Actual source code: ex39f90.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 (DAs) 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: ! Modified from ex5f90.F by Mike McCourt <mccomic@iit.edu>
10: ! for testing Fortran interface on
11: ! SNESLineSearchSet(), SNESLineSearchSetPreCheck(), SNESLineSearchSetPostCheck()
12: !
13: ! --------------------------------------------------------------------------
14: !
15: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
16: ! the partial differential equation
17: !
18: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
19: !
20: ! with boundary conditions
21: !
22: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
23: !
24: ! A finite difference approximation with the usual 5-point stencil
25: ! is used to discretize the boundary value problem to obtain a nonlinear
26: ! system of equations.
27: !
28: ! The uniprocessor version of this code is snes/examples/tutorials/ex4f.F
29: !
30: ! --------------------------------------------------------------------------
31: ! The following define must be used before including any PETSc include files
32: ! into a module or interface. This is because they can't handle declarations
33: ! in them
34: !
36: module f90module
37: type userctx
38: #include finclude/petscsysdef.h
39: #include finclude/petscvecdef.h
40: #include finclude/petscdadef.h
41: DA da
42: integer xs,xe,xm,gxs,gxe,gxm
43: integer ys,ye,ym,gys,gye,gym
44: integer mx,my,rank
45: double precision lambda
46: end type userctx
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 VecGetArrayF90() and VecRestoreArrayF90().
68: !
69: subroutine FormFunction(snes,X,F,user,ierr)
70: implicit none
72: #include finclude/petscsys.h
73: #include finclude/petscvec.h
74: #include finclude/petscda.h
75: #include finclude/petscis.h
76: #include finclude/petscmat.h
77: #include finclude/petscksp.h
78: #include finclude/petscpc.h
79: #include finclude/petscsnes.h
81: #include "finclude/petscvec.h90"
84: ! Input/output variables:
85: SNES snes
86: Vec X,F
87: integer ierr
88: type (userctx) user
90: ! Declarations for use with local arrays:
91: PetscScalar,pointer :: lx_v(:),lf_v(:)
92: Vec localX
94: write(*,*)"Inside FormFunction, user%xm=",user%xm
96: ! Scatter ghost points to local vector, using the 2-step process
97: ! DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
98: ! By placing code between these two statements, computations can
99: ! be done while messages are in transition.
101: call DAGetLocalVector(user%da,localX,ierr)
102: call DAGlobalToLocalBegin(user%da,X,INSERT_VALUES, &
103: & localX,ierr)
104: call DAGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
106: ! Get a pointer to vector data.
107: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
108: ! the data array. Otherwise, the routine is implementation dependent.
109: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
110: ! the array.
111: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
112: ! and is useable from Fortran-90 Only.
114: call VecGetArrayF90(localX,lx_v,ierr)
115: call VecGetArrayF90(F,lf_v,ierr)
117: ! Compute function over the locally owned part of the grid
119: call FormFunctionLocal(lx_v,lf_v,user,ierr)
121: ! Restore vectors
123: call VecRestoreArrayF90(localX,lx_v,ierr)
124: call VecRestoreArrayF90(F,lf_v,ierr)
126: ! Insert values into global vector
128: call DARestoreLocalVector(user%da,localX,ierr)
129: call PetscLogFlops(11.0d0*user%ym*user%xm,ierr)
131: ! call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
132: ! call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
134: return
135: end subroutine formfunction
136: end module f90module
140: program main
141: use f90module
142: implicit none
143: !
144: !
145: #include finclude/petscsys.h
146: #include finclude/petscvec.h
147: #include finclude/petscda.h
148: #include finclude/petscis.h
149: #include finclude/petscmat.h
150: #include finclude/petscksp.h
151: #include finclude/petscpc.h
152: #include finclude/petscsnes.h
153: #include "finclude/petscvec.h90"
154: #include "finclude/petscda.h90"
156: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: ! Variable declarations
158: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
159: !
160: ! Variables:
161: ! snes - nonlinear solver
162: ! x, r - solution, residual vectors
163: ! J - Jacobian matrix
164: ! its - iterations for convergence
165: ! Nx, Ny - number of preocessors in x- and y- directions
166: ! matrix_free - flag - 1 indicates matrix-free version
167: !
168: !
169: SNES snes
170: Vec x,r
171: Mat J
172: integer its,matrix_free,flg,ierr
173: double precision lambda_max,lambda_min
174: type (userctx) user
175: PetscTruth test_linesearch,test_check
177: ! Note: Any user-defined Fortran routines (such as FormJacobian)
178: ! MUST be declared as external.
