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: !
 32: #include <petsc/finclude/petscdmda.h>
 33: #include <petsc/finclude/petscsnes.h>
 34: module ex5f90tmodule
 35:   use petscsnes
 36:   use petscdmda
 37:   implicit none
 38:   type userctx
 39:     type(tDM) da
 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:   interface
 48:     subroutine SNESSetApplicationContext(snesIn, ctx, ierr)
 49:       use petscsnes
 50:       import userctx
 51:       type(tSNES) snesIn
 52:       type(userctx) ctx
 53:       PetscErrorCode ierr
 54:     end subroutine
 55:     subroutine SNESGetApplicationContext(snesIn, ctx, ierr)
 56:       use petscsnes
 57:       import userctx
 58:       type(tSNES) snesIn
 59:       type(userctx), pointer :: ctx
 60:       PetscErrorCode ierr
 61:     end subroutine
 62:   end interface

 64: contains
 65: ! ---------------------------------------------------------------------
 66: !
 67: !  FormFunction - Evaluates nonlinear function, F(x).
 68: !
 69: !  Input Parameters:
 70: !  snes - the SNES context
 71: !  X - input vector
 72: !  dummy - optional user-defined context, as set by SNESSetFunction()
 73: !          (not used here)
 74: !
 75: !  Output Parameter:
 76: !  F - function vector
 77: !
 78: !  Notes:
 79: !  This routine serves as a wrapper for the lower-level routine
 80: !  "FormFunctionLocal", where the actual computations are
 81: !  done using the standard Fortran style of treating the local
 82: !  vector data as a multidimensional array over the local mesh.
 83: !  This routine merely handles ghost point scatters and accesses
 84: !  the local vector data via VecGetArray() and VecRestoreArray().
 85: !
 86:   subroutine FormFunction(snesIn, X, F, user, ierr)
 87: !  Input/output variables:
 88:     type(tSNES) snesIn
 89:     type(tVec) X, F
 90:     PetscErrorCode ierr
 91:     type(userctx) user

 93: !  Declarations for use with local arrays:
 94:     PetscScalar, pointer :: lx_v(:), lf_v(:)
 95:     type(tVec) localX

 97: !  Scatter ghost points to local vector, using the 2-step process
 98: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
 99: !  By placing code between these two statements, computations can
100: !  be done while messages are in transition.
101:     PetscCall(DMGetLocalVector(user%da, localX, ierr))
102:     PetscCall(DMGlobalToLocalBegin(user%da, X, INSERT_VALUES, localX, ierr))
103:     PetscCall(DMGlobalToLocalEnd(user%da, X, INSERT_VALUES, localX, ierr))

105: !  Get a pointer to vector data.
106: !    - VecGetArray90() returns a pointer to the data array.
107: !    - You MUST call VecRestoreArray() when you no longer need access to
108: !      the array.

110:     PetscCall(VecGetArray(localX, lx_v, ierr))
111:     PetscCall(VecGetArray(F, lf_v, ierr))

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

116: !  Restore vectors
117:     PetscCall(VecRestoreArray(localX, lx_v, ierr))
118:     PetscCall(VecRestoreArray(F, lf_v, ierr))

120: !  Insert values into global vector

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

125: !      PetscCall(VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr))
126: !      PetscCall(VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr))
127:   end subroutine formfunction

129: ! ---------------------------------------------------------------------
130: !
131: !  FormInitialGuess - Forms initial approximation.
132: !
133: !  Input Parameters:
134: !  X - vector
135: !
136: !  Output Parameter:
137: !  X - vector
138: !
139: !  Notes:
140: !  This routine serves as a wrapper for the lower-level routine
141: !  "InitialGuessLocal", where the actual computations are
142: !  done using the standard Fortran style of treating the local
143: !  vector data as a multidimensional array over the local mesh.
144: !  This routine merely handles ghost point scatters and accesses
145: !  the local vector data via VecGetArray() and VecRestoreArray().
146: !
147:   subroutine FormInitialGuess(mysnes, X, ierr)
148: !  Input/output variables:
149:     type(tSNES) mysnes
150:     type(userctx), pointer:: puser
151:     type(tVec) X
152:     PetscErrorCode ierr

154: !  Declarations for use with local arrays:
155:     PetscScalar, pointer :: lx_v(:)

157:     ierr = 0
158:     PetscCallA(SNESGetApplicationContext(mysnes, puser, ierr))
159: !  Get a pointer to vector data.
160: !    - VecGetArray90() returns a pointer to the data array.
161: !    - You MUST call VecRestoreArray() when you no longer need access to
162: !      the array.

