Actual source code: ex5f90t.F90
1: !
2: ! Description: Solves a nonlinear system in parallel with SNES.
3: ! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
4: ! domain, using distributed arrays (DMDAs) to partition the parallel grid.
5: ! The command line options include:
6: ! -par <parameter>, where <parameter> indicates the nonlinearity of the problem
7: ! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)
8: !
9: !
10: ! --------------------------------------------------------------------------
11: !
12: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
13: ! the partial differential equation
14: !
15: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
16: !
17: ! with boundary conditions
18: !
19: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
20: !
21: ! A finite difference approximation with the usual 5-point stencil
22: ! is used to discretize the boundary value problem to obtain a nonlinear
23: ! system of equations.
24: !
25: ! The uniprocessor version of this code is snes/tutorials/ex4f.F
26: !
27: ! --------------------------------------------------------------------------
28: ! The following define must be used before including any PETSc include files
29: ! into a module or interface. This is because they can't handle declarations
30: ! in them
31: !
33: module ex5f90tmodule
34: #include <petsc/finclude/petscdmda.h>
35: use petscdmda
36: type userctx
37: type(tDM) da
38: PetscInt xs, xe, xm, gxs, gxe, gxm
39: PetscInt ys, ye, ym, gys, gye, gym
40: PetscInt mx, my
41: PetscMPIInt rank
42: PetscReal lambda
43: end type userctx
45: contains
46: ! ---------------------------------------------------------------------
47: !
48: ! FormFunction - Evaluates nonlinear function, F(x).
49: !
50: ! Input Parameters:
51: ! snes - the SNES context
52: ! X - input vector
53: ! dummy - optional user-defined context, as set by SNESSetFunction()
54: ! (not used here)
55: !
56: ! Output Parameter:
57: ! F - function vector
58: !
59: ! Notes:
60: ! This routine serves as a wrapper for the lower-level routine
61: ! "FormFunctionLocal", where the actual computations are
62: ! done using the standard Fortran style of treating the local
63: ! vector data as a multidimensional array over the local mesh.
64: ! This routine merely handles ghost point scatters and accesses
65: ! the local vector data via VecGetArray() and VecRestoreArray().
66: !
67: subroutine FormFunction(snesIn, X, F, user, ierr)
68: #include <petsc/finclude/petscsnes.h>
69: use petscsnes
70: use petscdmda
72: ! Input/output variables:
73: type(tSNES) snesIn
74: type(tVec) X, F
75: PetscErrorCode ierr
76: type(userctx) user
78: ! Declarations for use with local arrays:
79: PetscScalar, pointer :: lx_v(:), lf_v(:)
80: type(tVec) localX
82: ! Scatter ghost points to local vector, using the 2-step process
83: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
84: ! By placing code between these two statements, computations can
85: ! be done while messages are in transition.
86: PetscCall(DMGetLocalVector(user%da, localX, ierr))
87: PetscCall(DMGlobalToLocalBegin(user%da, X, INSERT_VALUES, localX, ierr))
88: PetscCall(DMGlobalToLocalEnd(user%da, X, INSERT_VALUES, localX, ierr))
90: ! Get a pointer to vector data.
91: ! - VecGetArray90() returns a pointer to the data array.
92: ! - You MUST call VecRestoreArray() when you no longer need access to
93: ! 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, user, 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(user%da, localX, ierr))
108: PetscCall(PetscLogFlops(11.0d0*user%ym*user%xm, ierr))
110: ! PetscCall(VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr))
111: ! PetscCall(VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr))
112: end subroutine formfunction
113: end module ex5f90tmodule
115: module f90moduleinterfacest
116: use ex5f90tmodule
118: Interface SNESSetApplicationContext
119: Subroutine SNESSetApplicationContext(snesIn, ctx, ierr)
120: #include <petsc/finclude/petscsnes.h>
121: use petscsnes
122: use ex5f90tmodule
123: type(tSNES) snesIn
124: type(userctx) ctx
125: PetscErrorCode ierr
126: End Subroutine
127: End Interface SNESSetApplicationContext
129: Interface SNESGetApplicationContext
130: Subroutine SNESGetApplicationContext(snesIn, ctx, ierr)
131: #include <petsc/finclude/petscsnes.h>
132: use petscsnes
133: use ex5f90tmodule
134: type(tSNES) snesIn
135: type(userctx), pointer :: ctx
136: PetscErrorCode ierr
137: End Subroutine
138: End Interface SNESGetApplicationContext
139: end module f90moduleinterfacest
141: program main
142: #include <petsc/finclude/petscdmda.h>
143: #include <petsc/finclude/petscsnes.h>
144: use petscdmda
145: use petscsnes
146: use ex5f90tmodule
147: use f90moduleinterfacest
148: implicit none
149: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: ! Variable declarations
151: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152: !
