Actual source code: ex5f90.F
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: !/*T
10: ! Concepts: SNES^parallel Bratu example
11: ! Concepts: DMDA^using distributed arrays;
12: ! Processors: n
13: !T*/
14: !
15: ! --------------------------------------------------------------------------
16: !
17: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
18: ! the partial differential equation
19: !
20: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
21: !
22: ! with boundary conditions
23: !
24: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
25: !
26: ! A finite difference approximation with the usual 5-point stencil
27: ! is used to discretize the boundary value problem to obtain a nonlinear
28: ! system of equations.
29: !
30: ! The uniprocessor version of this code is snes/examples/tutorials/ex4f.F
31: !
32: ! --------------------------------------------------------------------------
33: ! The following define must be used before including any PETSc include files
34: ! into a module or interface. This is because they can't handle declarations
35: ! in them
36: !
38: module f90module
39: type userctx
40: #include <finclude/petscsysdef.h>
41: #include <finclude/petscvecdef.h>
42: #include <finclude/petscdmdef.h>
43: DM da
44: PetscInt xs,xe,xm,gxs,gxe,gxm
45: PetscInt ys,ye,ym,gys,gye,gym
46: PetscInt mx,my
47: PetscMPIInt rank
48: double precision lambda
49: end type userctx
51: contains
52: ! ---------------------------------------------------------------------
53: !
54: ! FormFunction - Evaluates nonlinear function, F(x).
55: !
56: ! Input Parameters:
57: ! snes - the SNES context
58: ! X - input vector
59: ! dummy - optional user-defined context, as set by SNESSetFunction()
60: ! (not used here)
61: !
62: ! Output Parameter:
63: ! F - function vector
64: !
65: ! Notes:
66: ! This routine serves as a wrapper for the lower-level routine
67: ! "FormFunctionLocal", where the actual computations are
68: ! done using the standard Fortran style of treating the local
69: ! vector data as a multidimensional array over the local mesh.
70: ! This routine merely handles ghost point scatters and accesses
71: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
72: !
73: subroutine FormFunction(snes,X,F,user,ierr)
74: implicit none
76: #include <finclude/petscsys.h>
77: #include <finclude/petscvec.h>
78: #include <finclude/petscdmda.h>
79: #include <finclude/petscis.h>
80: #include <finclude/petscmat.h>
81: #include <finclude/petscksp.h>
82: #include <finclude/petscpc.h>
83: #include <finclude/petscsnes.h>
84: #include <finclude/petscvec.h90>
86: ! Input/output variables:
87: SNES snes
88: Vec X,F
89: PetscErrorCode ierr
90: type (userctx) user
92: ! Declarations for use with local arrays:
93: PetscScalar,pointer :: lx_v(:),lf_v(:)
94: Vec localX
96: ! Scatter ghost points to local vector, using the 2-step process
97: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
98: ! By placing code between these two statements, computations can
99: ! be done while messages are in transition.
100: call DMGetLocalVector(user%da,localX,ierr)
101: call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES, &
102: & localX,ierr)
103: call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
105: ! Get a pointer to vector data.
106: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
107: ! the data array. Otherwise, the routine is implementation dependent.
108: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
109: ! the array.
110: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
111: ! and is useable from Fortran-90 Only.
113: call VecGetArrayF90(localX,lx_v,ierr)
114: call VecGetArrayF90(F,lf_v,ierr)
116: ! Compute function over the locally owned part of the grid
117: call FormFunctionLocal(lx_v,lf_v,user,ierr)
119: ! Restore vectors
120: call VecRestoreArrayF90(localX,lx_v,ierr)
121: call VecRestoreArrayF90(F,lf_v,ierr)
123: ! Insert values into global vector
125: call DMRestoreLocalVector(user%da,localX,ierr)
126: call PetscLogFlops(11.0d0*user%ym*user%xm,ierr)
128: ! call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
129: ! call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
130: return
131: end subroutine formfunction
132: end module f90module
134: module f90moduleinterfaces
135: use f90module
136:
137: Interface SNESSetApplicationContext
138: Subroutine SNESSetApplicationContext(snes,ctx,ierr)
139: use f90module
140: SNES snes
141: type(userctx) ctx
142: PetscErrorCode ierr
143: End Subroutine
144: End Interface SNESSetApplicationContext
146: Interface SNESGetApplicationContext
147: Subroutine SNESGetApplicationContext(snes,ctx,ierr)
148: use f90module
149: SNES snes
150: type(userctx), pointer :: ctx
151: PetscErrorCode ierr
152: End Subroutine
153: End Interface SNESGetApplicationContext
154: end module f90moduleinterfaces
156: program main
157: use f90module
158: use f90moduleinterfaces
159: implicit none
160: !