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

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

169: !  Restore vector
170:     PetscCallA(VecRestoreArray(X, lx_v, ierr))

172: !  Insert values into global vector

174:   end

176: ! ---------------------------------------------------------------------
177: !
178: !  InitialGuessLocal - Computes initial approximation, called by
179: !  the higher level routine FormInitialGuess().
180: !
181: !  Input Parameter:
182: !  x - local vector data
183: !
184: !  Output Parameters:
185: !  x - local vector data
186: !  ierr - error code
187: !
188: !  Notes:
189: !  This routine uses standard Fortran-style computations over a 2-dim array.
190: !
191:   subroutine InitialGuessLocal(user, x, ierr)
192: !  Input/output variables:
193:     type(userctx) user
194:     PetscScalar x(user%xs:user%xe, user%ys:user%ye)
195:     PetscErrorCode ierr

197: !  Local variables:
198:     PetscInt i, j
199:     PetscScalar temp1, temp, hx, hy
200:     PetscScalar one

202: !  Set parameters

204:     ierr = 0
205:     one = 1.0
206:     hx = one/(PetscIntToReal(user%mx - 1))
207:     hy = one/(PetscIntToReal(user%my - 1))
208:     temp1 = user%lambda/(user%lambda + one)

210:     do j = user%ys, user%ye
211:       temp = PetscIntToReal(min(j - 1, user%my - j))*hy
212:       do i = user%xs, user%xe
213:         if (i == 1 .or. j == 1 .or. i == user%mx .or. j == user%my) then
214:           x(i, j) = 0.0
215:         else
216:           x(i, j) = temp1*sqrt(min(PetscIntToReal(min(i - 1, user%mx - i)*hx), PetscIntToReal(temp)))
217:         end if
218:       end do
219:     end do

221:   end

223: ! ---------------------------------------------------------------------
224: !
225: !  FormFunctionLocal - Computes nonlinear function, called by
226: !  the higher level routine FormFunction().
227: !
228: !  Input Parameter:
229: !  x - local vector data
230: !
231: !  Output Parameters:
232: !  f - local vector data, f(x)
233: !  ierr - error code
234: !
235: !  Notes:
236: !  This routine uses standard Fortran-style computations over a 2-dim array.
237: !
238:   subroutine FormFunctionLocal(x, f, user, ierr)
239: !  Input/output variables:
240:     type(userctx) user
241:     PetscScalar x(user%gxs:user%gxe, user%gys:user%gye)
242:     PetscScalar f(user%xs:user%xe, user%ys:user%ye)
243:     PetscErrorCode ierr

245: !  Local variables:
246:     PetscScalar two, one, hx, hy, hxdhy, hydhx, sc
247:     PetscScalar u, uxx, uyy
248:     PetscInt i, j

250:     one = 1.0
251:     two = 2.0
252:     hx = one/PetscIntToReal(user%mx - 1)
253:     hy = one/PetscIntToReal(user%my - 1)
254:     sc = hx*hy*user%lambda
255:     hxdhy = hx/hy
256:     hydhx = hy/hx

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

260:     do j = user%ys, user%ye
261:       do i = user%xs, user%xe
262:         if (i == 1 .or. j == 1 .or. i == user%mx .or. j == user%my) then
263:           f(i, j) = x(i, j)
264:         else
265:           u = x(i, j)
266:           uxx = hydhx*(two*u - x(i - 1, j) - x(i + 1, j))
267:           uyy = hxdhy*(two*u - x(i, j - 1) - x(i, j + 1))
268:           f(i, j) = uxx + uyy - sc*exp(u)
269:         end if
270:       end do
271:     end do
272:     ierr = 0
273:   end