153: ! Variables:
154: ! mysnes - nonlinear solver
155: ! x, r - solution, residual vectors
156: ! J - Jacobian matrix
157: ! its - iterations for convergence
158: ! Nx, Ny - number of preocessors in x- and y- directions
159: ! matrix_free - flag - 1 indicates matrix-free version
160: !
161: type(tSNES) mysnes
162: type(tVec) x, r
163: type(tMat) J
164: PetscErrorCode ierr
165: PetscInt its
166: PetscBool flg, matrix_free, set
167: PetscInt ione, nfour
168: PetscReal lambda_max, lambda_min
169: type(userctx) user
170: type(userctx), pointer:: puser
171: type(tPetscOptions) :: options
173: ! Note: Any user-defined Fortran routines (such as FormJacobian)
174: ! MUST be declared as external.
175: external FormInitialGuess, FormJacobian
177: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: ! Initialize program
179: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
180: PetscCallA(PetscInitialize(ierr))
181: PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD, user%rank, ierr))
183: ! Initialize problem parameters
184: options%v = 0
185: lambda_max = 6.81
186: lambda_min = 0.0
187: user%lambda = 6.0
188: ione = 1
189: nfour = 4
190: PetscCallA(PetscOptionsGetReal(options, PETSC_NULL_CHARACTER, '-par', user%lambda, flg, ierr))
191: PetscCheckA(user%lambda < lambda_max .and. user%lambda > lambda_min, PETSC_COMM_SELF, PETSC_ERR_USER, 'Lambda provided with -par is out of range')
193: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: ! Create nonlinear solver context
195: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196: PetscCallA(SNESCreate(PETSC_COMM_WORLD, mysnes, ierr))
198: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: ! Create vector data structures; set function evaluation routine
200: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202: ! Create distributed array (DMDA) to manage parallel grid and vectors
204: ! This really needs only the star-type stencil, but we use the box
205: ! stencil temporarily.
206: 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))
207: PetscCallA(DMSetFromOptions(user%da, ierr))
208: PetscCallA(DMSetUp(user%da, ierr))
209: 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))
211: !
212: ! Visualize the distribution of the array across the processors
213: !
214: ! PetscCallA(DMView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr))
216: ! Extract global and local vectors from DMDA; then duplicate for remaining
217: ! vectors that are the same types
218: PetscCallA(DMCreateGlobalVector(user%da, x, ierr))
219: PetscCallA(VecDuplicate(x, r, ierr))
221: ! Get local grid boundaries (for 2-dimensional DMDA)
222: PetscCallA(DMDAGetCorners(user%da, user%xs, user%ys, PETSC_NULL_INTEGER, user%xm, user%ym, PETSC_NULL_INTEGER, ierr))
223: PetscCallA(DMDAGetGhostCorners(user%da, user%gxs, user%gys, PETSC_NULL_INTEGER, user%gxm, user%gym, PETSC_NULL_INTEGER, ierr))
225: ! Here we shift the starting indices up by one so that we can easily
226: ! use the Fortran convention of 1-based indices (rather 0-based indices).
