Actual source code: ex5f90.F
petsc-3.5.4 2015-05-23
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: PetscInt xs,xe,xm,gxs,gxe,gxm
44: PetscInt ys,ye,ym,gys,gye,gym
45: PetscInt mx,my
46: PetscMPIInt rank
47: PetscReal lambda
48: end type userctx
50: contains
51: ! ---------------------------------------------------------------------
52: !
53: ! FormFunction - Evaluates nonlinear function, F(x).
54: !
55: ! Input Parameters:
56: ! snes - the SNES context
57: ! X - input vector
58: ! dummy - optional user-defined context, as set by SNESSetFunction()
59: ! (not used here)
60: !
61: ! Output Parameter:
62: ! F - function vector
63: !
64: ! Notes:
65: ! This routine serves as a wrapper for the lower-level routine
66: ! "FormFunctionLocal", where the actual computations are
67: ! done using the standard Fortran style of treating the local
68: ! vector data as a multidimensional array over the local mesh.
69: ! This routine merely handles ghost point scatters and accesses
70: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
71: !
72: subroutine FormFunction(snes,X,F,user,ierr)
73: implicit none
75: #include <finclude/petscsys.h>
76: #include <finclude/petscvec.h>
77: #include <finclude/petscdm.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>
85: #include <finclude/petscsnes.h90>
87: ! Input/output variables:
88: SNES snes
89: Vec X,F
90: PetscErrorCode ierr
91: type (userctx) user
92: DM da
94: ! Declarations for use with local arrays:
95: PetscScalar,pointer :: lx_v(:),lf_v(:)
96: Vec localX
98: ! Scatter ghost points to local vector, using the 2-step process
99: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
100: ! By placing code between these two statements, computations can
101: ! be done while messages are in transition.
102: call SNESGetDM(snes,da,ierr)
103: call DMGetLocalVector(da,localX,ierr)
104: call DMGlobalToLocalBegin(da,X,INSERT_VALUES, &
105: & localX,ierr)
106: call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr)
108: ! Get a pointer to vector data.
109: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
110: ! the data array. Otherwise, the routine is implementation dependent.
111: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
112: ! the array.
113: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
114: ! and is useable from Fortran-90 Only.
116: call VecGetArrayF90(localX,lx_v,ierr)
117: call VecGetArrayF90(F,lf_v,ierr)
119: ! Compute function over the locally owned part of the grid
120: call FormFunctionLocal(lx_v,lf_v,user,ierr)
122: ! Restore vectors
123: call VecRestoreArrayF90(localX,lx_v,ierr)
124: call VecRestoreArrayF90(F,lf_v,ierr)
126: ! Insert values into global vector
128: call DMRestoreLocalVector(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)
133: return
134: end subroutine formfunction
135: end module f90module
137: module f90moduleinterfaces
138: use f90module
140: Interface SNESSetApplicationContext
141: Subroutine SNESSetApplicationContext(snes,ctx,ierr)
142: use f90module
143: SNES snes
144: type(userctx) ctx
145: PetscErrorCode ierr
146: End Subroutine
147: End Interface SNESSetApplicationContext
149: Interface SNESGetApplicationContext
150: Subroutine SNESGetApplicationContext(snes,ctx,ierr)
151: use f90module
152: SNES snes
153: type(userctx), pointer :: ctx
154: PetscErrorCode ierr
155: End Subroutine
156: End Interface SNESGetApplicationContext
157: end module f90moduleinterfaces
159: program main
160: use f90module
161: use f90moduleinterfaces
162: implicit none
163: !
164: #include <finclude/petscsys.h>
165: #include <finclude/petscvec.h>
166: #include <finclude/petscdm.h>
167: #include <finclude/petscdmda.h>
168: #include <finclude/petscis.h>
169: #include <finclude/petscmat.h>
170: #include <finclude/petscksp.h>
171: #include <finclude/petscpc.h>
172: #include <finclude/petscsnes.h>
173: #include <finclude/petscvec.h90>
174: #include <finclude/petscdmda.h90>
176: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: ! Variable declarations
178: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179: !
