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: !
 33: #include <petsc/finclude/petscsnes.h>
 34: #include <petsc/finclude/petscdmda.h>
 35: module ex5module
 36:   use petscsnes
 37:   use petscdmda
 38:   implicit none
 39:   type AppCtx
 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 AppCtx

 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, ctx, ierr)
 70: !  Input/output variables:
 71:     SNES snes
 72:     Vec X, F
 73:     PetscErrorCode, intent(out) :: ierr
 74:     type(AppCtx) ctx
 75:     DM da

 77: !  Declarations for use with local arrays:
 78:     PetscScalar, pointer :: lx_v(:), lf_v(:)
 79:     Vec 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:     PetscCall(SNESGetDM(snes, da, ierr))
 86:     PetscCall(DMGetLocalVector(da, localX, ierr))
 87:     PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX, ierr))
 88:     PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX, ierr))

 90: !  Get a pointer to vector data.
 91: !    - For default PETSc vectors, VecGetArray() returns a pointer to
 92: !      the data array. Otherwise, the routine is implementation dependent.
 93: !    - You MUST call VecRestoreArray() when you no longer need access to
 94: !      the array.
 95:     PetscCall(VecGetArray(localX, lx_v, ierr))
 96:     PetscCall(VecGetArray(F, lf_v, ierr))

 98: !  Compute function over the locally owned part of the grid
 99:     PetscCall(FormFunctionLocal(lx_v, lf_v, ctx, ierr))

101: !  Restore vectors
102:     PetscCall(VecRestoreArray(localX, lx_v, ierr))
103:     PetscCall(VecRestoreArray(F, lf_v, ierr))

105: !  Insert values into global vector

107:     PetscCall(DMRestoreLocalVector(da, localX, ierr))
108:     PetscCall(PetscLogFlops(11.0d0*ctx%ym*ctx%xm, ierr))

110: !      PetscCallA(VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr))
111: !      PetscCallA(VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr))
112:   end subroutine formfunction

114: ! ---------------------------------------------------------------------
115: !
116: !  FormInitialGuess - Forms initial approximation.
117: !
118: !  Input Parameters:
119: !  X - vector
120: !
121: !  Output Parameter:
122: !  X - vector
123: !
124: !  Notes:
125: !  This routine serves as a wrapper for the lower-level routine
126: !  "InitialGuessLocal", where the actual computations are
127: !  done using the standard Fortran style of treating the local
128: !  vector data as a multidimensional array over the local mesh.
129: !  This routine merely handles ghost point scatters and accesses
130: !  the local vector data via VecGetArray() and VecRestoreArray().
131: !
132:   subroutine FormInitialGuess(snes, X, ierr)
133: !  Input/output variables:
134:     SNES snes
135:     type(AppCtx), pointer:: ctx
136:     Vec X
137:     PetscErrorCode, intent(out) :: ierr
138:     DM da

140: !  Declarations for use with local arrays:
141:     PetscScalar, pointer :: lx_v(:)

143:     PetscCallA(SNESGetDM(snes, da, ierr))
144:     PetscCallA(SNESGetApplicationContext(snes, ctx, ierr))
145: !  Get a pointer to vector data.
146: !    - For default PETSc vectors, VecGetArray() returns a pointer to
147: !      the data array. Otherwise, the routine is implementation dependent.
148: !    - You MUST call VecRestoreArray() when you no longer need access to
149: !      the array.
150:     PetscCallA(VecGetArray(X, lx_v, ierr))

152: !  Compute initial guess over the locally owned part of the grid
153:     PetscCallA(InitialGuessLocal(ctx, lx_v, ierr))

155: !  Restore vector
156:     PetscCallA(VecRestoreArray(X, lx_v, ierr))

158: !  Insert values into global vector

160:   end

162: ! ---------------------------------------------------------------------
163: !
164: !  InitialGuessLocal - Computes initial approximation, called by
165: !  the higher level routine FormInitialGuess().
166: !
167: !  Input Parameter:
168: !  x - local vector data
169: !
170: !  Output Parameters:
171: !  x - local vector data
172: !  ierr - error code
173: !
174: !  Notes:
175: !  This routine uses standard Fortran-style computations over a 2-dim array.
176: !
177:   subroutine InitialGuessLocal(ctx, x, ierr)
178: !  Input/output variables:
179:     type(AppCtx) ctx
180:     PetscScalar x(ctx%xs:ctx%xe, ctx%ys:ctx%ye)
181:     PetscErrorCode, intent(out) :: ierr
182: !  Local variables:
183:     PetscInt i, j
184:     PetscReal temp1, temp, hx, hy