275: ! ---------------------------------------------------------------------
276: !
277: !  FormJacobian - Evaluates Jacobian matrix.
278: !
279: !  Input Parameters:
280: !  snes     - the SNES context
281: !  x        - input vector
282: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
283: !             (not used here)
284: !
285: !  Output Parameters:
286: !  jac      - Jacobian matrix
287: !  jac_prec - optionally different matrix used to construct the preconditioner (not used here)
288: !
289: !  Notes:
290: !  This routine serves as a wrapper for the lower-level routine
291: !  "FormJacobianLocal", where the actual computations are
292: !  done using the standard Fortran style of treating the local
293: !  vector data as a multidimensional array over the local mesh.
294: !  This routine merely accesses the local vector data via
295: !  VecGetArray() and VecRestoreArray().
296: !
297: !  Notes:
298: !  Due to grid point reordering with DMDAs, we must always work
299: !  with the local grid points, and then transform them to the new
300: !  global numbering with the "ltog" mapping
301: !  We cannot work directly with the global numbers for the original
302: !  uniprocessor grid!
303: !
304: !  Two methods are available for imposing this transformation
305: !  when setting matrix entries:
306: !    (A) MatSetValuesLocal(), using the local ordering (including
307: !        ghost points!)
308: !        - Set matrix entries using the local ordering
309: !          by calling MatSetValuesLocal()
310: !    (B) MatSetValues(), using the global ordering
311: !        - Use DMGetLocalToGlobalMapping() then
312: !          ISLocalToGlobalMappingGetIndices() to extract the local-to-global map
313: !        - Then apply this map explicitly yourself
314: !        - Set matrix entries using the global ordering by calling
315: !          MatSetValues()
316: !  Option (A) seems cleaner/easier in many cases, and is the procedure
317: !  used in this example.
318: !
319:   subroutine FormJacobian(mysnes, X, jac, jac_prec, user, ierr)
320: !  Input/output variables:
321:     type(tSNES) mysnes
322:     type(tVec) X
323:     type(tMat) jac, jac_prec
324:     type(userctx) user
325:     PetscErrorCode ierr

327: !  Declarations for use with local arrays:
328:     PetscScalar, pointer :: lx_v(:)
329:     type(tVec) localX

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

336:     PetscCallA(DMGetLocalVector(user%da, localX, ierr))
337:     PetscCallA(DMGlobalToLocalBegin(user%da, X, INSERT_VALUES, localX, ierr))
338:     PetscCallA(DMGlobalToLocalEnd(user%da, X, INSERT_VALUES, localX, ierr))

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

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

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

351:     PetscCallA(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY, ierr))
352: !      if (jac .ne. jac_prec) then
353:     PetscCallA(MatAssemblyBegin(jac_prec, MAT_FINAL_ASSEMBLY, ierr))
354: !      endif
355:     PetscCallA(VecRestoreArray(localX, lx_v, ierr))
356:     PetscCallA(DMRestoreLocalVector(user%da, localX, ierr))
357:     PetscCallA(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY, ierr))
358: !      if (jac .ne. jac_prec) then
359:     PetscCallA(MatAssemblyEnd(jac_prec, MAT_FINAL_ASSEMBLY, ierr))
360: !      endif

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

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

367:   end

369: ! ---------------------------------------------------------------------
370: !
371: !  FormJacobianLocal - Computes Jacobian matrix used to compute the preconditioner,
372: !  called by the higher level routine FormJacobian().
373: !
374: !  Input Parameters:
375: !  x        - local vector data
376: !
377: !  Output Parameters:
378: !  jac_prec - Jacobian matrix used to compute the preconditioner
379: !  ierr     - error code
380: !
381: !  Notes:
382: !  This routine uses standard Fortran-style computations over a 2-dim array.
383: !
384: !  Notes:
385: !  Due to grid point reordering with DMDAs, we must always work
386: !  with the local grid points, and then transform them to the new
387: !  global numbering with the "ltog" mapping
388: !  We cannot work directly with the global numbers for the original
389: !  uniprocessor grid!
390: !
391: !  Two methods are available for imposing this transformation
392: !  when setting matrix entries:
393: !    (A) MatSetValuesLocal(), using the local ordering (including
394: !        ghost points!)
395: !        - Set matrix entries using the local ordering
396: !          by calling MatSetValuesLocal()
397: !    (B) MatSetValues(), using the global ordering
398: !        - Set matrix entries using the global ordering by calling
399: !          MatSetValues()
400: !  Option (A) seems cleaner/easier in many cases, and is the procedure
401: !  used in this example.
402: !
403:   subroutine FormJacobianLocal(x, jac_prec, user, ierr)
404: !  Input/output variables:
405:     type(userctx) user
406:     PetscScalar x(user%gxs:user%gxe, user%gys:user%gye)
407:     type(tMat) jac_prec
408:     PetscErrorCode ierr

410: !  Local variables:
411:     PetscInt row, col(5), i, j
412:     PetscInt ione, ifive
413:     PetscScalar two, one, hx, hy, hxdhy
414:     PetscScalar hydhx, sc, v(5)