180: ! Variables:
181: ! snes - nonlinear solver
182: ! x, r - solution, residual vectors
183: ! J - Jacobian matrix
184: ! its - iterations for convergence
185: ! Nx, Ny - number of preocessors in x- and y- directions
186: ! matrix_free - flag - 1 indicates matrix-free version
187: !
188: SNES snes
189: Vec x,r
190: Mat J
191: PetscErrorCode ierr
192: PetscInt its
193: PetscBool flg,matrix_free
194: PetscInt ione,nfour
195: PetscReal lambda_max,lambda_min
196: type (userctx) user
197: DM da
199: ! Note: Any user-defined Fortran routines (such as FormJacobian)
200: ! MUST be declared as external.
201: external FormInitialGuess,FormJacobian
203: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204: ! Initialize program
205: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
206: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
207: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
209: ! Initialize problem parameters
210: lambda_max = 6.81
211: lambda_min = 0.0
212: user%lambda = 6.0
213: ione = 1
214: nfour = -4
215: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par', &
216: & user%lambda,flg,ierr)
217: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) &
218: & then
219: if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
220: SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
221: endif
223: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
224: ! Create nonlinear solver context
225: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
226: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
228: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
229: ! Create vector data structures; set function evaluation routine
230: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
232: ! Create distributed array (DMDA) to manage parallel grid and vectors
234: ! This really needs only the star-type stencil, but we use the box
235: ! stencil temporarily.
236: call DMDACreate2d(PETSC_COMM_WORLD, &
237: & DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, &
238: & DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE, &
239: & ione,ione,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
240: call DMDAGetInfo(da,PETSC_NULL_INTEGER,user%mx,user%my, &
241: & PETSC_NULL_INTEGER, &
242: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
243: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
244: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
245: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
246: & PETSC_NULL_INTEGER,ierr)
248: !
249: ! Visualize the distribution of the array across the processors
250: !
251: ! call DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr)
253: ! Extract global and local vectors from DMDA; then duplicate for remaining
254: ! vectors that are the same types
255: call DMCreateGlobalVector(da,x,ierr)
256: call VecDuplicate(x,r,ierr)
258: ! Get local grid boundaries (for 2-dimensional DMDA)
259: call DMDAGetCorners(da,user%xs,user%ys,PETSC_NULL_INTEGER, &
260: & user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
261: call DMDAGetGhostCorners(da,user%gxs,user%gys, &
262: & PETSC_NULL_INTEGER,user%gxm,user%gym, &
263: & PETSC_NULL_INTEGER,ierr)
265: ! Here we shift the starting indices up by one so that we can easily
266: ! use the Fortran convention of 1-based indices (rather 0-based indices).
267: user%xs = user%xs+1
268: user%ys = user%ys+1
269: user%gxs = user%gxs+1
270: user%gys = user%gys+1
272: user%ye = user%ys+user%ym-1
273: user%xe = user%xs+user%xm-1
274: user%gye = user%gys+user%gym-1
275: user%gxe = user%gxs+user%gxm-1
277: call SNESSetApplicationContext(snes,user,ierr)
279: ! Set function evaluation routine and vector
280: call SNESSetFunction(snes,r,FormFunction,user,ierr)
282: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
283: ! Create matrix data structure; set Jacobian evaluation routine
284: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
286: ! Set Jacobian matrix data structure and default Jacobian evaluation
287: ! routine. User can override with:
288: ! -snes_fd : default finite differencing approximation of Jacobian
289: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
290: ! (unless user explicitly sets preconditioner)
291: ! -snes_mf_operator : form preconditioning matrix as set by the user,
292: ! but use matrix-free approx for Jacobian-vector
293: ! products within Newton-Krylov method
294: !
