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: !    - Note that the interface to VecGetArray() differs from VecGetArray().

 97:     PetscCall(VecGetArray(localX, lx_v, ierr))
 98:     PetscCall(VecGetArray(F, lf_v, ierr))

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

103: !  Restore vectors
104:     PetscCall(VecRestoreArray(localX, lx_v, ierr))
105:     PetscCall(VecRestoreArray(F, lf_v, ierr))

107: !  Insert values into global vector

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

112: !      PetscCallA(VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr))
113: !      PetscCallA(VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr))
114:   end subroutine formfunction

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

142: !  Declarations for use with local arrays:
143:     PetscScalar, pointer :: lx_v(:)

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

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

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

159: !  Restore vector
160:     PetscCallA(VecRestoreArray(X, lx_v, ierr))

162: !  Insert values into global vector

164:   end

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

190:     hx = 1._PETSC_REAL_KIND/(ctx%mx - 1)
191:     hy = 1._PETSC_REAL_KIND/(ctx%my - 1)
192:     temp1 = ctx%lambda/(ctx%lambda + 1._PETSC_REAL_KIND)

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

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

234:     hx = one/(ctx%mx - 1)
235:     hy = one/(ctx%my - 1)
236:     sc = hx*hy*ctx%lambda
237:     hxdhy = hx/hy
238:     hydhx = hy/hx

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

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

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

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

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

316:     PetscCallA(SNESGetDM(snes, da, ierr))
317:     PetscCallA(DMGetLocalVector(da, localX, ierr))
318:     PetscCallA(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX, ierr))
319:     PetscCallA(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX, ierr))

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

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

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

332:     PetscCallA(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY, ierr))
333:     if (jac /= jac_prec) then
334:       PetscCallA(MatAssemblyBegin(jac_prec, MAT_FINAL_ASSEMBLY, ierr))
335:     end if
336:     PetscCallA(VecRestoreArray(localX, lx_v, ierr))
337:     PetscCallA(DMRestoreLocalVector(da, localX, ierr))
338:     PetscCallA(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY, ierr))
339:     if (jac /= jac_prec) then
340:       PetscCallA(MatAssemblyEnd(jac_prec, MAT_FINAL_ASSEMBLY, ierr))
341:     end if

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

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

348:   end

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

392: !  Local variables:
393:     PetscInt row, col(5), i, j
394:     PetscScalar, parameter :: two = 2.0, one = 1.0
395:     PetscScalar hx, hy, hxdhy, hydhx, sc, v(5)

397: !  Set parameters
398:     hx = one/(ctx%mx - 1)
399:     hy = one/(ctx%my - 1)
400:     sc = hx*hy
401:     hxdhy = hx/hy
402:     hydhx = hy/hx

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

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

442:   end

444: end module ex5module

446: program main
447:   use ex5module
448:   implicit none
449: !

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

473: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
474: !  Initialize program
475: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
476:   PetscCallA(PetscInitialize(ierr))
477:   PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD, ctx%rank, ierr))

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

484: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
485: !  Create nonlinear solver context
486: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
487:   PetscCallA(SNESCreate(PETSC_COMM_WORLD, snes, ierr))

489: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
490: !  Create vector data structures; set function evaluation routine
491: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

495: ! This really needs only the star-type stencil, but we use the box
496: ! stencil temporarily.
497:   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))
498:   PetscCallA(DMSetFromOptions(da, ierr))
499:   PetscCallA(DMSetUp(da, ierr))

501:   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))

503: !
504: !   Visualize the distribution of the array across the processors
505: !
506: !     PetscCallA(DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr))

508: !  Extract global and local vectors from DMDA; then duplicate for remaining
509: !  vectors that are the same types
510:   PetscCallA(DMCreateGlobalVector(da, x, ierr))
511:   PetscCallA(VecDuplicate(x, r, ierr))

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

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

524:   ctx%ye = ctx%ys + ctx%ym - 1
525:   ctx%xe = ctx%xs + ctx%xm - 1
526:   ctx%gye = ctx%gys + ctx%gym - 1
527:   ctx%gxe = ctx%gxs + ctx%gxm - 1

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

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

534: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
535: !  Create matrix data structure; set Jacobian evaluation routine
536: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

538: !  Set Jacobian matrix data structure and default Jacobian evaluation
539: !  routine. User can override with:
540: !     -snes_fd : default finite differencing approximation of Jacobian
541: !     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
542: !                (unless user explicitly sets preconditioner)
543: !     -snes_mf_operator : form matrix used to construct the preconditioner as set by the user,
544: !                         but use matrix-free approx for Jacobian-vector
545: !                         products within Newton-Krylov method
546: !
547: !  Note:  For the parallel case, vectors and matrices MUST be partitioned
548: !     accordingly.  When using distributed arrays (DMDAs) to create vectors,
549: !     the DMDAs determine the problem partitioning.  We must explicitly
550: !     specify the local matrix dimensions upon its creation for compatibility
551: !     with the vector distribution.  Thus, the generic MatCreate() routine
552: !     is NOT sufficient when working with distributed arrays.
553: !
554: !     Note: Here we only approximately preallocate storage space for the
555: !     Jacobian.  See the users manual for a discussion of better techniques
556: !     for preallocating matrix memory.

558:   PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS, PETSC_NULL_CHARACTER, '-snes_mf', matrix_free, ierr))
559:   if (.not. matrix_free) then
560:     PetscCallA(DMSetMatType(da, MATAIJ, ierr))
561:     PetscCallA(DMCreateMatrix(da, J, ierr))
562:     PetscCallA(SNESSetJacobian(snes, J, J, FormJacobian, ctx, ierr))
563:   end if

565: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
566: !  Customize nonlinear solver; set runtime options
567: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
568: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
569:   PetscCallA(SNESSetDM(snes, da, ierr))
570:   PetscCallA(SNESSetFromOptions(snes, ierr))

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

580:   PetscCallA(FormInitialGuess(snes, x, ierr))
581:   PetscCallA(SNESSolve(snes, PETSC_NULL_VEC, x, ierr))
582:   PetscCallA(SNESGetIterationNumber(snes, its, ierr))
583:   if (ctx%rank == 0) then
584:     write (6, 100) its
585:   end if
586: 100 format('Number of SNES iterations = ', i5)

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

598:   PetscCallA(PetscFinalize(ierr))
599: end
600: !
601: !/*TEST
602: !
603: !   test:
604: !      nsize: 4
605: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
606: !      requires: !single
607: !
608: !   test:
609: !      suffix: 2
610: !      nsize: 4
611: !      args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
612: !      requires: !single
613: !
614: !   test:
615: !      suffix: 3
616: !      nsize: 3
617: !      args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
618: !      requires: !single
619: !
620: !   test:
621: !      suffix: 4
622: !      nsize: 3
623: !      args: -snes_mf_operator -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
624: !      requires: !single
625: !
626: !   test:
627: !      suffix: 5
628: !      requires: !single
629: !
630: !TEST*/