416: !  Set parameters
417:     ione = 1
418:     ifive = 5
419:     one = 1.0
420:     two = 2.0
421:     hx = one/PetscIntToReal(user%mx - 1)
422:     hy = one/PetscIntToReal(user%my - 1)
423:     sc = hx*hy
424:     hxdhy = hx/hy
425:     hydhx = hy/hx

427: !  Compute entries for the locally owned part of the Jacobian.
428: !   - Currently, all PETSc parallel matrix formats are partitioned by
429: !     contiguous chunks of rows across the processors.
430: !   - Each processor needs to insert only elements that it owns
431: !     locally (but any non-local elements will be sent to the
432: !     appropriate processor during matrix assembly).
433: !   - Here, we set all entries for a particular row at once.
434: !   - We can set matrix entries either using either
435: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
436: !   - Note that MatSetValues() uses 0-based row and column numbers
437: !     in Fortran as well as in C.

439:     do j = user%ys, user%ye
440:       row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
441:       do i = user%xs, user%xe
442:         row = row + 1
443: !           boundary points
444:         if (i == 1 .or. j == 1 .or. i == user%mx .or. j == user%my) then
445:           col(1) = row
446:           v(1) = one
447:           PetscCallA(MatSetValuesLocal(jac_prec, ione, [row], ione, col, v, INSERT_VALUES, ierr))
448: !           interior grid points
449:         else
450:           v(1) = -hxdhy
451:           v(2) = -hydhx
452:           v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i, j))
453:           v(4) = -hydhx
454:           v(5) = -hxdhy
455:           col(1) = row - user%gxm
456:           col(2) = row - 1
457:           col(3) = row
458:           col(4) = row + 1
459:           col(5) = row + user%gxm
460:           PetscCallA(MatSetValuesLocal(jac_prec, ione, [row], ifive, col, v, INSERT_VALUES, ierr))
461:         end if
462:       end do
463:     end do
464:   end

466: end module

468: program main
469:   use petscdmda
470:   use petscsnes
471:   use ex5f90tmodule
472:   implicit none
473: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
474: !                   Variable declarations
475: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
476: !
477: !  Variables:
478: !     mysnes      - nonlinear solver
479: !     x, r        - solution, residual vectors
480: !     J           - Jacobian matrix
481: !     its         - iterations for convergence
482: !     Nx, Ny      - number of preocessors in x- and y- directions
483: !     matrix_free - flag - 1 indicates matrix-free version
484: !
485:   type(tSNES) mysnes
486:   type(tVec) x, r
487:   type(tMat) J
488:   PetscErrorCode ierr
489:   PetscInt its
490:   PetscBool flg, matrix_free, set
491:   PetscInt ione, nfour
492:   PetscReal lambda_max, lambda_min
493:   type(userctx) user
494:   type(userctx), pointer:: puser
495:   type(tPetscOptions) :: options

497: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
498: !  Initialize program
499: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
500:   PetscCallA(PetscInitialize(ierr))
501:   PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD, user%rank, ierr))

503: !  Initialize problem parameters
504:   options%v = 0
505:   lambda_max = 6.81
506:   lambda_min = 0.0
507:   user%lambda = 6.0
508:   ione = 1
509:   nfour = 4
510:   PetscCallA(PetscOptionsGetReal(options, PETSC_NULL_CHARACTER, '-par', user%lambda, flg, ierr))
511:   PetscCheckA(user%lambda < lambda_max .and. user%lambda > lambda_min, PETSC_COMM_SELF, PETSC_ERR_USER, 'Lambda provided with -par is out of range')

513: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
514: !  Create nonlinear solver context
515: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
516:   PetscCallA(SNESCreate(PETSC_COMM_WORLD, mysnes, ierr))

518: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
519: !  Create vector data structures; set function evaluation routine
520: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

524: ! This really needs only the star-type stencil, but we use the box
525: ! stencil temporarily.
526:   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, user%da, ierr))
527:   PetscCallA(DMSetFromOptions(user%da, ierr))
528:   PetscCallA(DMSetUp(user%da, ierr))
529:   PetscCallA(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, PETSC_NULL_INTEGER, PETSC_NULL_DMBOUNDARYTYPE, PETSC_NULL_DMBOUNDARYTYPE, PETSC_NULL_DMBOUNDARYTYPE, PETSC_NULL_DMDASTENCILTYPE, ierr))

531: !
532: !   Visualize the distribution of the array across the processors
533: !
534: !     PetscCallA(DMView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr))