180: external FormInitialGuess,FormJacobian,FormLineSearch
181: external FormPostCheck,FormPreCheck
183: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184: ! Initialize program
185: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
188: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
190: ! Initialize problem parameters
192: lambda_max = 6.81
193: lambda_min = 0.0
194: user%lambda = 6.0
195: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par', &
196: & user%lambda,flg,ierr)
197: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) &
198: & then
199: if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
200: SETERRQ(1,' ',ierr)
201: endif
204: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205: ! Create nonlinear solver context
206: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
210: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211: ! Create vector data structures; set function evaluation routine
212: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214: ! Create distributed array (DA) to manage parallel grid and vectors
216: ! This really needs only the star-type stencil, but we use the box
217: ! stencil temporarily.
218: call DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX, &
219: & -4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1, &
220: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr)
221: call DAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my, &
222: & PETSC_NULL_INTEGER, &
223: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
224: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
225: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
226: & PETSC_NULL_INTEGER,ierr)
227:
228: !
229: ! Visualize the distribution of the array across the processors
230: !
231: ! call DAView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)
233: ! Extract global and local vectors from DA; then duplicate for remaining
234: ! vectors that are the same types
236: call DACreateGlobalVector(user%da,x,ierr)
237: call VecDuplicate(x,r,ierr)
239: ! Get local grid boundaries (for 2-dimensional DA)
241: call DAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER, &
242: & user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
243: call DAGetGhostCorners(user%da,user%gxs,user%gys, &
244: & PETSC_NULL_INTEGER,user%gxm,user%gym, &
245: & PETSC_NULL_INTEGER,ierr)
247: ! Here we shift the starting indices up by one so that we can easily
248: ! use the Fortran convention of 1-based indices (rather 0-based indices).
250: user%xs = user%xs+1
251: user%ys = user%ys+1
252: user%gxs = user%gxs+1
253: user%gys = user%gys+1
255: user%ye = user%ys+user%ym-1
256: user%xe = user%xs+user%xm-1
257: user%gye = user%gys+user%gym-1
258: user%gxe = user%gxs+user%gxm-1
260: ! Set function evaluation routine and vector
262: call SNESSetFunction(snes,r,FormFunction,user,ierr)
264: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
265: ! Create matrix data structure; set Jacobian evaluation routine
266: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
268: ! Set Jacobian matrix data structure and default Jacobian evaluation
269: ! routine. User can override with:
270: ! -snes_fd : default finite differencing approximation of Jacobian
271: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
272: ! (unless user explicitly sets preconditioner)
273: ! -snes_mf_operator : form preconditioning matrix as set by the user,
274: ! but use matrix-free approx for Jacobian-vector
275: ! products within Newton-Krylov method
276: !
277: ! Note: For the parallel case, vectors and matrices MUST be partitioned
278: ! accordingly. When using distributed arrays (DAs) to create vectors,
279: ! the DAs determine the problem partitioning. We must explicitly
280: ! specify the local matrix dimensions upon its creation for compatibility
281: ! with the vector distribution. Thus, the generic MatCreate() routine
282: ! is NOT sufficient when working with distributed arrays.
283: !
284: ! Note: Here we only approximately preallocate storage space for the
285: ! Jacobian. See the users manual for a discussion of better techniques
286: ! for preallocating matrix memory.
288: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf', &
289: & matrix_free,ierr)
290: if (matrix_free .eq. 0) then
291: call DAGetMatrix(user%da,MATAIJ,J,ierr)
292: call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)
293: endif
295: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
296: ! Customize nonlinear solver; set runtime options
297: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
299: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
301: call SNESSetFromOptions(snes,ierr)
302: test_linesearch = 0
303: test_check = 0
304: call PetscOptionsGetTruth(PETSC_NULL_CHARACTER,'-test_check',
305: & test_check,PETSC_NULL_INTEGER,ierr)
306: if (test_check.eq.1) then
307: call SNESLineSearchSetPreCheck(snes,FormPreCheck,user,ierr)
308: call SNESLineSearchSetPostCheck(snes,FormPostCheck,user,ierr)
309: else
310: call PetscOptionsGetTruth(PETSC_NULL_CHARACTER,
311: & '-test_linesearch',test_linesearch,PETSC_NULL_INTEGER,ierr)
312: if (test_linesearch.eq.1) then
313: call SNESLineSearchSet(snes,FormLineSearch,user,ierr)
314: end if
315: end if
316:
317: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
318: ! Evaluate initial guess; then solve nonlinear system.