295: ! Note: For the parallel case, vectors and matrices MUST be partitioned
296: ! accordingly. When using distributed arrays (DMDAs) to create vectors,
297: ! the DMDAs determine the problem partitioning. We must explicitly
298: ! specify the local matrix dimensions upon its creation for compatibility
299: ! with the vector distribution. Thus, the generic MatCreate() routine
300: ! is NOT sufficient when working with distributed arrays.
301: !
302: ! Note: Here we only approximately preallocate storage space for the
303: ! Jacobian. See the users manual for a discussion of better techniques
304: ! for preallocating matrix memory.
306: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf', &
307: & matrix_free,ierr)
308: if (.not. matrix_free) then
309: call DMSetMatType(da,MATAIJ,ierr)
310: call DMCreateMatrix(da,J,ierr)
311: call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)
312: endif
314: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
315: ! Customize nonlinear solver; set runtime options
316: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
317: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
318: call SNESSetDM(snes,da,ierr)
319: call SNESSetFromOptions(snes,ierr)
322: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
323: ! Evaluate initial guess; then solve nonlinear system.
324: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
325: ! Note: The user should initialize the vector, x, with the initial guess
326: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
327: ! to employ an initial guess of zero, the user should explicitly set
328: ! this vector to zero by calling VecSet().
330: call FormInitialGuess(snes,x,ierr)
331: call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
332: call SNESGetIterationNumber(snes,its,ierr);
333: if (user%rank .eq. 0) then
334: write(6,100) its
335: endif
336: 100 format('Number of SNES iterations = ',i5)
338: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
339: ! Free work space. All PETSc objects should be destroyed when they
340: ! are no longer needed.
341: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
342: if (.not. matrix_free) call MatDestroy(J,ierr)
343: call VecDestroy(x,ierr)
344: call VecDestroy(r,ierr)
345: call SNESDestroy(snes,ierr)
346: call DMDestroy(da,ierr)
348: call PetscFinalize(ierr)
349: end
351: ! ---------------------------------------------------------------------
352: !
353: ! FormInitialGuess - Forms initial approximation.
354: !
355: ! Input Parameters:
356: ! X - vector
357: !
358: ! Output Parameter:
359: ! X - vector
360: !
361: ! Notes:
362: ! This routine serves as a wrapper for the lower-level routine
363: ! "InitialGuessLocal", where the actual computations are
364: ! done using the standard Fortran style of treating the local
365: ! vector data as a multidimensional array over the local mesh.
366: ! This routine merely handles ghost point scatters and accesses
367: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
368: !
369: subroutine FormInitialGuess(snes,X,ierr)
370: use f90module
371: use f90moduleinterfaces
372: implicit none
374: #include <finclude/petscvec.h90>
375: #include <finclude/petscsys.h>
376: #include <finclude/petscvec.h>
377: #include <finclude/petscdm.h>
378: #include <finclude/petscdmda.h>
379: #include <finclude/petscis.h>
380: #include <finclude/petscmat.h>
381: #include <finclude/petscksp.h>
382: #include <finclude/petscpc.h>
383: #include <finclude/petscsnes.h>
385: ! Input/output variables:
386: SNES snes
387: type(userctx), pointer:: puser
388: Vec X
389: PetscErrorCode ierr
390: DM da
392: ! Declarations for use with local arrays:
393: PetscScalar,pointer :: lx_v(:)
394: Vec localX
396: 0
397: call SNESGetDM(snes,da,ierr)
398: call SNESGetApplicationContext(snes,puser,ierr)
399: ! Get a pointer to vector data.
400: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
401: ! the data array. Otherwise, the routine is implementation dependent.
402: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
403: ! the array.
404: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
405: ! and is useable from Fortran-90 Only.
407: call DMGetLocalVector(da,localX,ierr)
408: call VecGetArrayF90(localX,lx_v,ierr)
410: ! Compute initial guess over the locally owned part of the grid
411: call InitialGuessLocal(puser,lx_v,ierr)
413: ! Restore vector
414: call VecRestoreArrayF90(localX,lx_v,ierr)
416: ! Insert values into global vector
417: call DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X,ierr)
418: call DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X,ierr)
419: call DMRestoreLocalVector(da,localX,ierr)
421: return
422: end
424: ! ---------------------------------------------------------------------
425: !