161: #include <finclude/petscsys.h>
162: #include <finclude/petscvec.h>
163: #include <finclude/petscdmda.h>
164: #include <finclude/petscis.h>
165: #include <finclude/petscmat.h>
166: #include <finclude/petscksp.h>
167: #include <finclude/petscpc.h>
168: #include <finclude/petscsnes.h>
169: #include <finclude/petscvec.h90>
170: #include <finclude/petscdmda.h90>
172: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
173: ! Variable declarations
174: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: !
176: ! Variables:
177: ! snes - nonlinear solver
178: ! x, r - solution, residual vectors
179: ! J - Jacobian matrix
180: ! its - iterations for convergence
181: ! Nx, Ny - number of preocessors in x- and y- directions
182: ! matrix_free - flag - 1 indicates matrix-free version
183: !
184: SNES snes
185: Vec x,r
186: Mat J
187: PetscErrorCode ierr
188: PetscInt its
189: PetscBool flg,matrix_free
190: PetscInt ione,nfour
191: double precision lambda_max,lambda_min
192: type (userctx) user
193: type(userctx), pointer:: puser
195: ! Note: Any user-defined Fortran routines (such as FormJacobian)
196: ! MUST be declared as external.
197: external FormInitialGuess,FormJacobian
199: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
200: ! Initialize program
201: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
203: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
205: ! Initialize problem parameters
206: lambda_max = 6.81
207: lambda_min = 0.0
208: user%lambda = 6.0
209: ione = 1
210: nfour = -4
211: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par', &
212: & user%lambda,flg,ierr)
213: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) &
214: & then
215: if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
216: SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
217: endif
219: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
220: ! Create nonlinear solver context
221: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
222: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
224: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
225: ! Create vector data structures; set function evaluation routine
226: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
228: ! Create distributed array (DMDA) to manage parallel grid and vectors
230: ! This really needs only the star-type stencil, but we use the box
231: ! stencil temporarily.
232: call DMDACreate2d(PETSC_COMM_WORLD, &
233: & DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE, &
234: & DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE, &
235: & ione,ione,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr)
236: call DMDAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my, &
237: & PETSC_NULL_INTEGER, &
238: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
239: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
240: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
241: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
242: & PETSC_NULL_INTEGER,ierr)
243:
244: !
245: ! Visualize the distribution of the array across the processors
246: !
247: ! call DMView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)
249: ! Extract global and local vectors from DMDA; then duplicate for remaining
250: ! vectors that are the same types
251: call DMCreateGlobalVector(user%da,x,ierr)
252: call VecDuplicate(x,r,ierr)
254: ! Get local grid boundaries (for 2-dimensional DMDA)
255: call DMDAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER, &
256: & user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
257: call DMDAGetGhostCorners(user%da,user%gxs,user%gys, &
258: & PETSC_NULL_INTEGER,user%gxm,user%gym, &
259: & PETSC_NULL_INTEGER,ierr)
261: ! Here we shift the starting indices up by one so that we can easily
262: ! use the Fortran convention of 1-based indices (rather 0-based indices).
263: user%xs = user%xs+1
264: user%ys = user%ys+1
265: user%gxs = user%gxs+1
266: user%gys = user%gys+1
268: user%ye = user%ys+user%ym-1
269: user%xe = user%xs+user%xm-1
270: user%gye = user%gys+user%gym-1
271: user%gxe = user%gxs+user%gxm-1
273: call SNESSetApplicationContext(snes,user,ierr)
275: ! Set function evaluation routine and vector
276: call SNESSetFunction(snes,r,FormFunction,user,ierr)
278: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
279: ! Create matrix data structure; set Jacobian evaluation routine
280: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
282: ! Set Jacobian matrix data structure and default Jacobian evaluation
283: ! routine. User can override with:
284: ! -snes_fd : default finite differencing approximation of Jacobian
285: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
286: ! (unless user explicitly sets preconditioner)
287: ! -snes_mf_operator : form preconditioning matrix as set by the user,
288: ! but use matrix-free approx for Jacobian-vector
289: ! products within Newton-Krylov method
290: !