319: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
321: ! Note: The user should initialize the vector, x, with the initial guess
322: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
323: ! to employ an initial guess of zero, the user should explicitly set
324: ! this vector to zero by calling VecSet().
326: call FormInitialGuess(user,x,ierr)
327: write(*,*)"Before SNESSolve"
328: write(*,*)"user%xm=",user%xm
329: call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
330: call SNESGetIterationNumber(snes,its,ierr);
331: if (user%rank .eq. 0) then
332: write(6,100) its
333: endif
334: 100 format('Number of Newton iterations = ',i5)
336: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
337: ! Free work space. All PETSc objects should be destroyed when they
338: ! are no longer needed.
339: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
341: if (matrix_free .eq. 0) call MatDestroy(J,ierr)
342: call VecDestroy(x,ierr)
343: call VecDestroy(r,ierr)
344: call SNESDestroy(snes,ierr)
345: call DADestroy(user%da,ierr)
346: call PetscFinalize(ierr)
347: end
349: ! ---------------------------------------------------------------------
350: !
351: ! FormLineSearch - Applies the line search to the step size
352: !
353: subroutine FormLineSearch(snes,user,x,f,g,y,w,fnorm,ynorm,gnorm,
354: & flag,ierr)
356: use f90module
358: #include finclude/petscsys.h
359: #include finclude/petscvec.h
360: #include "finclude/petscvec.h90"
361: #include finclude/petscmat.h
362: #include "finclude/petscmat.h90"
363: #include finclude/petscksp.h
364: #include finclude/petscpc.h
365: #include finclude/petscsnes.h
367: SNES snes
368: type (userctx) user
369: Vec x,f,g,y,w
370: PetscReal fnorm,ynorm,gnorm
371: PetscTruth flag
372: PetscErrorCode ierr
374: PetscScalar mone
376: write(*,*)"Inside FormLineSearch, user%xm=",user%xm
377: mone = -1.0d0
378: flag = 0
379: call VecNorm(y,NORM_2,ynorm,ierr)
380: call VecAYPX(y,mone,x,ierr)
381: call SNESComputeFunction(snes,y,g,ierr)
382: call VecNorm(g,NORM_2,gnorm,ierr)
383: return
384: end
386: ! ---------------------------------------------------------------------
387: !
388: ! FormInitialGuess - Forms initial approximation.
389: !
390: ! Input Parameters:
391: ! X - vector
392: !
393: ! Output Parameter:
394: ! X - vector
395: !
396: ! Notes:
397: ! This routine serves as a wrapper for the lower-level routine
398: ! "InitialGuessLocal", where the actual computations are
399: ! done using the standard Fortran style of treating the local
400: ! vector data as a multidimensional array over the local mesh.
401: ! This routine merely handles ghost point scatters and accesses
402: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
403: !
404: subroutine FormInitialGuess(user,X,ierr)
405: use f90module
406: implicit none
408: #include "finclude/petscvec.h90"
409: #include finclude/petscsys.h
410: #include finclude/petscvec.h
411: #include finclude/petscda.h
412: #include finclude/petscis.h
413: #include finclude/petscmat.h
414: #include finclude/petscksp.h
415: #include finclude/petscpc.h
416: #include finclude/petscsnes.h
418: ! Input/output variables:
419: type (userctx) user
420: Vec X
421: integer ierr
422:
423: ! Declarations for use with local arrays:
424: PetscScalar,pointer :: lx_v(:)
425: Vec localX
427: 0
429: ! Get a pointer to vector data.
430: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
431: ! the data array. Otherwise, the routine is implementation dependent.
432: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
433: ! the array.
434: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
435: ! and is useable from Fortran-90 Only.
437: call DAGetLocalVector(user%da,localX,ierr)
438: call VecGetArrayF90(localX,lx_v,ierr)
440: ! Compute initial guess over the locally owned part of the grid
442: call InitialGuessLocal(user,lx_v,ierr)
444: ! Restore vector
446: call VecRestoreArrayF90(localX,lx_v,ierr)
448: ! Insert values into global vector
450: call DALocalToGlobal(user%da,localX,INSERT_VALUES,X,ierr)
451: call DARestoreLocalVector(user%da,localX,ierr)
453: return
454: end
456: ! ---------------------------------------------------------------------
457: !