186:     hx = 1._PETSC_REAL_KIND/(ctx%mx - 1)
187:     hy = 1._PETSC_REAL_KIND/(ctx%my - 1)
188:     temp1 = ctx%lambda/(ctx%lambda + 1._PETSC_REAL_KIND)

190:     do j = ctx%ys, ctx%ye
191:       temp = min(j - 1, ctx%my - j)*hy
192:       do i = ctx%xs, ctx%xe
193:         if (i == 1 .or. j == 1 .or. i == ctx%mx .or. j == ctx%my) then
194:           x(i, j) = 0.0
195:         else
196:           x(i, j) = temp1*sqrt(min(hx*min(i - 1, ctx%mx - i), temp))
197:         end if
198:       end do
199:     end do
200:     ierr = 0
201:   end

203: ! ---------------------------------------------------------------------
204: !
205: !  FormFunctionLocal - Computes nonlinear function, called by
206: !  the higher level routine FormFunction().
207: !
208: !  Input Parameter:
209: !  x - local vector data
210: !
211: !  Output Parameters:
212: !  f - local vector data, f(x)
213: !  ierr - error code
214: !
215: !  Notes:
216: !  This routine uses standard Fortran-style computations over a 2-dim array.
217: !
218:   subroutine FormFunctionLocal(x, f, ctx, ierr)
219: !  Input/output variables:
220:     type(AppCtx), intent(in) :: ctx
221:     PetscScalar x(ctx%gxs:ctx%gxe, ctx%gys:ctx%gye)
222:     PetscScalar f(ctx%xs:ctx%xe, ctx%ys:ctx%ye)
223:     PetscErrorCode, intent(out) :: ierr
224: !  Local variables:
225:     PetscScalar, parameter :: two = 2.0, one = 1.0
226:     PetscScalar hx, hy, hxdhy, hydhx, sc
227:     PetscScalar u, uxx, uyy
228:     PetscInt i, j

230:     hx = one/(ctx%mx - 1)
231:     hy = one/(ctx%my - 1)
232:     sc = hx*hy*ctx%lambda
233:     hxdhy = hx/hy
234:     hydhx = hy/hx

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

238:     do j = ctx%ys, ctx%ye
239:       do i = ctx%xs, ctx%xe
240:         if (i == 1 .or. j == 1 .or. i == ctx%mx .or. j == ctx%my) then
241:           f(i, j) = x(i, j)
242:         else
243:           u = x(i, j)
244:           uxx = hydhx*(two*u - x(i - 1, j) - x(i + 1, j))
245:           uyy = hxdhy*(two*u - x(i, j - 1) - x(i, j + 1))
246:           f(i, j) = uxx + uyy - sc*exp(u)
247:         end if
248:       end do
249:     end do
250:     ierr = 0
251:   end

253: ! ---------------------------------------------------------------------
254: !
255: !  FormJacobian - Evaluates Jacobian matrix.
256: !
257: !  Input Parameters:
258: !  snes     - the SNES context
259: !  x        - input vector
260: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
261: !             (not used here)
262: !
263: !  Output Parameters:
264: !  jac      - Jacobian matrix
265: !  jac_prec - optionally different matrix used to construct the preconditioner (not used here)
266: !
267: !  Notes:
268: !  This routine serves as a wrapper for the lower-level routine
269: !  "FormJacobianLocal", where the actual computations are
270: !  done using the standard Fortran style of treating the local
271: !  vector data as a multidimensional array over the local mesh.
272: !  This routine merely accesses the local vector data via
273: !  VecGetArray() and VecRestoreArray().
274: !
275: !  Notes:
276: !  Due to grid point reordering with DMDAs, we must always work
277: !  with the local grid points, and then transform them to the new
278: !  global numbering with the "ltog" mapping
279: !  We cannot work directly with the global numbers for the original
280: !  uniprocessor grid!
281: !
282: !  Two methods are available for imposing this transformation
283: !  when setting matrix entries:
284: !    (A) MatSetValuesLocal(), using the local ordering (including
285: !        ghost points!)
286: !        - Set matrix entries using the local ordering
287: !          by calling MatSetValuesLocal()
288: !    (B) MatSetValues(), using the global ordering