291: ! Note: For the parallel case, vectors and matrices MUST be partitioned
292: ! accordingly. When using distributed arrays (DMDAs) to create vectors,
293: ! the DMDAs determine the problem partitioning. We must explicitly
294: ! specify the local matrix dimensions upon its creation for compatibility
295: ! with the vector distribution. Thus, the generic MatCreate() routine
296: ! is NOT sufficient when working with distributed arrays.
297: !
298: ! Note: Here we only approximately preallocate storage space for the
299: ! Jacobian. See the users manual for a discussion of better techniques
300: ! for preallocating matrix memory.
301:
302: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf', &
303: & matrix_free,ierr)
304: if (.not. matrix_free) then
305: call DMGetMatrix(user%da,MATAIJ,J,ierr)
306: call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)
307: endif
309: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
310: ! Customize nonlinear solver; set runtime options
311: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
312: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
313: call SNESSetFromOptions(snes,ierr)
315: ! Test Fortran90 wrapper for SNESSet/Get ApplicationContext()
316: call PetscOptionsGetBool(PETSC_NULL_CHARACTER,'-test_appctx', &
317: & flg,PETSC_NULL_CHARACTER,ierr)
318: if (flg) then
319: call SNESGetApplicationContext(snes,puser,ierr)
320: if (user%da .ne. puser%da) then
321: write(*,*) "Error: uesr != puesr"
322: write(*,*) "user: ", user
323: write(*,*) "puesr: ", puser
324: endif
325: endif
327: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
328: ! Evaluate initial guess; then solve nonlinear system.
329: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
330: ! Note: The user should initialize the vector, x, with the initial guess
331: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
332: ! to employ an initial guess of zero, the user should explicitly set
333: ! this vector to zero by calling VecSet().
335: call FormInitialGuess(snes,x,ierr)
336: call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
337: call SNESGetIterationNumber(snes,its,ierr);
338: if (user%rank .eq. 0) then
339: write(6,100) its
340: endif
341: 100 format('Number of Newton iterations = ',i5)
343: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
344: ! Free work space. All PETSc objects should be destroyed when they
345: ! are no longer needed.
346: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
347: if (.not. matrix_free) call MatDestroy(J,ierr)
348: call VecDestroy(x,ierr)
349: call VecDestroy(r,ierr)
350: call SNESDestroy(snes,ierr)
351: call DMDestroy(user%da,ierr)
353: call PetscFinalize(ierr)
354: end
356: ! ---------------------------------------------------------------------
357: !
358: ! FormInitialGuess - Forms initial approximation.
359: !
360: ! Input Parameters:
361: ! X - vector
362: !
363: ! Output Parameter:
364: ! X - vector
365: !
366: ! Notes:
367: ! This routine serves as a wrapper for the lower-level routine
368: ! "InitialGuessLocal", where the actual computations are
369: ! done using the standard Fortran style of treating the local
370: ! vector data as a multidimensional array over the local mesh.
371: ! This routine merely handles ghost point scatters and accesses
372: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
373: !
374: subroutine FormInitialGuess(snes,X,ierr)
375: use f90module
376: use f90moduleinterfaces
377: implicit none
379: #include <finclude/petscvec.h90>
380: #include <finclude/petscsys.h>
381: #include <finclude/petscvec.h>
382: #include <finclude/petscdmda.h>
383: #include <finclude/petscis.h>
384: #include <finclude/petscmat.h>
385: #include <finclude/petscksp.h>
386: #include <finclude/petscpc.h>
387: #include <finclude/petscsnes.h>
389: ! Input/output variables:
390: SNES snes
391: type(userctx), pointer:: puser
392: Vec X
393: PetscErrorCode ierr
394:
395: ! Declarations for use with local arrays:
396: PetscScalar,pointer :: lx_v(:)
397: Vec localX
399: 0
400: call SNESGetApplicationContext(snes,puser,ierr)
401: ! Get a pointer to vector data.
402: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
403: ! the data array. Otherwise, the routine is implementation dependent.
404: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
405: ! the array.
406: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
407: ! and is useable from Fortran-90 Only.