426: ! InitialGuessLocal - Computes initial approximation, called by
427: ! the higher level routine FormInitialGuess().
428: !
429: ! Input Parameter:
430: ! x - local vector data
431: !
432: ! Output Parameters:
433: ! x - local vector data
434: ! ierr - error code
435: !
436: ! Notes:
437: ! This routine uses standard Fortran-style computations over a 2-dim array.
438: !
439: subroutine InitialGuessLocal(user,x,ierr)
440: use f90module
441: implicit none
443: #include <finclude/petscsys.h>
444: #include <finclude/petscvec.h>
445: #include <finclude/petscdm.h>
446: #include <finclude/petscdmda.h>
447: #include <finclude/petscis.h>
448: #include <finclude/petscmat.h>
449: #include <finclude/petscksp.h>
450: #include <finclude/petscpc.h>
451: #include <finclude/petscsnes.h>
453: ! Input/output variables:
454: type (userctx) user
455: PetscScalar x(user%gxs:user%gxe, &
456: & user%gys:user%gye)
457: PetscErrorCode ierr
459: ! Local variables:
460: PetscInt i,j
461: PetscScalar temp1,temp,hx,hy
462: PetscScalar one
464: ! Set parameters
466: 0
467: one = 1.0
468: hx = one/(dble(user%mx-1))
469: hy = one/(dble(user%my-1))
470: temp1 = user%lambda/(user%lambda + one)
472: do 20 j=user%ys,user%ye
473: temp = dble(min(j-1,user%my-j))*hy
474: do 10 i=user%xs,user%xe
475: if (i .eq. 1 .or. j .eq. 1 &
476: & .or. i .eq. user%mx .or. j .eq. user%my) then
477: x(i,j) = 0.0
478: else
479: x(i,j) = temp1 * &
480: & sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
481: endif
482: 10 continue
483: 20 continue
485: return
486: end
488: ! ---------------------------------------------------------------------
489: !
490: ! FormFunctionLocal - Computes nonlinear function, called by
491: ! the higher level routine FormFunction().
492: !
493: ! Input Parameter:
494: ! x - local vector data
495: !
496: ! Output Parameters:
497: ! f - local vector data, f(x)
498: ! ierr - error code
499: !
500: ! Notes:
501: ! This routine uses standard Fortran-style computations over a 2-dim array.
502: !
503: subroutine FormFunctionLocal(x,f,user,ierr)
504: use f90module
506: implicit none
508: ! Input/output variables:
509: type (userctx) user
510: PetscScalar x(user%gxs:user%gxe, &
511: & user%gys:user%gye)
512: PetscScalar f(user%xs:user%xe, &
513: & user%ys:user%ye)
514: PetscErrorCode ierr
516: ! Local variables:
517: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
518: PetscScalar u,uxx,uyy
519: PetscInt i,j
521: one = 1.0
522: two = 2.0
523: hx = one/dble(user%mx-1)
524: hy = one/dble(user%my-1)
525: sc = hx*hy*user%lambda
526: hxdhy = hx/hy
527: hydhx = hy/hx
529: ! Compute function over the locally owned part of the grid
531: do 20 j=user%ys,user%ye
532: do 10 i=user%xs,user%xe
533: if (i .eq. 1 .or. j .eq. 1 &
534: & .or. i .eq. user%mx .or. j .eq. user%my) then
535: f(i,j) = x(i,j)
536: else
537: u = x(i,j)
538: uxx = hydhx * (two*u &
539: & - x(i-1,j) - x(i+1,j))
540: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
541: f(i,j) = uxx + uyy - sc*exp(u)
542: endif
543: 10 continue
544: 20 continue
546: return
547: end
549: ! ---------------------------------------------------------------------
550: !
551: ! FormJacobian - Evaluates Jacobian matrix.