290: !        - Set matrix entries using the global ordering by calling
291: !          MatSetValues()
292: !  Option (A) seems cleaner/easier in many cases, and is the procedure
293: !  used in this example.
294: !
295:   subroutine FormJacobian(snes, X, jac, jac_prec, ctx, ierr)
296: !  Input/output variables:
297:     SNES snes
298:     Vec X
299:     Mat jac, jac_prec
300:     type(AppCtx) ctx
301:     PetscErrorCode, intent(out) :: ierr
302:     DM da
303: !  Declarations for use with local arrays:
304:     PetscScalar, pointer :: lx_v(:)
305:     Vec localX

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

312:     PetscCallA(SNESGetDM(snes, da, ierr))
313:     PetscCallA(DMGetLocalVector(da, localX, ierr))
314:     PetscCallA(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX, ierr))
315:     PetscCallA(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX, ierr))

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

320: !  Compute entries for the locally owned part of the Jacobian preconditioner.
321:     PetscCallA(FormJacobianLocal(lx_v, jac_prec, ctx, ierr))

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

328:     PetscCallA(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY, ierr))
329:     if (jac /= jac_prec) then
330:       PetscCallA(MatAssemblyBegin(jac_prec, MAT_FINAL_ASSEMBLY, ierr))
331:     end if
332:     PetscCallA(VecRestoreArray(localX, lx_v, ierr))
333:     PetscCallA(DMRestoreLocalVector(da, localX, ierr))
334:     PetscCallA(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY, ierr))
335:     if (jac /= jac_prec) then
336:       PetscCallA(MatAssemblyEnd(jac_prec, MAT_FINAL_ASSEMBLY, ierr))
337:     end if

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

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

344:   end

346: ! ---------------------------------------------------------------------
347: !
348: !  FormJacobianLocal - Computes Jacobian matrix used to compute the preconditioner,
349: !  called by the higher level routine FormJacobian().
350: !
351: !  Input Parameters:
352: !  x        - local vector data
353: !
354: !  Output Parameters:
355: !  jac_prec - Jacobian matrix used to compute the preconditioner
356: !  ierr     - error code
357: !
358: !  Notes:
359: !  This routine uses standard Fortran-style computations over a 2-dim array.
360: !
361: !  Notes:
362: !  Due to grid point reordering with DMDAs, we must always work
363: !  with the local grid points, and then transform them to the new
364: !  global numbering with the "ltog" mapping
365: !  We cannot work directly with the global numbers for the original
366: !  uniprocessor grid!
367: !
368: !  Two methods are available for imposing this transformation
369: !  when setting matrix entries:
370: !    (A) MatSetValuesLocal(), using the local ordering (including
371: !        ghost points!)
372: !        - Set matrix entries using the local ordering
373: !          by calling MatSetValuesLocal()
374: !    (B) MatSetValues(), using the global ordering
375: !        - Then apply this map explicitly yourself
376: !        - Set matrix entries using the global ordering by calling
377: !          MatSetValues()
378: !  Option (A) seems cleaner/easier in many cases, and is the procedure
379: !  used in this example.
380: !
381:   subroutine FormJacobianLocal(x, jac_prec, ctx, ierr)
382: !  Input/output variables:
383:     type(AppCtx) ctx
384:     PetscScalar x(ctx%gxs:ctx%gxe, ctx%gys:ctx%gye)
385:     Mat jac_prec
386:     PetscErrorCode ierr

388: !  Local variables:
389:     PetscInt row, col(5), i, j
390:     PetscScalar, parameter :: two = 2.0, one = 1.0
391:     PetscScalar hx, hy, hxdhy, hydhx, sc, v(5)

393: !  Set parameters
394:     hx = one/(ctx%mx - 1)
395:     hy = one/(ctx%my - 1)
396:     sc = hx*hy
397:     hxdhy = hx/hy
398:     hydhx = hy/hx

400: !  Compute entries for the locally owned part of the Jacobian.
401: !   - Currently, all PETSc parallel matrix formats are partitioned by
402: !     contiguous chunks of rows across the processors.
403: !   - Each processor needs to insert only elements that it owns
404: !     locally (but any non-local elements will be sent to the
405: !     appropriate processor during matrix assembly).
406: !   - Here, we set all entries for a particular row at once.
407: !   - We can set matrix entries either using either
408: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
409: !   - Note that MatSetValues() uses 0-based row and column numbers
410: !     in Fortran as well as in C.