409: call DMGetLocalVector(puser%da,localX,ierr)
410: call VecGetArrayF90(localX,lx_v,ierr)
412: ! Compute initial guess over the locally owned part of the grid
413: call InitialGuessLocal(puser,lx_v,ierr)
415: ! Restore vector
416: call VecRestoreArrayF90(localX,lx_v,ierr)
418: ! Insert values into global vector
419: call DMLocalToGlobalBegin(puser%da,localX,INSERT_VALUES,X,ierr)
420: call DMLocalToGlobalEnd(puser%da,localX,INSERT_VALUES,X,ierr)
421: call DMRestoreLocalVector(puser%da,localX,ierr)
423: return
424: end
426: ! ---------------------------------------------------------------------
427: !
428: ! InitialGuessLocal - Computes initial approximation, called by
429: ! the higher level routine FormInitialGuess().
430: !
431: ! Input Parameter:
432: ! x - local vector data
433: !
434: ! Output Parameters:
435: ! x - local vector data
436: ! ierr - error code
437: !
438: ! Notes:
439: ! This routine uses standard Fortran-style computations over a 2-dim array.
440: !
441: subroutine InitialGuessLocal(user,x,ierr)
442: use f90module
443: implicit none
445: #include <finclude/petscsys.h>
446: #include <finclude/petscvec.h>
447: #include <finclude/petscdmda.h>
448: #include <finclude/petscis.h>
449: #include <finclude/petscmat.h>
450: #include <finclude/petscksp.h>
451: #include <finclude/petscpc.h>
452: #include <finclude/petscsnes.h>
454: ! Input/output variables:
455: type (userctx) user
456: PetscScalar x(user%gxs:user%gxe, &
457: & user%gys:user%gye)
458: PetscErrorCode ierr
460: ! Local variables:
461: PetscInt i,j
462: PetscScalar temp1,temp,hx,hy
463: PetscScalar one
465: ! Set parameters
467: 0
468: one = 1.0
469: hx = one/(dble(user%mx-1))
470: hy = one/(dble(user%my-1))
471: temp1 = user%lambda/(user%lambda + one)
473: do 20 j=user%ys,user%ye
474: temp = dble(min(j-1,user%my-j))*hy
475: do 10 i=user%xs,user%xe
476: if (i .eq. 1 .or. j .eq. 1 &
477: & .or. i .eq. user%mx .or. j .eq. user%my) then
478: x(i,j) = 0.0
479: else
480: x(i,j) = temp1 * &
481: & sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
482: endif
483: 10 continue
484: 20 continue
486: return
487: end
489: ! ---------------------------------------------------------------------
490: !
491: ! FormFunctionLocal - Computes nonlinear function, called by
492: ! the higher level routine FormFunction().
493: !
494: ! Input Parameter:
495: ! x - local vector data
496: !
497: ! Output Parameters:
498: ! f - local vector data, f(x)
499: ! ierr - error code
500: !
501: ! Notes:
502: ! This routine uses standard Fortran-style computations over a 2-dim array.
503: !
504: subroutine FormFunctionLocal(x,f,user,ierr)
505: use f90module
507: implicit none
509: ! Input/output variables:
510: type (userctx) user
511: PetscScalar x(user%gxs:user%gxe, &
512: & user%gys:user%gye)
513: PetscScalar f(user%xs:user%xe, &
514: & user%ys:user%ye)
515: PetscErrorCode ierr
517: ! Local variables:
518: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
519: PetscScalar u,uxx,uyy
520: PetscInt i,j
522: one = 1.0
523: two = 2.0
524: hx = one/dble(user%mx-1)
525: hy = one/dble(user%my-1)
526: sc = hx*hy*user%lambda
527: hxdhy = hx/hy
528: hydhx = hy/hx
530: ! Compute function over the locally owned part of the grid
532: do 20 j=user%ys,user%ye
533: do 10 i=user%xs,user%xe
534: if (i .eq. 1 .or. j .eq. 1 &
535: & .or. i .eq. user%mx .or. j .eq. user%my) then
536: f(i,j) = x(i,j)
537: else
538: u = x(i,j)
539: uxx = hydhx * (two*u &
540: & - x(i-1,j) - x(i+1,j))
541: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
542: f(i,j) = uxx + uyy - sc*exp(u)
543: endif
544: 10 continue
545: 20 continue
547: return
548: end
550: ! ---------------------------------------------------------------------
551: !
552: ! FormJacobian - Evaluates Jacobian matrix.
553: !