536: !  Extract global and local vectors from DMDA; then duplicate for remaining
537: !  vectors that are the same types
538:   PetscCallA(DMCreateGlobalVector(user%da, x, ierr))
539:   PetscCallA(VecDuplicate(x, r, ierr))

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

545: !  Here we shift the starting indices up by one so that we can easily
546: !  use the Fortran convention of 1-based indices (rather 0-based indices).
547:   user%xs = user%xs + 1
548:   user%ys = user%ys + 1
549:   user%gxs = user%gxs + 1
550:   user%gys = user%gys + 1

552:   user%ye = user%ys + user%ym - 1
553:   user%xe = user%xs + user%xm - 1
554:   user%gye = user%gys + user%gym - 1
555:   user%gxe = user%gxs + user%gxm - 1

557:   PetscCallA(SNESSetApplicationContext(mysnes, user, ierr))

559: !  Set function evaluation routine and vector
560:   PetscCallA(SNESSetFunction(mysnes, r, FormFunction, user, ierr))

562: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
563: !  Create matrix data structure; set Jacobian evaluation routine
564: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

566: !  Set Jacobian matrix data structure and default Jacobian evaluation
567: !  routine. User can override with:
568: !     -snes_fd : default finite differencing approximation of Jacobian
569: !     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
570: !                (unless user explicitly sets preconditioner)
571: !     -snes_mf_operator : form matrix used to construct the preconditioner as set by the user,
572: !                         but use matrix-free approx for Jacobian-vector
573: !                         products within Newton-Krylov method
574: !
575: !  Note:  For the parallel case, vectors and matrices MUST be partitioned
576: !     accordingly.  When using distributed arrays (DMDAs) to create vectors,
577: !     the DMDAs determine the problem partitioning.  We must explicitly
578: !     specify the local matrix dimensions upon its creation for compatibility
579: !     with the vector distribution.  Thus, the generic MatCreate() routine
580: !     is NOT sufficient when working with distributed arrays.
581: !
582: !     Note: Here we only approximately preallocate storage space for the
583: !     Jacobian.  See the users manual for a discussion of better techniques
584: !     for preallocating matrix memory.

586:   PetscCallA(PetscOptionsHasName(options, PETSC_NULL_CHARACTER, '-snes_mf', matrix_free, ierr))
587:   if (.not. matrix_free) then
588:     PetscCallA(DMSetMatType(user%da, MATAIJ, ierr))
589:     PetscCallA(DMCreateMatrix(user%da, J, ierr))
590:     PetscCallA(SNESSetJacobian(mysnes, J, J, FormJacobian, user, ierr))
591:   end if

593: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
594: !  Customize nonlinear solver; set runtime options
595: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
596: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
597:   PetscCallA(SNESSetFromOptions(mysnes, ierr))

599: !     Test Fortran90 wrapper for SNESSet/Get ApplicationContext()
600:   PetscCallA(PetscOptionsGetBool(options, PETSC_NULL_CHARACTER, '-test_appctx', flg, set, ierr))
601:   if (flg) then
602:     PetscCallA(SNESGetApplicationContext(mysnes, puser, ierr))
603:   end if

605: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
606: !  Evaluate initial guess; then solve nonlinear system.
607: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
608: !  Note: The user should initialize the vector, x, with the initial guess
609: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
610: !  to employ an initial guess of zero, the user should explicitly set
611: !  this vector to zero by calling VecSet().

613:   PetscCallA(FormInitialGuess(mysnes, x, ierr))
614:   PetscCallA(SNESSolve(mysnes, PETSC_NULL_VEC, x, ierr))
615:   PetscCallA(SNESGetIterationNumber(mysnes, its, ierr))
616:   if (user%rank == 0) then
617:     write (6, 100) its
618:   end if
619: 100 format('Number of SNES iterations = ', i5)

621: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
622: !  Free work space.  All PETSc objects should be destroyed when they
623: !  are no longer needed.
624: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
625:   if (.not. matrix_free) PetscCallA(MatDestroy(J, ierr))
626:   PetscCallA(VecDestroy(x, ierr))
627:   PetscCallA(VecDestroy(r, ierr))
628:   PetscCallA(SNESDestroy(mysnes, ierr))
629:   PetscCallA(DMDestroy(user%da, ierr))

631:   PetscCallA(PetscFinalize(ierr))
632: end
633: !/*TEST
634: !
635: !   test:
636: !      nsize: 4
637: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
638: !
639: !TEST*/