552: !
553: ! Input Parameters:
554: ! snes - the SNES context
555: ! x - input vector
556: ! dummy - optional user-defined context, as set by SNESSetJacobian()
557: ! (not used here)
558: !
559: ! Output Parameters:
560: ! jac - Jacobian matrix
561: ! jac_prec - optionally different preconditioning matrix (not used here)
562: ! flag - flag indicating matrix structure
563: !
564: ! Notes:
565: ! This routine serves as a wrapper for the lower-level routine
566: ! "FormJacobianLocal", where the actual computations are
567: ! done using the standard Fortran style of treating the local
568: ! vector data as a multidimensional array over the local mesh.
569: ! This routine merely accesses the local vector data via
570: ! VecGetArrayF90() and VecRestoreArrayF90().
571: !
572: ! Notes:
573: ! Due to grid point reordering with DMDAs, we must always work
574: ! with the local grid points, and then transform them to the new
575: ! global numbering with the "ltog" mapping
576: ! We cannot work directly with the global numbers for the original
577: ! uniprocessor grid!
578: !
579: ! Two methods are available for imposing this transformation
580: ! when setting matrix entries:
581: ! (A) MatSetValuesLocal(), using the local ordering (including
582: ! ghost points!)
583: ! - Set matrix entries using the local ordering
584: ! by calling MatSetValuesLocal()
585: ! (B) MatSetValues(), using the global ordering
587: ! - Set matrix entries using the global ordering by calling
588: ! MatSetValues()
589: ! Option (A) seems cleaner/easier in many cases, and is the procedure
590: ! used in this example.
591: !
592: subroutine FormJacobian(snes,X,jac,jac_prec,user,ierr)
593: use f90module
594: implicit none
596: #include <finclude/petscsys.h>
597: #include <finclude/petscvec.h>
598: #include <finclude/petscdm.h>
599: #include <finclude/petscdmda.h>
600: #include <finclude/petscis.h>
601: #include <finclude/petscmat.h>
602: #include <finclude/petscksp.h>
603: #include <finclude/petscpc.h>
604: #include <finclude/petscsnes.h>
606: #include <finclude/petscvec.h90>
608: ! Input/output variables:
609: SNES snes
610: Vec X
611: Mat jac,jac_prec
612: type(userctx) user
613: PetscErrorCode ierr
614: DM da
616: ! Declarations for use with local arrays:
617: PetscScalar,pointer :: lx_v(:)
618: Vec localX
620: ! Scatter ghost points to local vector, using the 2-step process
621: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
622: ! Computations can be done while messages are in transition,
623: ! by placing code between these two statements.
625: call SNESGetDM(snes,da,ierr)
626: call DMGetLocalVector(da,localX,ierr)
627: call DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX, &
628: & ierr)
629: call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr)
631: ! Get a pointer to vector data
632: call VecGetArrayF90(localX,lx_v,ierr)
634: ! Compute entries for the locally owned part of the Jacobian preconditioner.
635: call FormJacobianLocal(lx_v,jac_prec,user,ierr)
637: ! Assemble matrix, using the 2-step process:
638: ! MatAssemblyBegin(), MatAssemblyEnd()
639: ! Computations can be done while messages are in transition,
640: ! by placing code between these two statements.
642: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
643: if (jac .ne. jac_prec) then
644: call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
645: endif
646: call VecRestoreArrayF90(localX,lx_v,ierr)
647: call DMRestoreLocalVector(da,localX,ierr)
648: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
649: if (jac .ne. jac_prec) then
650: call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
651: endif
653: ! Tell the matrix we will never add a new nonzero location to the
654: ! matrix. If we do it will generate an error.
656: call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE, &
657: & ierr)
659: return
660: end
662: ! ---------------------------------------------------------------------
663: !
664: ! FormJacobianLocal - Computes Jacobian preconditioner matrix,
665: ! called by the higher level routine FormJacobian().
666: !