458: ! InitialGuessLocal - Computes initial approximation, called by
459: ! the higher level routine FormInitialGuess().
460: !
461: ! Input Parameter:
462: ! x - local vector data
463: !
464: ! Output Parameters:
465: ! x - local vector data
466: ! ierr - error code
467: !
468: ! Notes:
469: ! This routine uses standard Fortran-style computations over a 2-dim array.
470: !
471: subroutine InitialGuessLocal(user,x,ierr)
472: use f90module
473: implicit none
475: #include finclude/petscsys.h
476: #include finclude/petscvec.h
477: #include finclude/petscda.h
478: #include finclude/petscis.h
479: #include finclude/petscmat.h
480: #include finclude/petscksp.h
481: #include finclude/petscpc.h
482: #include finclude/petscsnes.h
484: ! Input/output variables:
485: type (userctx) user
486: PetscScalar x(user%gxs:user%gxe, &
487: & user%gys:user%gye)
488: integer ierr
490: ! Local variables:
491: integer i,j
492: PetscScalar temp1,temp,hx,hy
493: PetscScalar one
495: ! Set parameters
497: 0
498: one = 1.0
499: hx = one/(dble(user%mx-1))
500: hy = one/(dble(user%my-1))
501: temp1 = user%lambda/(user%lambda + one)
503: do 20 j=user%ys,user%ye
504: temp = dble(min(j-1,user%my-j))*hy
505: do 10 i=user%xs,user%xe
506: if (i .eq. 1 .or. j .eq. 1 &
507: & .or. i .eq. user%mx .or. j .eq. user%my) then
508: x(i,j) = 0.0
509: else
510: x(i,j) = temp1 * &
511: & sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
512: endif
513: 10 continue
514: 20 continue
516: return
517: end
519: ! ---------------------------------------------------------------------
520: !
521: ! FormFunctionLocal - Computes nonlinear function, called by
522: ! the higher level routine FormFunction().
523: !
524: ! Input Parameter:
525: ! x - local vector data
526: !
527: ! Output Parameters:
528: ! f - local vector data, f(x)
529: ! ierr - error code
530: !
531: ! Notes:
532: ! This routine uses standard Fortran-style computations over a 2-dim array.
533: !
534: subroutine FormFunctionLocal(x,f,user,ierr)
535: use f90module
537: implicit none
539: ! Input/output variables:
540: type (userctx) user
541: PetscScalar x(user%gxs:user%gxe, &
542: & user%gys:user%gye)
543: PetscScalar f(user%xs:user%xe, &
544: & user%ys:user%ye)
545: integer ierr
547: ! Local variables:
548: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
549: PetscScalar u,uxx,uyy
550: integer i,j
552: one = 1.0
553: two = 2.0
554: hx = one/dble(user%mx-1)
555: hy = one/dble(user%my-1)
556: sc = hx*hy*user%lambda
557: hxdhy = hx/hy
558: hydhx = hy/hx
560: ! Compute function over the locally owned part of the grid
562: do 20 j=user%ys,user%ye
563: do 10 i=user%xs,user%xe
564: if (i .eq. 1 .or. j .eq. 1 &
565: & .or. i .eq. user%mx .or. j .eq. user%my) then
566: f(i,j) = x(i,j)
567: else
568: u = x(i,j)
569: uxx = hydhx * (two*u &
570: & - x(i-1,j) - x(i+1,j))
571: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
572: f(i,j) = uxx + uyy - sc*exp(u)
573: endif
574: 10 continue
575: 20 continue
577: return
578: end
580: ! ---------------------------------------------------------------------
581: !
582: ! FormJacobian - Evaluates Jacobian matrix.
583: !
584: ! Input Parameters:
585: ! snes - the SNES context
586: ! x - input vector
587: ! dummy - optional user-defined context, as set by SNESSetJacobian()
588: ! (not used here)
589: !
590: ! Output Parameters:
591: ! jac - Jacobian matrix
592: ! jac_prec - optionally different preconditioning matrix (not used here)
593: ! flag - flag indicating matrix structure
594: !
595: ! Notes:
596: ! This routine serves as a wrapper for the lower-level routine
597: ! "FormJacobianLocal", where the actual computations are
598: ! done using the standard Fortran style of treating the local
599: ! vector data as a multidimensional array over the local mesh.