227: user%xs = user%xs + 1
228: user%ys = user%ys + 1
229: user%gxs = user%gxs + 1
230: user%gys = user%gys + 1
232: user%ye = user%ys + user%ym - 1
233: user%xe = user%xs + user%xm - 1
234: user%gye = user%gys + user%gym - 1
235: user%gxe = user%gxs + user%gxm - 1
237: PetscCallA(SNESSetApplicationContext(mysnes, user, ierr))
239: ! Set function evaluation routine and vector
240: PetscCallA(SNESSetFunction(mysnes, r, FormFunction, user, ierr))
242: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
243: ! Create matrix data structure; set Jacobian evaluation routine
244: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
246: ! Set Jacobian matrix data structure and default Jacobian evaluation
247: ! routine. User can override with:
248: ! -snes_fd : default finite differencing approximation of Jacobian
249: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
250: ! (unless user explicitly sets preconditioner)
251: ! -snes_mf_operator : form matrix used to construct the preconditioner as set by the user,
252: ! but use matrix-free approx for Jacobian-vector
253: ! products within Newton-Krylov method
254: !
255: ! Note: For the parallel case, vectors and matrices MUST be partitioned
256: ! accordingly. When using distributed arrays (DMDAs) to create vectors,
257: ! the DMDAs determine the problem partitioning. We must explicitly
258: ! specify the local matrix dimensions upon its creation for compatibility
259: ! with the vector distribution. Thus, the generic MatCreate() routine
260: ! is NOT sufficient when working with distributed arrays.
261: !
262: ! Note: Here we only approximately preallocate storage space for the
263: ! Jacobian. See the users manual for a discussion of better techniques
264: ! for preallocating matrix memory.
266: PetscCallA(PetscOptionsHasName(options, PETSC_NULL_CHARACTER, '-snes_mf', matrix_free, ierr))
267: if (.not. matrix_free) then
268: PetscCallA(DMSetMatType(user%da, MATAIJ, ierr))
269: PetscCallA(DMCreateMatrix(user%da, J, ierr))
270: PetscCallA(SNESSetJacobian(mysnes, J, J, FormJacobian, user, ierr))
271: end if
273: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
274: ! Customize nonlinear solver; set runtime options
275: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
276: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
277: PetscCallA(SNESSetFromOptions(mysnes, ierr))
279: ! Test Fortran90 wrapper for SNESSet/Get ApplicationContext()
280: PetscCallA(PetscOptionsGetBool(options, PETSC_NULL_CHARACTER, '-test_appctx', flg, set, ierr))
281: if (flg) then
282: PetscCallA(SNESGetApplicationContext(mysnes, puser, ierr))
283: end if
285: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
286: ! Evaluate initial guess; then solve nonlinear system.
287: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
288: ! Note: The user should initialize the vector, x, with the initial guess
289: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
290: ! to employ an initial guess of zero, the user should explicitly set
291: ! this vector to zero by calling VecSet().
293: PetscCallA(FormInitialGuess(mysnes, x, ierr))
294: PetscCallA(SNESSolve(mysnes, PETSC_NULL_VEC, x, ierr))
295: PetscCallA(SNESGetIterationNumber(mysnes, its, ierr))
296: if (user%rank == 0) then
297: write (6, 100) its
298: end if
299: 100 format('Number of SNES iterations = ', i5)
301: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
302: ! Free work space. All PETSc objects should be destroyed when they
303: ! are no longer needed.
304: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
305: if (.not. matrix_free) PetscCallA(MatDestroy(J, ierr))
306: PetscCallA(VecDestroy(x, ierr))
307: PetscCallA(VecDestroy(r, ierr))
308: PetscCallA(SNESDestroy(mysnes, ierr))
309: PetscCallA(DMDestroy(user%da, ierr))
311: PetscCallA(PetscFinalize(ierr))
312: end
314: ! ---------------------------------------------------------------------
315: !
316: ! FormInitialGuess - Forms initial approximation.
317: !
318: ! Input Parameters:
319: ! X - vector
320: !
321: ! Output Parameter:
322: ! X - vector
323: !
324: ! Notes:
325: ! This routine serves as a wrapper for the lower-level routine
326: ! "InitialGuessLocal", where the actual computations are
327: ! done using the standard Fortran style of treating the local
328: ! vector data as a multidimensional array over the local mesh.
329: ! This routine merely handles ghost point scatters and accesses
330: ! the local vector data via VecGetArray() and VecRestoreArray().
331: !
