFinalize(ierr))
304: end

306: ! ---------------------------------------------------------------------
307: !
308: !  FormInitialGuess - Forms initial approximation.
309: !
310: !  Input Parameters:
311: !  X - vector
312: !
313: !  Output Parameter:
314: !  X - vector
315: !
316: !  Notes:
317: !  This routine serves as a wrapper for the lower-level routine
318: !  "InitialGuessLocal", where the actual computations are
319: !  done using the standard Fortran style of treating the local
320: !  vector data as a multidimensional array over the local mesh.
321: !  This routine merely handles ghost point scatters and accesses
322: !  the local vector data via VecGetArray() and VecRestoreArray().
323: !
324: subroutine FormInitialGuess(snes, X, ierr)
325:   use ex5f90module
326:   use ex5f90moduleinterfaces
327:   implicit none

329: !  Input/output variables:
330:   SNES snes
331:   type(userctx), pointer:: puser
332:   Vec X
333:   PetscErrorCode ierr
334:   DM da

336: !  Declarations for use with local arrays:
337:   PetscScalar, pointer :: lx_v(:)

339:   ierr = 0
340:   PetscCallA(SNESGetDM(snes, da, ierr))
341:   PetscCallA(SNESGetApplicationContext(snes, puser, ierr))
342: !  Get a pointer to vector data.
343: !    - For default PETSc vectors, VecGetArray() returns a pointer to
344: !      the data array. Otherwise, the routine is implementation dependent.
345: !    - You MUST call VecRestoreArray() when you no longer need access to
346: !      the array.
347: !    - Note that the interface to VecGetArray() differs from VecGetArray().

349:   PetscCallA(VecGetArray(X, lx_v, ierr))

351: !  Compute initial guess over the locally owned part of the grid
352:   PetscCallA(InitialGuessLocal(puser, lx_v, ierr))

354: !  Restore vector
355:   PetscCallA(VecRestoreArray(X, lx_v, ierr))

357: !  Insert values into global vector

359: end

361: ! ---------------------------------------------------------------------
362: !
363: !  InitialGuessLocal - Computes initial approximation, called by
364: !  the higher level routine FormInitialGuess().
365: !
366: !  Input Parameter:
367: !  x - local vector data
368: !
369: !  Output Parameters:
370: !  x - local vector data
371: !  ierr - error code
372: !
373: !  Notes:
374: !  This routine uses standard Fortran-style computations over a 2-dim array.
375: !
376: subroutine InitialGuessLocal(user, x, ierr)
377:   use ex5f90module
378:   implicit none

380: !  Input/output variables:
381:   type(userctx) user
382:   PetscScalar x(user%xs:user%xe, user%ys:user%ye)
383:   PetscErrorCode ierr

385: !  Local variables:
386:   PetscInt i, j
387:   PetscReal temp1, temp, hx, hy
388:   PetscReal one

390: !  Set parameters

392:   ierr = 0
393:   one = 1.0
394:   hx = one/(user%mx - 1)
395:   hy = one/(user%my - 1)
396:   temp1 = user%lambda/(user%lambda + one)

398:   do 20 j = user%ys, user%ye
399:     temp = min(j - 1, user%my - j)*hy
400:     do 10 i = user%xs, user%xe
401:       if (i == 1 .or. j == 1 .or. i == user%mx .or. j == user%my) then
402:         x(i, j) = 0.0
403:       else
404:         x(i, j) = temp1*sqrt(min(hx*min(i - 1, user%mx - i), temp))
405:       end if
406: 10    continue
407: 20    continue

409:     end

411: ! ---------------------------------------------------------------------
412: !
413: !  FormFunctionLocal - Computes nonlinear function, called by
414: !  the higher level routine FormFunction().
415: !
416: !  Input Parameter:
417: !  x - local vector data
418: !
419: !  Output Parameters:
420: !  f - local vector data, f(x)
421: !  ierr - error code
422: !
423: !  Notes:
424: !  This routine uses standard Fortran-style computations over a 2-dim array.
425: !
426:     subroutine FormFunctionLocal(x, f, user, ierr)
427:       use ex5f90module

429:       implicit none

431: !  Input/output variables:
432:       type(userctx) user
433:       PetscScalar x(user%gxs:user%gxe, user%gys:user%gye)
434:       PetscScalar f(user%xs:user%xe, user%ys:user%ye)
435:       PetscErrorCode ierr

