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 (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: !/*T
10: ! Concepts: SNES^parallel Bratu example
11: ! Concepts: DA^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/petscdadef.h
43: DA 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/petscda.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: ! DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
98: ! By placing code between these two statements, computations can
99: ! be done while messages are in transition.
100: call DAGetLocalVector(user%da,localX,ierr)
101: call DAGlobalToLocalBegin(user%da,X,INSERT_VALUES, &
102: & localX,ierr)
103: call DAGlobalToLocalEnd(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 DARestoreLocalVector(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/petscda.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/petscda.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: PetscTruth 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(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 (DA) 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 DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX, &
233: & nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,ione,ione, &
234: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr)
235: call DAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my, &
236: & PETSC_NULL_INTEGER, &
237: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
238: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
239: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
240: & PETSC_NULL_INTEGER,ierr)
241:
242: !
243: ! Visualize the distribution of the array across the processors
244: !
245: ! call DAView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)
247: ! Extract global and local vectors from DA; then duplicate for remaining
248: ! vectors that are the same types
249: call DACreateGlobalVector(user%da,x,ierr)
250: call VecDuplicate(x,r,ierr)
252: ! Get local grid boundaries (for 2-dimensional DA)
253: call DAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER, &
254: & user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
255: call DAGetGhostCorners(user%da,user%gxs,user%gys, &
256: & PETSC_NULL_INTEGER,user%gxm,user%gym, &
257: & PETSC_NULL_INTEGER,ierr)
259: ! Here we shift the starting indices up by one so that we can easily
260: ! use the Fortran convention of 1-based indices (rather 0-based indices).
261: user%xs = user%xs+1
262: user%ys = user%ys+1
263: user%gxs = user%gxs+1
264: user%gys = user%gys+1
266: user%ye = user%ys+user%ym-1
267: user%xe = user%xs+user%xm-1
268: user%gye = user%gys+user%gym-1
269: user%gxe = user%gxs+user%gxm-1
271: call SNESSetApplicationContext(snes,user,ierr)
273: ! Set function evaluation routine and vector
274: call SNESSetFunction(snes,r,FormFunction,user,ierr)
276: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
277: ! Create matrix data structure; set Jacobian evaluation routine
278: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
280: ! Set Jacobian matrix data structure and default Jacobian evaluation
281: ! routine. User can override with:
282: ! -snes_fd : default finite differencing approximation of Jacobian
283: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
284: ! (unless user explicitly sets preconditioner)
285: ! -snes_mf_operator : form preconditioning matrix as set by the user,
286: ! but use matrix-free approx for Jacobian-vector
287: ! products within Newton-Krylov method
288: !
289: ! Note: For the parallel case, vectors and matrices MUST be partitioned
290: ! accordingly. When using distributed arrays (DAs) to create vectors,
291: ! the DAs determine the problem partitioning. We must explicitly
292: ! specify the local matrix dimensions upon its creation for compatibility
293: ! with the vector distribution. Thus, the generic MatCreate() routine
294: ! is NOT sufficient when working with distributed arrays.
295: !
296: ! Note: Here we only approximately preallocate storage space for the
297: ! Jacobian. See the users manual for a discussion of better techniques
298: ! for preallocating matrix memory.
299:
300: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf', &
301: & matrix_free,ierr)
302: if (.not. matrix_free) then
303: call DAGetMatrix(user%da,MATAIJ,J,ierr)
304: call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)
305: endif
307: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
308: ! Customize nonlinear solver; set runtime options
309: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
310: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
311: call SNESSetFromOptions(snes,ierr)
313: ! Test Fortran90 wrapper for SNESSet/Get ApplicationContext()
314: call PetscOptionsGetTruth(PETSC_NULL_CHARACTER,'-test_appctx', &
315: & flg,PETSC_NULL_CHARACTER,ierr)
316: if (flg) then
317: call SNESGetApplicationContext(snes,puser,ierr)
318: if (user%da .ne. puser%da) then
319: write(*,*) "Error: uesr != puesr"
320: write(*,*) "user: ", user
321: write(*,*) "puesr: ", puser
322: endif
323: endif
325: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
326: ! Evaluate initial guess; then solve nonlinear system.
327: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
328: ! Note: The user should initialize the vector, x, with the initial guess
329: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
330: ! to employ an initial guess of zero, the user should explicitly set
331: ! this vector to zero by calling VecSet().