332: subroutine FormInitialGuess(mysnes, X, ierr)
333: #include <petsc/finclude/petscsnes.h>
334: use petscsnes
335: use ex5f90tmodule
336: use f90moduleinterfacest
337: ! Input/output variables:
338: type(tSNES) mysnes
339: type(userctx), pointer:: puser
340: type(tVec) X
341: PetscErrorCode ierr
343: ! Declarations for use with local arrays:
344: PetscScalar, pointer :: lx_v(:)
346: ierr = 0
347: PetscCallA(SNESGetApplicationContext(mysnes, puser, ierr))
348: ! Get a pointer to vector data.
349: ! - VecGetArray90() returns a pointer to the data array.
350: ! - You MUST call VecRestoreArray() when you no longer need access to
351: ! the array.
353: PetscCallA(VecGetArray(X, lx_v, ierr))
355: ! Compute initial guess over the locally owned part of the grid
356: PetscCallA(InitialGuessLocal(puser, lx_v, ierr))
358: ! Restore vector
359: PetscCallA(VecRestoreArray(X, lx_v, ierr))
361: ! Insert values into global vector
363: end
365: ! ---------------------------------------------------------------------
366: !
367: ! InitialGuessLocal - Computes initial approximation, called by
368: ! the higher level routine FormInitialGuess().
369: !
370: ! Input Parameter:
371: ! x - local vector data
372: !
373: ! Output Parameters:
374: ! x - local vector data
375: ! ierr - error code
376: !
377: ! Notes:
378: ! This routine uses standard Fortran-style computations over a 2-dim array.
379: !
380: subroutine InitialGuessLocal(user, x, ierr)
381: #include <petsc/finclude/petscsys.h>
382: use petscsys
383: use ex5f90tmodule
384: ! Input/output variables:
385: type(userctx) user
386: PetscScalar x(user%xs:user%xe, user%ys:user%ye)
387: PetscErrorCode ierr
389: ! Local variables:
390: PetscInt i, j
391: PetscScalar temp1, temp, hx, hy
392: PetscScalar one
394: ! Set parameters
396: ierr = 0
397: one = 1.0
398: hx = one/(PetscIntToReal(user%mx - 1))
399: hy = one/(PetscIntToReal(user%my - 1))
400: temp1 = user%lambda/(user%lambda + one)
402: do 20 j = user%ys, user%ye
403: temp = PetscIntToReal(min(j - 1, user%my - j))*hy
404: do 10 i = user%xs, user%xe
405: if (i == 1 .or. j == 1 .or. i == user%mx .or. j == user%my) then
406: x(i, j) = 0.0
407: else
408: x(i, j) = temp1*sqrt(min(PetscIntToReal(min(i - 1, user%mx - i)*hx), PetscIntToReal(temp)))
409: end if
410: 10 continue
411: 20 continue
413: end
415: ! ---------------------------------------------------------------------
416: !
417: ! FormFunctionLocal - Computes nonlinear function, called by
418: ! the higher level routine FormFunction().
419: !
420: ! Input Parameter:
421: ! x - local vector data
422: !
423: ! Output Parameters:
424: ! f - local vector data, f(x)
425: ! ierr - error code
426: !
427: ! Notes:
428: ! This routine uses standard Fortran-style computations over a 2-dim array.
429: !
430: subroutine FormFunctionLocal(x, f, user, ierr)
431: #include <petsc/finclude/petscsys.h>
432: use petscsys
433: use ex5f90tmodule
434: ! Input/output variables:
435: type(userctx) user
436: PetscScalar x(user%gxs:user%gxe, user%gys:user%gye)
437: PetscScalar f(user%xs:user%xe, user%ys:user%ye)
438: PetscErrorCode ierr
440: ! Local variables:
441: PetscScalar two, one, hx, hy, hxdhy, hydhx, sc
442: PetscScalar u, uxx, uyy
443: PetscInt i, j
445: one = 1.0
446: two = 2.0
447: hx = one/PetscIntToReal(user%mx - 1)
448: hy = one/PetscIntToReal(user%my - 1)
449: sc = hx*hy*user%lambda
450: hxdhy = hx/hy
451: hydhx = hy/hx
453: ! Compute function over the locally owned part of the grid
455: do 20 j = user%ys, user%ye
456: do 10 i = user%xs, user%xe
457: if (i == 1 .or. j == 1 .or. i == user%mx .or. j == user%my) then
458: f(i, j) = x(i, j)
459: else
460: u = x(i, j)
461: uxx = hydhx*(two*u - x(i - 1, j) - x(i + 1, j))
462: uyy = hxdhy*(two*u - x(i, j - 1) - x(i, j + 1))
463: f(i, j) = uxx + uyy - sc*exp(u)
464: end if
465: 10 continue
466: 20 continue
467: ierr = 0
468: end
470: ! ---------------------------------------------------------------------
471: !