554: ! Input Parameters:
555: ! snes - the SNES context
556: ! x - input vector
557: ! dummy - optional user-defined context, as set by SNESSetJacobian()
558: ! (not used here)
559: !
560: ! Output Parameters:
561: ! jac - Jacobian matrix
562: ! jac_prec - optionally different preconditioning matrix (not used here)
563: ! flag - flag indicating matrix structure
564: !
565: ! Notes:
566: ! This routine serves as a wrapper for the lower-level routine
567: ! "FormJacobianLocal", where the actual computations are
568: ! done using the standard Fortran style of treating the local
569: ! vector data as a multidimensional array over the local mesh.
570: ! This routine merely accesses the local vector data via
571: ! VecGetArrayF90() and VecRestoreArrayF90().
572: !
573: ! Notes:
574: ! Due to grid point reordering with DMDAs, we must always work
575: ! with the local grid points, and then transform them to the new
576: ! global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
577: ! We cannot work directly with the global numbers for the original
578: ! uniprocessor grid!
579: !
580: ! Two methods are available for imposing this transformation
581: ! when setting matrix entries:
582: ! (A) MatSetValuesLocal(), using the local ordering (including
583: ! ghost points!)
584: ! - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
585: ! - Associate this map with the matrix by calling
586: ! MatSetLocalToGlobalMapping() once
587: ! - Set matrix entries using the local ordering
588: ! by calling MatSetValuesLocal()
589: ! (B) MatSetValues(), using the global ordering
590: ! - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
591: ! - Then apply this map explicitly yourself
592: ! - Set matrix entries using the global ordering by calling
593: ! MatSetValues()
594: ! Option (A) seems cleaner/easier in many cases, and is the procedure
595: ! used in this example.
596: !
597: subroutine FormJacobian(snes,X,jac,jac_prec,flag,user,ierr)
598: use f90module
599: implicit none
601: #include <finclude/petscsys.h>
602: #include <finclude/petscvec.h>
603: #include <finclude/petscdmda.h>
604: #include <finclude/petscis.h>
605: #include <finclude/petscmat.h>
606: #include <finclude/petscksp.h>
607: #include <finclude/petscpc.h>
608: #include <finclude/petscsnes.h>
610: #include <finclude/petscvec.h90>
612: ! Input/output variables:
613: SNES snes
614: Vec X
615: Mat jac,jac_prec
616: MatStructure flag
617: type(userctx) user
618: PetscErrorCode ierr
620: ! Declarations for use with local arrays:
621: PetscScalar,pointer :: lx_v(:)
622: Vec localX
624: ! Scatter ghost points to local vector, using the 2-step process
625: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
626: ! Computations can be done while messages are in transition,
627: ! by placing code between these two statements.
629: call DMGetLocalVector(user%da,localX,ierr)
630: call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX, &
631: & ierr)
632: call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
634: ! Get a pointer to vector data
635: call VecGetArrayF90(localX,lx_v,ierr)
637: ! Compute entries for the locally owned part of the Jacobian preconditioner.
638: call FormJacobianLocal(lx_v,jac_prec,user,ierr)
640: ! Assemble matrix, using the 2-step process:
641: ! MatAssemblyBegin(), MatAssemblyEnd()
642: ! Computations can be done while messages are in transition,
643: ! by placing code between these two statements.
645: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
646: if (jac .ne. jac_prec) then
647: call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
648: endif
649: call VecRestoreArrayF90(localX,lx_v,ierr)
650: call DMRestoreLocalVector(user%da,localX,ierr)
651: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
652: if (jac .ne. jac_prec) then
653: call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
654: endif
655:
656: ! Set flag to indicate that the Jacobian matrix retains an identical
657: ! nonzero structure throughout all nonlinear iterations (although the
658: ! values of the entries change). Thus, we can save some work in setting
659: ! up the preconditioner (e.g., no need to redo symbolic factorization for
660: ! ILU/ICC preconditioners).
661: ! - If the nonzero structure of the matrix is different during
662: ! successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
663: ! must be used instead. If you are unsure whether the matrix
664: ! structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
665: ! - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
666: ! believes your assertion and does not check the structure
667: ! of the matrix. If you erroneously claim that the structure
668: ! is the same when it actually is not, the new preconditioner
669: ! will not function correctly. Thus, use this optimization
670: ! feature with caution!
672: flag = SAME_NONZERO_PATTERN
674: ! Tell the matrix we will never add a new nonzero location to the
675: ! matrix. If we do it will generate an error.
