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/petscdm.h>
35: use petscdmdef
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 VecGetArrayF90() and VecRestoreArrayF90().
66: !
67: subroutine FormFunction(snesIn,X,F,user,ierr)
68: #include <petsc/finclude/petscsnes.h>
69: use petscsnes
71: ! Input/output variables:
72: type(tSNES) snesIn
73: type(tVec) X,F
74: PetscErrorCode ierr
75: type (userctx) user
77: ! Declarations for use with local arrays:
78: PetscScalar,pointer :: lx_v(:),lf_v(:)
79: type(tVec) 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(DMGetLocalVector(user%da,localX,ierr))
86: PetscCall(DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,ierr))
87: PetscCall(DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr))
89: ! Get a pointer to vector data.
90: ! - VecGetArray90() returns a pointer to the data array.
91: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
92: ! the array.
94: PetscCall(VecGetArrayF90(localX,lx_v,ierr))
95: PetscCall(VecGetArrayF90(F,lf_v,ierr))
97: ! Compute function over the locally owned part of the grid
98: PetscCall(FormFunctionLocal(lx_v,lf_v,user,ierr))
100: ! Restore vectors
101: PetscCall(VecRestoreArrayF90(localX,lx_v,ierr))
102: PetscCall(VecRestoreArrayF90(F,lf_v,ierr))
104: ! Insert values into global vector
106: PetscCall(DMRestoreLocalVector(user%da,localX,ierr))
107: PetscCall(PetscLogFlops(11.0d0*user%ym*user%xm,ierr))
109: ! PetscCall(VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr))
110: ! PetscCall(VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr))
111: end subroutine formfunction
112: end module ex5f90tmodule
114: module f90moduleinterfacest
115: use ex5f90tmodule
117: Interface SNESSetApplicationContext
118: Subroutine SNESSetApplicationContext(snesIn,ctx,ierr)
119: #include <petsc/finclude/petscsnes.h>
120: use petscsnes
121: use ex5f90tmodule
122: type(tSNES) snesIn
123: type(userctx) ctx
124: PetscErrorCode ierr
125: End Subroutine
126: End Interface SNESSetApplicationContext
128: Interface SNESGetApplicationContext
129: Subroutine SNESGetApplicationContext(snesIn,ctx,ierr)
130: #include <petsc/finclude/petscsnes.h>
131: use petscsnes
132: use ex5f90tmodule
133: type(tSNES) snesIn
134: type(userctx), pointer :: ctx
135: PetscErrorCode ierr
136: End Subroutine
137: End Interface SNESGetApplicationContext
138: end module f90moduleinterfacest
140: program main
141: #include <petsc/finclude/petscdm.h>
142: #include <petsc/finclude/petscsnes.h>
143: use petscdmda
144: use petscdm
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 .lt. lambda_max .and. user%lambda .gt. 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_ENUM,PETSC_NULL_ENUM,PETSC_NULL_ENUM,PETSC_NULL_ENUM,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 preconditioning matrix 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: endif
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: endif
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 .eq. 0) then
297: write(6,100) its
298: endif
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 VecGetArrayF90() and VecRestoreArrayF90().
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 VecRestoreArrayF90() when you no longer need access to
351: ! the array.
353: PetscCallA(VecGetArrayF90(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(VecRestoreArrayF90(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 .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. 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: endif
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 .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. 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: endif
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 preconditioning matrix (not used here)
483: ! flag - flag indicating matrix structure
484: !
485: ! Notes:
486: ! This routine serves as a wrapper for the lower-level routine
487: ! "FormJacobianLocal", where the actual computations are
488: ! done using the standard Fortran style of treating the local
489: ! vector data as a multidimensional array over the local mesh.
490: ! This routine merely accesses the local vector data via
491: ! VecGetArrayF90() and VecRestoreArrayF90().
492: !
493: ! Notes:
494: ! Due to grid point reordering with DMDAs, we must always work
495: ! with the local grid points, and then transform them to the new
496: ! global numbering with the "ltog" mapping
497: ! We cannot work directly with the global numbers for the original
498: ! uniprocessor grid!
499: !
500: ! Two methods are available for imposing this transformation
501: ! when setting matrix entries:
502: ! (A) MatSetValuesLocal(), using the local ordering (including
503: ! ghost points!)
504: ! - Set matrix entries using the local ordering
505: ! by calling MatSetValuesLocal()
506: ! (B) MatSetValues(), using the global ordering
507: ! - Use DMGetLocalToGlobalMapping() then
508: ! ISLocalToGlobalMappingGetIndicesF90() to extract the local-to-global map
509: ! - Then apply this map explicitly yourself
510: ! - Set matrix entries using the global ordering by calling
511: ! MatSetValues()
512: ! Option (A) seems cleaner/easier in many cases, and is the procedure
513: ! used in this example.
514: !
515: subroutine FormJacobian(mysnes,X,jac,jac_prec,user,ierr)
516: #include <petsc/finclude/petscsnes.h>
517: use petscsnes
518: use ex5f90tmodule
519: ! Input/output variables:
520: type(tSNES) mysnes
521: type(tVec) X
522: type(tMat) jac,jac_prec
523: type(userctx) user
524: PetscErrorCode ierr
526: ! Declarations for use with local arrays:
527: PetscScalar,pointer :: lx_v(:)
528: type(tVec) localX
530: ! Scatter ghost points to local vector, using the 2-step process
531: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
532: ! Computations can be done while messages are in transition,
533: ! by placing code between these two statements.