667: ! Input Parameters:
668: ! x - local vector data
669: !
670: ! Output Parameters:
671: ! jac_prec - Jacobian preconditioner matrix
672: ! ierr - error code
673: !
674: ! Notes:
675: ! This routine uses standard Fortran-style computations over a 2-dim array.
676: !
677: ! Notes:
678: ! Due to grid point reordering with DMDAs, we must always work
679: ! with the local grid points, and then transform them to the new
680: ! global numbering with the "ltog" mapping
681: ! We cannot work directly with the global numbers for the original
682: ! uniprocessor grid!
683: !
684: ! Two methods are available for imposing this transformation
685: ! when setting matrix entries:
686: ! (A) MatSetValuesLocal(), using the local ordering (including
687: ! ghost points!)
688: ! - Set matrix entries using the local ordering
689: ! by calling MatSetValuesLocal()
690: ! (B) MatSetValues(), using the global ordering
691: ! - Then apply this map explicitly yourself
692: ! - Set matrix entries using the global ordering by calling
693: ! MatSetValues()
694: ! Option (A) seems cleaner/easier in many cases, and is the procedure
695: ! used in this example.
696: !
697: subroutine FormJacobianLocal(x,jac_prec,user,ierr)
698: use f90module
699: implicit none
701: #include <finclude/petscsys.h>
702: #include <finclude/petscvec.h>
703: #include <finclude/petscdm.h>
704: #include <finclude/petscdmda.h>
705: #include <finclude/petscis.h>
706: #include <finclude/petscmat.h>
707: #include <finclude/petscksp.h>
708: #include <finclude/petscpc.h>
709: #include <finclude/petscsnes.h>
711: ! Input/output variables:
712: type (userctx) user
713: PetscScalar x(user%gxs:user%gxe, &
714: & user%gys:user%gye)
715: Mat jac_prec
716: PetscErrorCode ierr
718: ! Local variables:
719: PetscInt row,col(5),i,j
720: PetscInt ione,ifive
721: PetscScalar two,one,hx,hy,hxdhy
722: PetscScalar hydhx,sc,v(5)
724: ! Set parameters
725: ione = 1
726: ifive = 5
727: one = 1.0
728: two = 2.0
729: hx = one/dble(user%mx-1)
730: hy = one/dble(user%my-1)
731: sc = hx*hy
732: hxdhy = hx/hy
733: hydhx = hy/hx
735: ! Compute entries for the locally owned part of the Jacobian.
736: ! - Currently, all PETSc parallel matrix formats are partitioned by
737: ! contiguous chunks of rows across the processors.
738: ! - Each processor needs to insert only elements that it owns
739: ! locally (but any non-local elements will be sent to the
740: ! appropriate processor during matrix assembly).
741: ! - Here, we set all entries for a particular row at once.
742: ! - We can set matrix entries either using either
743: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
744: ! - Note that MatSetValues() uses 0-based row and column numbers
745: ! in Fortran as well as in C.
747: do 20 j=user%ys,user%ye
748: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
749: do 10 i=user%xs,user%xe
750: row = row + 1
751: ! boundary points
752: if (i .eq. 1 .or. j .eq. 1 &
753: & .or. i .eq. user%mx .or. j .eq. user%my) then
754: col(1) = row
755: v(1) = one
756: call MatSetValuesLocal(jac_prec,ione,row,ione,col,v, &
757: & INSERT_VALUES,ierr)
758: ! interior grid points
759: else
760: v(1) = -hxdhy
761: v(2) = -hydhx
762: v(3) = two*(hydhx + hxdhy) &
763: & - sc*user%lambda*exp(x(i,j))
764: v(4) = -hydhx
765: v(5) = -hxdhy
766: col(1) = row - user%gxm
767: col(2) = row - 1
768: col(3) = row
769: col(4) = row + 1
770: col(5) = row + user%gxm
771: call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v, &
772: & INSERT_VALUES,ierr)
773: endif
774: 10 continue
775: 20 continue
777: return
778: end