412:     do j = ctx%ys, ctx%ye
413:       row = (j - ctx%gys)*ctx%gxm + ctx%xs - ctx%gxs - 1
414:       do i = ctx%xs, ctx%xe
415:         row = row + 1
416: !           boundary points
417:         if (i == 1 .or. j == 1 .or. i == ctx%mx .or. j == ctx%my) then
418:           col(1) = row
419:           v(1) = one
420:           PetscCallA(MatSetValuesLocal(jac_prec, 1_PETSC_INT_KIND, [row], 1_PETSC_INT_KIND, col, v, INSERT_VALUES, ierr))
421: !           interior grid points
422:         else
423:           v(1) = -hxdhy
424:           v(2) = -hydhx
425:           v(3) = two*(hydhx + hxdhy) - sc*ctx%lambda*exp(x(i, j))
426:           v(4) = -hydhx
427:           v(5) = -hxdhy
428:           col(1) = row - ctx%gxm
429:           col(2) = row - 1
430:           col(3) = row
431:           col(4) = row + 1
432:           col(5) = row + ctx%gxm
433:           PetscCallA(MatSetValuesLocal(jac_prec, 1_PETSC_INT_KIND, [row], 5_PETSC_INT_KIND, col, v, INSERT_VALUES, ierr))
434:         end if
435:       end do
436:     end do

438:   end

440: end module ex5module

442: program main
443:   use ex5module
444:   implicit none
445: !

447: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
448: !                   Variable declarations
449: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
450: !
451: !  Variables:
452: !     snes        - nonlinear solver
453: !     x, r        - solution, residual vectors
454: !     J           - Jacobian matrix
455: !     its         - iterations for convergence
456: !     Nx, Ny      - number of preocessors in x- and y- directions
457: !     matrix_free - flag - 1 indicates matrix-free version
458: !
459:   SNES snes
460:   Vec x, r
461:   Mat J
462:   PetscErrorCode ierr
463:   PetscInt its
464:   PetscBool flg, matrix_free
465:   PetscReal, parameter :: lambda_min = 0.0_PETSC_REAL_KIND, lambda_max = 6.81_PETSC_REAL_KIND
466:   type(AppCtx) ctx
467:   DM da

469: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
470: !  Initialize program
471: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
472:   PetscCallA(PetscInitialize(ierr))
473:   PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD, ctx%rank, ierr))

475: !  Initialize problem parameters
476:   ctx%lambda = 6.0
477:   PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS, PETSC_NULL_CHARACTER, '-par', ctx%lambda, flg, ierr))
478:   PetscCheckA(ctx%lambda < lambda_max .and. ctx%lambda > lambda_min, PETSC_COMM_SELF, PETSC_ERR_USER, 'Lambda provided with -par is out of range')

480: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
481: !  Create nonlinear solver context
482: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
483:   PetscCallA(SNESCreate(PETSC_COMM_WORLD, snes, ierr))

485: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
486: !  Create vector data structures; set function evaluation routine
487: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

491: ! This really needs only the star-type stencil, but we use the box
492: ! stencil temporarily.
493:   PetscCallA(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_BOX, 4_PETSC_INT_KIND, 4_PETSC_INT_KIND, PETSC_DECIDE, PETSC_DECIDE, 1_PETSC_INT_KIND, 1_PETSC_INT_KIND, PETSC_NULL_INTEGER_ARRAY, PETSC_NULL_INTEGER_ARRAY, da, ierr))
494:   PetscCallA(DMSetFromOptions(da, ierr))
495:   PetscCallA(DMSetUp(da, ierr))

497:   PetscCallA(DMDAGetInfo(da, PETSC_NULL_INTEGER, ctx%mx, ctx%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))

499: !
500: !   Visualize the distribution of the array across the processors
501: !
502: !     PetscCallA(DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr))

504: !  Extract global and local vectors from DMDA; then duplicate for remaining
505: !  vectors that are the same types
506:   PetscCallA(DMCreateGlobalVector(da, x, ierr))
507:   PetscCallA(VecDuplicate(x, r, ierr))

509: !  Get local grid boundaries (for 2-dimensional DMDA)
510:   PetscCallA(DMDAGetCorners(da, ctx%xs, ctx%ys, PETSC_NULL_INTEGER, ctx%xm, ctx%ym, PETSC_NULL_INTEGER, ierr))
511:   PetscCallA(DMDAGetGhostCorners(da, ctx%gxs, ctx%gys, PETSC_NULL_INTEGER, ctx%gxm, ctx%gym, PETSC_NULL_INTEGER, ierr))