472: ! FormJacobian - Evaluates Jacobian matrix.
473: !
474: ! Input Parameters:
475: ! snes - the SNES context
476: ! x - input vector
477: ! dummy - optional user-defined context, as set by SNESSetJacobian()
478: ! (not used here)
479: !
480: ! Output Parameters:
481: ! jac - Jacobian matrix
482: ! jac_prec - optionally different matrix used to construct the preconditioner (not used here)
483: !
484: ! Notes:
485: ! This routine serves as a wrapper for the lower-level routine
486: ! "FormJacobianLocal", where the actual computations are
487: ! done using the standard Fortran style of treating the local
488: ! vector data as a multidimensional array over the local mesh.
489: ! This routine merely accesses the local vector data via
490: ! VecGetArray() and VecRestoreArray().
491: !
492: ! Notes:
493: ! Due to grid point reordering with DMDAs, we must always work
494: ! with the local grid points, and then transform them to the new
495: ! global numbering with the "ltog" mapping
496: ! We cannot work directly with the global numbers for the original
497: ! uniprocessor grid!
498: !
499: ! Two methods are available for imposing this transformation
500: ! when setting matrix entries:
501: ! (A) MatSetValuesLocal(), using the local ordering (including
502: ! ghost points!)
503: ! - Set matrix entries using the local ordering
504: ! by calling MatSetValuesLocal()
505: ! (B) MatSetValues(), using the global ordering
506: ! - Use DMGetLocalToGlobalMapping() then
507: ! ISLocalToGlobalMappingGetIndices() to extract the local-to-global map
508: ! - Then apply this map explicitly yourself
509: ! - Set matrix entries using the global ordering by calling
510: ! MatSetValues()
511: ! Option (A) seems cleaner/easier in many cases, and is the procedure
512: ! used in this example.
513: !
514: subroutine FormJacobian(mysnes, X, jac, jac_prec, user, ierr)
515: #include <petsc/finclude/petscsnes.h>
516: use petscsnes
517: use ex5f90tmodule
518: ! Input/output variables:
519: type(tSNES) mysnes
520: type(tVec) X
521: type(tMat) jac, jac_prec
522: type(userctx) user
523: PetscErrorCode ierr
525: ! Declarations for use with local arrays:
526: PetscScalar, pointer :: lx_v(:)
527: type(tVec) localX
529: ! Scatter ghost points to local vector, using the 2-step process
530: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
531: ! Computations can be done while messages are in transition,
532: ! by placing code between these two statements.
534: PetscCallA(DMGetLocalVector(user%da, localX, ierr))
535: PetscCallA(DMGlobalToLocalBegin(user%da, X, INSERT_VALUES, localX, ierr))
536: PetscCallA(DMGlobalToLocalEnd(user%da, X, INSERT_VALUES, localX, ierr))
538: ! Get a pointer to vector data
539: PetscCallA(VecGetArray(localX, lx_v, ierr))
541: ! Compute entries for the locally owned part of the Jacobian preconditioner.
542: PetscCallA(FormJacobianLocal(lx_v, jac_prec, user, ierr))
544: ! Assemble matrix, using the 2-step process:
545: ! MatAssemblyBegin(), MatAssemblyEnd()
546: ! Computations can be done while messages are in transition,
547: ! by placing code between these two statements.
549: PetscCallA(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY, ierr))
550: ! if (jac .ne. jac_prec) then
551: PetscCallA(MatAssemblyBegin(jac_prec, MAT_FINAL_ASSEMBLY, ierr))
552: ! endif
553: PetscCallA(VecRestoreArray(localX, lx_v, ierr))
554: PetscCallA(DMRestoreLocalVector(user%da, localX, ierr))
555: PetscCallA(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY, ierr))
556: ! if (jac .ne. jac_prec) then
557: PetscCallA(MatAssemblyEnd(jac_prec, MAT_FINAL_ASSEMBLY, ierr))
558: ! endif
560: ! Tell the matrix we will never add a new nonzero location to the
561: ! matrix. If we do it will generate an error.