535: PetscCallA(DMGetLocalVector(user%da,localX,ierr))
536: PetscCallA(DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,ierr))
537: PetscCallA(DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr))
539: ! Get a pointer to vector data
540: PetscCallA(VecGetArrayF90(localX,lx_v,ierr))
542: ! Compute entries for the locally owned part of the Jacobian preconditioner.
543: PetscCallA(FormJacobianLocal(lx_v,jac_prec,user,ierr))
545: ! Assemble matrix, using the 2-step process:
546: ! MatAssemblyBegin(), MatAssemblyEnd()
547: ! Computations can be done while messages are in transition,
548: ! by placing code between these two statements.
550: PetscCallA(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr))
551: ! if (jac .ne. jac_prec) then
552: PetscCallA(MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr))
553: ! endif
554: PetscCallA(VecRestoreArrayF90(localX,lx_v,ierr))
555: PetscCallA(DMRestoreLocalVector(user%da,localX,ierr))
556: PetscCallA(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr))
557: ! if (jac .ne. jac_prec) then
558: PetscCallA(MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr))
559: ! endif
561: ! Tell the matrix we will never add a new nonzero location to the
562: ! matrix. If we do it will generate an error.
564: PetscCallA(MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr))
566: end
568: ! ---------------------------------------------------------------------
569: !
570: ! FormJacobianLocal - Computes Jacobian preconditioner matrix,
571: ! called by the higher level routine FormJacobian().
572: !
573: ! Input Parameters:
574: ! x - local vector data
575: !
576: ! Output Parameters:
577: ! jac_prec - Jacobian preconditioner matrix
578: ! ierr - error code
579: !
580: ! Notes:
581: ! This routine uses standard Fortran-style computations over a 2-dim array.
582: !
583: ! Notes:
584: ! Due to grid point reordering with DMDAs, we must always work
585: ! with the local grid points, and then transform them to the new
586: ! global numbering with the "ltog" mapping
587: ! We cannot work directly with the global numbers for the original
588: ! uniprocessor grid!
589: !
590: ! Two methods are available for imposing this transformation
591: ! when setting matrix entries:
592: ! (A) MatSetValuesLocal(), using the local ordering (including
593: ! ghost points!)
594: ! - Set matrix entries using the local ordering
595: ! by calling MatSetValuesLocal()
596: ! (B) MatSetValues(), using the global ordering
597: ! - Set matrix entries using the global ordering by calling
598: ! MatSetValues()
599: ! Option (A) seems cleaner/easier in many cases, and is the procedure
600: ! used in this example.
601: !
602: subroutine FormJacobianLocal(x,jac_prec,user,ierr)
603: #include <petsc/finclude/petscmat.h>
604: use petscmat
605: use ex5f90tmodule
606: ! Input/output variables:
607: type (userctx) user
608: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
609: type(tMat) jac_prec
610: PetscErrorCode ierr
612: ! Local variables:
613: PetscInt row,col(5),i,j
614: PetscInt ione,ifive
615: PetscScalar two,one,hx,hy,hxdhy
616: PetscScalar hydhx,sc,v(5)
618: ! Set parameters
619: ione = 1
620: ifive = 5
621: one = 1.0
622: two = 2.0
623: hx = one/PetscIntToReal(user%mx-1)
624: hy = one/PetscIntToReal(user%my-1)
625: sc = hx*hy
626: hxdhy = hx/hy
627: hydhx = hy/hx
629: ! Compute entries for the locally owned part of the Jacobian.
630: ! - Currently, all PETSc parallel matrix formats are partitioned by
631: ! contiguous chunks of rows across the processors.
632: ! - Each processor needs to insert only elements that it owns
633: ! locally (but any non-local elements will be sent to the
634: ! appropriate processor during matrix assembly).
635: ! - Here, we set all entries for a particular row at once.
636: ! - We can set matrix entries either using either
637: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
638: ! - Note that MatSetValues() uses 0-based row and column numbers
639: ! in Fortran as well as in C.
641: do 20 j=user%ys,user%ye
642: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
643: do 10 i=user%xs,user%xe
644: row = row + 1
645: ! boundary points
646: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
647: col(1) = row
648: v(1) = one
649: PetscCallA(MatSetValuesLocal(jac_prec,ione,[row],ione,col,v,INSERT_VALUES,ierr))
650: ! interior grid points
651: else
652: v(1) = -hxdhy
653: v(2) = -hydhx
654: v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i,j))
655: v(4) = -hydhx
656: v(5) = -hxdhy
657: col(1) = row - user%gxm
658: col(2) = row - 1
659: col(3) = row
660: col(4) = row + 1
661: col(5) = row + user%gxm
662: PetscCallA(MatSetValuesLocal(jac_prec,ione,[row],ifive,col,v,INSERT_VALUES,ierr))
663: endif
664: 10 continue
665: 20 continue
666: end
668: !/*TEST
669: !
670: ! test:
671: ! nsize: 4
672: ! args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
673: !
674: !TEST*/