677: call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE, &
678: & ierr)
680: return
681: end
683: ! ---------------------------------------------------------------------
684: !
685: ! FormJacobianLocal - Computes Jacobian preconditioner matrix,
686: ! called by the higher level routine FormJacobian().
687: !
688: ! Input Parameters:
689: ! x - local vector data
690: !
691: ! Output Parameters:
692: ! jac_prec - Jacobian preconditioner matrix
693: ! ierr - error code
694: !
695: ! Notes:
696: ! This routine uses standard Fortran-style computations over a 2-dim array.
697: !
698: ! Notes:
699: ! Due to grid point reordering with DMDAs, we must always work
700: ! with the local grid points, and then transform them to the new
701: ! global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
702: ! We cannot work directly with the global numbers for the original
703: ! uniprocessor grid!
704: !
705: ! Two methods are available for imposing this transformation
706: ! when setting matrix entries:
707: ! (A) MatSetValuesLocal(), using the local ordering (including
708: ! ghost points!)
709: ! - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
710: ! - Associate this map with the matrix by calling
711: ! MatSetLocalToGlobalMapping() once
712: ! - Set matrix entries using the local ordering
713: ! by calling MatSetValuesLocal()
714: ! (B) MatSetValues(), using the global ordering
715: ! - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
716: ! - Then apply this map explicitly yourself
717: ! - Set matrix entries using the global ordering by calling
718: ! MatSetValues()
719: ! Option (A) seems cleaner/easier in many cases, and is the procedure
720: ! used in this example.
721: !
722: subroutine FormJacobianLocal(x,jac_prec,user,ierr)
723: use f90module
724: implicit none
726: #include <finclude/petscsys.h>
727: #include <finclude/petscvec.h>
728: #include <finclude/petscdmda.h>
729: #include <finclude/petscis.h>
730: #include <finclude/petscmat.h>
731: #include <finclude/petscksp.h>
732: #include <finclude/petscpc.h>
733: #include <finclude/petscsnes.h>
735: ! Input/output variables:
736: type (userctx) user
737: PetscScalar x(user%gxs:user%gxe, &
738: & user%gys:user%gye)
739: Mat jac_prec
740: PetscErrorCode ierr
742: ! Local variables:
743: PetscInt row,col(5),i,j
744: PetscInt ione,ifive
745: PetscScalar two,one,hx,hy,hxdhy
746: PetscScalar hydhx,sc,v(5)
748: ! Set parameters
749: ione = 1
750: ifive = 5
751: one = 1.0
752: two = 2.0
753: hx = one/dble(user%mx-1)
754: hy = one/dble(user%my-1)
755: sc = hx*hy
756: hxdhy = hx/hy
757: hydhx = hy/hx
759: ! Compute entries for the locally owned part of the Jacobian.
760: ! - Currently, all PETSc parallel matrix formats are partitioned by
761: ! contiguous chunks of rows across the processors.
762: ! - Each processor needs to insert only elements that it owns
763: ! locally (but any non-local elements will be sent to the
764: ! appropriate processor during matrix assembly).
765: ! - Here, we set all entries for a particular row at once.
766: ! - We can set matrix entries either using either
767: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
768: ! - Note that MatSetValues() uses 0-based row and column numbers
769: ! in Fortran as well as in C.
771: do 20 j=user%ys,user%ye
772: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
773: do 10 i=user%xs,user%xe
774: row = row + 1
775: ! boundary points
776: if (i .eq. 1 .or. j .eq. 1 &
777: & .or. i .eq. user%mx .or. j .eq. user%my) then
778: col(1) = row
779: v(1) = one
780: call MatSetValuesLocal(jac_prec,ione,row,ione,col,v, &
781: & INSERT_VALUES,ierr)
782: ! interior grid points
783: else
784: v(1) = -hxdhy
785: v(2) = -hydhx
786: v(3) = two*(hydhx + hxdhy) &
787: & - sc*user%lambda*exp(x(i,j))
788: v(4) = -hydhx
789: v(5) = -hxdhy
790: col(1) = row - user%gxm
791: col(2) = row - 1
792: col(3) = row
793: col(4) = row + 1
794: col(5) = row + user%gxm
795: call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v, &
796: & INSERT_VALUES,ierr)
797: endif
798: 10 continue
799: 20 continue
801: return
802: end