563: PetscCallA(MatSetOption(jac, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE, ierr))
565: end
567: ! ---------------------------------------------------------------------
568: !
569: ! FormJacobianLocal - Computes Jacobian matrix used to compute the preconditioner,
570: ! called by the higher level routine FormJacobian().
571: !
572: ! Input Parameters:
573: ! x - local vector data
574: !
575: ! Output Parameters:
576: ! jac_prec - Jacobian matrix used to compute the preconditioner
577: ! ierr - error code
578: !
579: ! Notes:
580: ! This routine uses standard Fortran-style computations over a 2-dim array.
581: !
582: ! Notes:
583: ! Due to grid point reordering with DMDAs, we must always work
584: ! with the local grid points, and then transform them to the new
585: ! global numbering with the "ltog" mapping
586: ! We cannot work directly with the global numbers for the original
587: ! uniprocessor grid!
588: !
589: ! Two methods are available for imposing this transformation
590: ! when setting matrix entries:
591: ! (A) MatSetValuesLocal(), using the local ordering (including
592: ! ghost points!)
593: ! - Set matrix entries using the local ordering
594: ! by calling MatSetValuesLocal()
595: ! (B) MatSetValues(), using the global ordering
596: ! - Set matrix entries using the global ordering by calling
597: ! MatSetValues()
598: ! Option (A) seems cleaner/easier in many cases, and is the procedure
599: ! used in this example.
600: !
601: subroutine FormJacobianLocal(x, jac_prec, user, ierr)
602: #include <petsc/finclude/petscmat.h>
603: use petscmat
604: use ex5f90tmodule
605: ! Input/output variables:
606: type(userctx) user
607: PetscScalar x(user%gxs:user%gxe, user%gys:user%gye)
608: type(tMat) jac_prec
609: PetscErrorCode ierr
611: ! Local variables:
612: PetscInt row, col(5), i, j
613: PetscInt ione, ifive
614: PetscScalar two, one, hx, hy, hxdhy
615: PetscScalar hydhx, sc, v(5)
617: ! Set parameters
618: ione = 1
619: ifive = 5
620: one = 1.0
621: two = 2.0
622: hx = one/PetscIntToReal(user%mx - 1)
623: hy = one/PetscIntToReal(user%my - 1)
624: sc = hx*hy
625: hxdhy = hx/hy
626: hydhx = hy/hx
628: ! Compute entries for the locally owned part of the Jacobian.
629: ! - Currently, all PETSc parallel matrix formats are partitioned by
630: ! contiguous chunks of rows across the processors.
631: ! - Each processor needs to insert only elements that it owns
632: ! locally (but any non-local elements will be sent to the
633: ! appropriate processor during matrix assembly).
634: ! - Here, we set all entries for a particular row at once.
635: ! - We can set matrix entries either using either
636: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
637: ! - Note that MatSetValues() uses 0-based row and column numbers
638: ! in Fortran as well as in C.
640: do 20 j = user%ys, user%ye
641: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
642: do 10 i = user%xs, user%xe
643: row = row + 1
644: ! boundary points
645: if (i == 1 .or. j == 1 .or. i == user%mx .or. j == user%my) then
646: col(1) = row
647: v(1) = one
648: PetscCallA(MatSetValuesLocal(jac_prec, ione, [row], ione, col, v, INSERT_VALUES, ierr))
649: ! interior grid points
650: else
651: v(1) = -hxdhy
652: v(2) = -hydhx
653: v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i, j))
654: v(4) = -hydhx
655: v(5) = -hxdhy
656: col(1) = row - user%gxm
657: col(2) = row - 1
658: col(3) = row
659: col(4) = row + 1
660: col(5) = row + user%gxm
661: PetscCallA(MatSetValuesLocal(jac_prec, ione, [row], ifive, col, v, INSERT_VALUES, ierr))
662: end if
663: 10 continue
664: 20 continue
665: end
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: !
673: !TEST*/