600: ! This routine merely accesses the local vector data via
601: ! VecGetArrayF90() and VecRestoreArrayF90().
602: !
603: ! Notes:
604: ! Due to grid point reordering with DAs, we must always work
605: ! with the local grid points, and then transform them to the new
606: ! global numbering with the "ltog" mapping (via DAGetGlobalIndicesF90()).
607: ! We cannot work directly with the global numbers for the original
608: ! uniprocessor grid!
609: !
610: ! Two methods are available for imposing this transformation
611: ! when setting matrix entries:
612: ! (A) MatSetValuesLocal(), using the local ordering (including
613: ! ghost points!)
614: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
615: ! - Associate this map with the matrix by calling
616: ! MatSetLocalToGlobalMapping() once
617: ! - Set matrix entries using the local ordering
618: ! by calling MatSetValuesLocal()
619: ! (B) MatSetValues(), using the global ordering
620: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
621: ! - Then apply this map explicitly yourself
622: ! - Set matrix entries using the global ordering by calling
623: ! MatSetValues()
624: ! Option (A) seems cleaner/easier in many cases, and is the procedure
625: ! used in this example.
626: !
627: subroutine FormJacobian(snes,X,jac,jac_prec,flag,user,ierr)
628: use f90module
629: implicit none
631: #include finclude/petscsys.h
632: #include finclude/petscvec.h
633: #include finclude/petscda.h
634: #include finclude/petscis.h
635: #include finclude/petscmat.h
636: #include finclude/petscksp.h
637: #include finclude/petscpc.h
638: #include finclude/petscsnes.h
640: #include "finclude/petscvec.h90"
642: ! Input/output variables:
643: SNES snes
644: Vec X
645: Mat jac,jac_prec
646: MatStructure flag
647: type(userctx) user
648: integer ierr
650: ! Declarations for use with local arrays:
651: PetscScalar,pointer :: lx_v(:)
652: Vec localX
654: ! Scatter ghost points to local vector, using the 2-step process
655: ! DAGlobalToLocalBegin(), DAGlobalToLocalEnd()
656: ! Computations can be done while messages are in transition,
657: ! by placing code between these two statements.
659: call DAGetLocalVector(user%da,localX,ierr)
660: call DAGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX, &
661: & ierr)
662: call DAGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
664: ! Get a pointer to vector data
666: call VecGetArrayF90(localX,lx_v,ierr)
668: ! Compute entries for the locally owned part of the Jacobian.
670: call FormJacobianLocal(lx_v,jac,jac_prec,user,ierr)
672: ! Assemble matrix, using the 2-step process:
673: ! MatAssemblyBegin(), MatAssemblyEnd()
674: ! Computations can be done while messages are in transition,
675: ! by placing code between these two statements.
677: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
678: call VecRestoreArrayF90(localX,lx_v,ierr)
679: call DARestoreLocalVector(user%da,localX,ierr)
680: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
682: ! Set flag to indicate that the Jacobian matrix retains an identical
683: ! nonzero structure throughout all nonlinear iterations (although the
684: ! values of the entries change). Thus, we can save some work in setting
685: ! up the preconditioner (e.g., no need to redo symbolic factorization for
686: ! ILU/ICC preconditioners).
687: ! - If the nonzero structure of the matrix is different during
688: ! successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
689: ! must be used instead. If you are unsure whether the matrix
690: ! structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
691: ! - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
692: ! believes your assertion and does not check the structure
693: ! of the matrix. If you erroneously claim that the structure
694: ! is the same when it actually is not, the new preconditioner
695: ! will not function correctly. Thus, use this optimization
696: ! feature with caution!
698: flag = SAME_NONZERO_PATTERN
700: ! Tell the matrix we will never add a new nonzero location to the
701: ! matrix. If we do it will generate an error.
703: ! call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,ierr)
705: return
706: end
708: ! ---------------------------------------------------------------------
709: !
710: ! FormJacobianLocal - Computes Jacobian matrix, called by
711: ! the higher level routine FormJacobian().
712: !
713: ! Input Parameters:
714: ! x - local vector data
715: !
716: ! Output Parameters:
717: ! jac - Jacobian matrix
718: ! jac_prec - optionally different preconditioning matrix (not used here)
719: ! ierr - error code
720: !
721: ! Notes:
722: ! This routine uses standard Fortran-style computations over a 2-dim array.
723: !