437: !  Local variables:
438:       PetscScalar two, one, hx, hy, hxdhy, hydhx, sc
439:       PetscScalar u, uxx, uyy
440:       PetscInt i, j

442:       one = 1.0
443:       two = 2.0
444:       hx = one/(user%mx - 1)
445:       hy = one/(user%my - 1)
446:       sc = hx*hy*user%lambda
447:       hxdhy = hx/hy
448:       hydhx = hy/hx

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

452:       do 20 j = user%ys, user%ye
453:         do 10 i = user%xs, user%xe
454:           if (i == 1 .or. j == 1 .or. i == user%mx .or. j == user%my) then
455:             f(i, j) = x(i, j)
456:           else
457:             u = x(i, j)
458:             uxx = hydhx*(two*u - x(i - 1, j) - x(i + 1, j))
459:             uyy = hxdhy*(two*u - x(i, j - 1) - x(i, j + 1))
460:             f(i, j) = uxx + uyy - sc*exp(u)
461:           end if
462: 10        continue
463: 20        continue

465:         end

467: ! ---------------------------------------------------------------------
468: !
469: !  FormJacobian - Evaluates Jacobian matrix.
470: !
471: !  Input Parameters:
472: !  snes     - the SNES context
473: !  x        - input vector
474: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
475: !             (not used here)
476: !
477: !  Output Parameters:
478: !  jac      - Jacobian matrix
479: !  jac_prec - optionally different matrix used to construct the preconditioner (not used here)
480: !
481: !  Notes:
482: !  This routine serves as a wrapper for the lower-level routine
483: !  "FormJacobianLocal", where the actual computations are
484: !  done using the standard Fortran style of treating the local
485: !  vector data as a multidimensional array over the local mesh.
486: !  This routine merely accesses the local vector data via
487: !  VecGetArray() and VecRestoreArray().
488: !
489: !  Notes:
490: !  Due to grid point reordering with DMDAs, we must always work
491: !  with the local grid points, and then transform them to the new
492: !  global numbering with the "ltog" mapping
493: !  We cannot work directly with the global numbers for the original
494: !  uniprocessor grid!
495: !
496: !  Two methods are available for imposing this transformation
497: !  when setting matrix entries:
498: !    (A) MatSetValuesLocal(), using the local ordering (including
499: !        ghost points!)
500: !        - Set matrix entries using the local ordering
501: !          by calling MatSetValuesLocal()
502: !    (B) MatSetValues(), using the global ordering

504: !        - Set matrix entries using the global ordering by calling
505: !          MatSetValues()
506: !  Option (A) seems cleaner/easier in many cases, and is the procedure
507: !  used in this example.
508: !
509:         subroutine FormJacobian(snes, X, jac, jac_prec, user, ierr)
510:           use ex5f90module
511:           implicit none

513: !  Input/output variables:
514:           SNES snes
515:           Vec X
516:           Mat jac, jac_prec
517:           type(userctx) user
518:           PetscErrorCode ierr
519:           DM da

521: !  Declarations for use with local arrays:
522:           PetscScalar, pointer :: lx_v(:)
523:           Vec localX

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

530:           PetscCallA(SNESGetDM(snes, da, ierr))
531:           PetscCallA(DMGetLocalVector(da, localX, ierr))
532:           PetscCallA(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX, ierr))
533:           PetscCallA(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX, ierr))

535: !  Get a pointer to vector data
536:           PetscCallA(VecGetArray(localX, lx_v, ierr))

538: !  Compute entries for the locally owned part of the Jacobian preconditioner.
539:           PetscCallA(FormJacobianLocal(lx_v, jac_prec, user, ierr))

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

546:           PetscCallA(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY, ierr))
547:           if (jac /= jac_prec) then
548:             PetscCallA(MatAssemblyBegin(jac_prec, MAT_FINAL_ASSEMBLY, ierr))
549:           end if
550:           PetscCallA(VecRestoreArray(localX, lx_v, ierr))
551:           PetscCallA(DMRestoreLocalVector(da, localX, ierr))
552:           PetscCallA(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY, ierr))
553:           if (jac /= jac_prec) then
554:             PetscCallA(MatAssemblyEnd(jac_prec, MAT_FINAL_ASSEMBLY, ierr))
555:           end if

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

560:           PetscCallA(MatSetOption(jac, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE, ierr))