513: !  Here we shift the starting indices up by one so that we can easily
514: !  use the Fortran convention of 1-based indices (rather 0-based indices).
515:   ctx%xs = ctx%xs + 1
516:   ctx%ys = ctx%ys + 1
517:   ctx%gxs = ctx%gxs + 1
518:   ctx%gys = ctx%gys + 1

520:   ctx%ye = ctx%ys + ctx%ym - 1
521:   ctx%xe = ctx%xs + ctx%xm - 1
522:   ctx%gye = ctx%gys + ctx%gym - 1
523:   ctx%gxe = ctx%gxs + ctx%gxm - 1

525:   PetscCallA(SNESSetApplicationContext(snes, ctx, ierr))

527: !  Set function evaluation routine and vector
528:   PetscCallA(SNESSetFunction(snes, r, FormFunction, ctx, ierr))

530: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
531: !  Create matrix data structure; set Jacobian evaluation routine
532: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

534: !  Set Jacobian matrix data structure and default Jacobian evaluation
535: !  routine. User can override with:
536: !     -snes_fd : default finite differencing approximation of Jacobian
537: !     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
538: !                (unless user explicitly sets preconditioner)
539: !     -snes_mf_operator : form matrix used to construct the preconditioner as set by the user,
540: !                         but use matrix-free approx for Jacobian-vector
541: !                         products within Newton-Krylov method
542: !
543: !  Note:  For the parallel case, vectors and matrices MUST be partitioned
544: !     accordingly.  When using distributed arrays (DMDAs) to create vectors,
545: !     the DMDAs determine the problem partitioning.  We must explicitly
546: !     specify the local matrix dimensions upon its creation for compatibility
547: !     with the vector distribution.  Thus, the generic MatCreate() routine
548: !     is NOT sufficient when working with distributed arrays.
549: !
550: !     Note: Here we only approximately preallocate storage space for the
551: !     Jacobian.  See the users manual for a discussion of better techniques
552: !     for preallocating matrix memory.

554:   PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS, PETSC_NULL_CHARACTER, '-snes_mf', matrix_free, ierr))
555:   if (.not. matrix_free) then
556:     PetscCallA(DMSetMatType(da, MATAIJ, ierr))
557:     PetscCallA(DMCreateMatrix(da, J, ierr))
558:     PetscCallA(SNESSetJacobian(snes, J, J, FormJacobian, ctx, ierr))
559:   end if

561: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
562: !  Customize nonlinear solver; set runtime options
563: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
564: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
565:   PetscCallA(SNESSetDM(snes, da, ierr))
566:   PetscCallA(SNESSetFromOptions(snes, ierr))

568: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
569: !  Evaluate initial guess; then solve nonlinear system.
570: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
571: !  Note: The user should initialize the vector, x, with the initial guess
572: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
573: !  to employ an initial guess of zero, the user should explicitly set
574: !  this vector to zero by calling VecSet().

576:   PetscCallA(FormInitialGuess(snes, x, ierr))
577:   PetscCallA(SNESSolve(snes, PETSC_NULL_VEC, x, ierr))
578:   PetscCallA(SNESGetIterationNumber(snes, its, ierr))
579:   if (ctx%rank == 0) then
580:     write (6, 100) its
581:   end if
582: 100 format('Number of SNES iterations = ', i5)

584: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
585: !  Free work space.  All PETSc objects should be destroyed when they
586: !  are no longer needed.
587: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
588:   if (.not. matrix_free) PetscCallA(MatDestroy(J, ierr))
589:   PetscCallA(VecDestroy(x, ierr))
590:   PetscCallA(VecDestroy(r, ierr))
591:   PetscCallA(SNESDestroy(snes, ierr))
592:   PetscCallA(DMDestroy(da, ierr))

594:   PetscCallA(PetscFinalize(ierr))
595: end
596: !
597: !/*TEST
598: !
599: !   test:
600: !      nsize: 4
601: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
602: !      requires: !single
603: !
604: !   test:
605: !      suffix: 2
606: !      nsize: 4
607: !      args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
608: !      requires: !single
609: !
610: !   test:
611: !      suffix: 3
612: !      nsize: 3
613: !      args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
614: !      requires: !single
615: !
616: !   test:
617: !      suffix: 4
618: !      nsize: 3
619: !      args: -snes_mf_operator -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
620: !      requires: !single
621: !
622: !   test:
623: !      suffix: 5
624: !      requires: !single
625: !
626: !TEST*/