724: ! Notes:
725: ! Due to grid point reordering with DAs, we must always work
726: ! with the local grid points, and then transform them to the new
727: ! global numbering with the "ltog" mapping (via DAGetGlobalIndicesF90()).
728: ! We cannot work directly with the global numbers for the original
729: ! uniprocessor grid!
730: !
731: ! Two methods are available for imposing this transformation
732: ! when setting matrix entries:
733: ! (A) MatSetValuesLocal(), using the local ordering (including
734: ! ghost points!)
735: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
736: ! - Associate this map with the matrix by calling
737: ! MatSetLocalToGlobalMapping() once
738: ! - Set matrix entries using the local ordering
739: ! by calling MatSetValuesLocal()
740: ! (B) MatSetValues(), using the global ordering
741: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
742: ! - Then apply this map explicitly yourself
743: ! - Set matrix entries using the global ordering by calling
744: ! MatSetValues()
745: ! Option (A) seems cleaner/easier in many cases, and is the procedure
746: ! used in this example.
747: !
748: subroutine FormJacobianLocal(x,jac,jac_prec,user,ierr)
749: use f90module
750: implicit none
752: #include finclude/petscsys.h
753: #include finclude/petscvec.h
754: #include finclude/petscda.h
755: #include finclude/petscis.h
756: #include finclude/petscmat.h
757: #include finclude/petscksp.h
758: #include finclude/petscpc.h
759: #include finclude/petscsnes.h
761: ! Input/output variables:
762: type (userctx) user
763: PetscScalar x(user%gxs:user%gxe, &
764: & user%gys:user%gye)
765: Mat jac,jac_prec
766: integer ierr
768: ! Local variables:
769: integer row,col(5),i,j
770: PetscScalar two,one,hx,hy,hxdhy
771: PetscScalar hydhx,sc,v(5)
773: ! Set parameters
775: one = 1.0
776: two = 2.0
777: hx = one/dble(user%mx-1)
778: hy = one/dble(user%my-1)
779: sc = hx*hy
780: hxdhy = hx/hy
781: hydhx = hy/hx
783: ! Compute entries for the locally owned part of the Jacobian.
784: ! - Currently, all PETSc parallel matrix formats are partitioned by
785: ! contiguous chunks of rows across the processors.
786: ! - Each processor needs to insert only elements that it owns
787: ! locally (but any non-local elements will be sent to the
788: ! appropriate processor during matrix assembly).
789: ! - Here, we set all entries for a particular row at once.
790: ! - We can set matrix entries either using either
791: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
792: ! - Note that MatSetValues() uses 0-based row and column numbers
793: ! in Fortran as well as in C.
795: do 20 j=user%ys,user%ye
796: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
797: do 10 i=user%xs,user%xe
798: row = row + 1
799: ! boundary points
800: if (i .eq. 1 .or. j .eq. 1 &
801: & .or. i .eq. user%mx .or. j .eq. user%my) then
802: col(1) = row
803: v(1) = one
804: call MatSetValuesLocal(jac,1,row,1,col,v, &
805: & INSERT_VALUES,ierr)
806: ! interior grid points
807: else
808: v(1) = -hxdhy
809: v(2) = -hydhx
810: v(3) = two*(hydhx + hxdhy) &
811: & - sc*user%lambda*exp(x(i,j))
812: v(4) = -hydhx
813: v(5) = -hxdhy
814: col(1) = row - user%gxm
815: col(2) = row - 1
816: col(3) = row
817: col(4) = row + 1
818: col(5) = row + user%gxm
819: call MatSetValuesLocal(jac,1,row,5,col,v, &
820: & INSERT_VALUES,ierr)
821: endif
822: 10 continue
823: 20 continue
825: return
826: end
828: subroutine FormPreCheck(snes,X,Y,user,changed_Y,ierr)
829: use f90module
831: SNES snes
832: Vec X,Y
833: type (userctx) user
834: PetscTruth changed_Y
835: PetscErrorCode ierr
837: write(*,*)"Inside formPreCheck, user%xm=",user%xm
838: end subroutine formPreCheck
840: subroutine FormPostCheck(snes,X,Y,W,user,changed_Y,changed_W,ierr)
841: use f90module
843: SNES snes
844: Vec X,Y,W
845: type (userctx) user
846: PetscTruth changed_Y,changed_W
847: PetscErrorCode ierr
849: write(*,*)"Inside formPostCheck, user%xm=",user%xm
850: end subroutine formPostCheck