562:         end

564: ! ---------------------------------------------------------------------
565: !
566: !  FormJacobianLocal - Computes Jacobian matrix used to compute the preconditioner,
567: !  called by the higher level routine FormJacobian().
568: !
569: !  Input Parameters:
570: !  x        - local vector data
571: !
572: !  Output Parameters:
573: !  jac_prec - Jacobian matrix used to compute the preconditioner
574: !  ierr     - error code
575: !
576: !  Notes:
577: !  This routine uses standard Fortran-style computations over a 2-dim array.
578: !
579: !  Notes:
580: !  Due to grid point reordering with DMDAs, we must always work
581: !  with the local grid points, and then transform them to the new
582: !  global numbering with the "ltog" mapping
583: !  We cannot work directly with the global numbers for the original
584: !  uniprocessor grid!
585: !
586: !  Two methods are available for imposing this transformation
587: !  when setting matrix entries:
588: !    (A) MatSetValuesLocal(), using the local ordering (including
589: !        ghost points!)
590: !        - Set matrix entries using the local ordering
591: !          by calling MatSetValuesLocal()
592: !    (B) MatSetValues(), using the global ordering
593: !        - Then apply this map explicitly yourself
594: !        - Set matrix entries using the global ordering by calling
595: !          MatSetValues()
596: !  Option (A) seems cleaner/easier in many cases, and is the procedure
597: !  used in this example.
598: !
599:         subroutine FormJacobianLocal(x, jac_prec, user, ierr)
600:           use ex5f90module
601:           implicit none

603: !  Input/output variables:
604:           type(userctx) user
605:           PetscScalar x(user%gxs:user%gxe, user%gys:user%gye)
606:           Mat jac_prec
607:           PetscErrorCode ierr

609: !  Local variables:
610:           PetscInt row, col(5), i, j
611:           PetscInt ione, ifive
612:           PetscScalar two, one, hx, hy, hxdhy
613:           PetscScalar hydhx, sc, v(5)

615: !  Set parameters
616:           ione = 1
617:           ifive = 5
618:           one = 1.0
619:           two = 2.0
620:           hx = one/(user%mx - 1)
621:           hy = one/(user%my - 1)
622:           sc = hx*hy
623:           hxdhy = hx/hy
624:           hydhx = hy/hx

626: !  Compute entries for the locally owned part of the Jacobian.
627: !   - Currently, all PETSc parallel matrix formats are partitioned by
628: !     contiguous chunks of rows across the processors.
629: !   - Each processor needs to insert only elements that it owns
630: !     locally (but any non-local elements will be sent to the
631: !     appropriate processor during matrix assembly).
632: !   - Here, we set all entries for a particular row at once.
633: !   - We can set matrix entries either using either
634: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
635: !   - Note that MatSetValues() uses 0-based row and column numbers
636: !     in Fortran as well as in C.

638:           do 20 j = user%ys, user%ye
639:             row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
640:             do 10 i = user%xs, user%xe
641:               row = row + 1
642: !           boundary points
643:               if (i == 1 .or. j == 1 .or. i == user%mx .or. j == user%my) then
644:                 col(1) = row
645:                 v(1) = one
646:                 PetscCallA(MatSetValuesLocal(jac_prec, ione, [row], ione, col, v, INSERT_VALUES, ierr))
647: !           interior grid points
648:               else
649:                 v(1) = -hxdhy
650:                 v(2) = -hydhx
651:                 v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i, j))
652:                 v(4) = -hydhx
653:                 v(5) = -hxdhy
654:                 col(1) = row - user%gxm
655:                 col(2) = row - 1
656:                 col(3) = row
657:                 col(4) = row + 1
658:                 col(5) = row + user%gxm
659:                 PetscCallA(MatSetValuesLocal(jac_prec, ione, [row], ifive, col, v, INSERT_VALUES, ierr))
660:               end if
661: 10            continue
662: 20            continue

664:             end

666: !
667: !/*TEST
668: !
669: !   test:
670: !      nsize: 4
671: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
672: !      requires: !single
673: !
674: !   test:
675: !      suffix: 2
676: !      nsize: 4
677: !      args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
678: !      requires: !single
679: !
680: !   test:
681: !      suffix: 3
682: !      nsize: 3
683: !      args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
684: !      requires: !single
685: !
686: !   test:
687: !      suffix: 4
688: !      nsize: 3
689: !      args: -snes_mf_operator -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
690: !      requires: !single
691: !
692: !   test:
693: !      suffix: 5
694: !      requires: !single
695: !
696: !TEST*/