333: call FormInitialGuess(snes,x,ierr)
334: call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
335: call SNESGetIterationNumber(snes,its,ierr);
336: if (user%rank .eq. 0) then
337: write(6,100) its
338: endif
339: 100 format('Number of Newton iterations = ',i5)
341: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
342: ! Free work space. All PETSc objects should be destroyed when they
343: ! are no longer needed.
344: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
345: if (.not. matrix_free) call MatDestroy(J,ierr)
346: call VecDestroy(x,ierr)
347: call VecDestroy(r,ierr)
348: call SNESDestroy(snes,ierr)
349: call DADestroy(user%da,ierr)
351: call PetscFinalize(ierr)
352: end
354: ! ---------------------------------------------------------------------
355: !
356: ! FormInitialGuess - Forms initial approximation.
357: !
358: ! Input Parameters:
359: ! X - vector
360: !
361: ! Output Parameter:
362: ! X - vector
363: !
364: ! Notes:
365: ! This routine serves as a wrapper for the lower-level routine
366: ! "InitialGuessLocal", where the actual computations are
367: ! done using the standard Fortran style of treating the local
368: ! vector data as a multidimensional array over the local mesh.
369: ! This routine merely handles ghost point scatters and accesses
370: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
371: !
372: subroutine FormInitialGuess(snes,X,ierr)
373: use f90module
374: use f90moduleinterfaces
375: implicit none
377: #include "finclude/petscvec.h90"
378: #include finclude/petscsys.h
379: #include finclude/petscvec.h
380: #include finclude/petscda.h
381: #include finclude/petscis.h
382: #include finclude/petscmat.h
383: #include finclude/petscksp.h
384: #include finclude/petscpc.h
385: #include finclude/petscsnes.h
387: ! Input/output variables:
388: SNES snes
389: type(userctx), pointer:: puser
390: Vec X
391: PetscErrorCode ierr
392:
393: ! Declarations for use with local arrays:
394: PetscScalar,pointer :: lx_v(:)
395: Vec localX
397: 0
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 DAGetLocalVector(puser%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 DALocalToGlobal(puser%da,localX,INSERT_VALUES,X,ierr)
418: call DARestoreLocalVector(puser%da,localX,ierr)
420: return
421: end
423: ! ---------------------------------------------------------------------
424: !
425: ! InitialGuessLocal - Computes initial approximation, called by
426: ! the higher level routine FormInitialGuess().
427: !
428: ! Input Parameter:
429: ! x - local vector data
430: !
431: ! Output Parameters:
432: ! x - local vector data
433: ! ierr - error code
434: !
435: ! Notes:
436: ! This routine uses standard Fortran-style computations over a 2-dim array.
437: !
438: subroutine InitialGuessLocal(user,x,ierr)
439: use f90module
440: implicit none
442: #include finclude/petscsys.h
443: #include finclude/petscvec.h
444: #include finclude/petscda.h
445: #include finclude/petscis.h
446: #include finclude/petscmat.h
447: #include finclude/petscksp.h
448: #include finclude/petscpc.h
449: #include finclude/petscsnes.h
451: ! Input/output variables:
452: type (userctx) user
453: PetscScalar x(user%gxs:user%gxe, &
454: & user%gys:user%gye)
455: PetscErrorCode ierr
457: ! Local variables:
458: PetscInt i,j
459: PetscScalar temp1,temp,hx,hy
460: PetscScalar one
462: ! Set parameters
464: 0
465: one = 1.0
466: hx = one/(dble(user%mx-1))
467: hy = one/(dble(user%my-1))
468: temp1 = user%lambda/(user%lambda + one)
470: do 20 j=user%ys,user%ye
471: temp = dble(min(j-1,user%my-j))*hy
472: do 10 i=user%xs,user%xe
473: if (i .eq. 1 .or. j .eq. 1 &
474: & .or. i .eq. user%mx .or. j .eq. user%my) then
475: x(i,j) = 0.0
476: else
477: x(i,j) = temp1 * &
478: & sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
479: endif
480: 10 continue
481: 20 continue
483: return
484: end
486: ! ---------------------------------------------------------------------
487: !
488: ! FormFunctionLocal - Computes nonlinear function, called by
489: ! the higher level routine FormFunction().
490: !
491: ! Input Parameter:
492: ! x - local vector data
493: !
494: ! Output Parameters:
495: ! f - local vector data, f(x)
496: ! ierr - error code
497: !
498: ! Notes:
499: ! This routine uses standard Fortran-style computations over a 2-dim array.
500: !
501: subroutine FormFunctionLocal(x,f,user,ierr)
502: use f90module
504: implicit none
506: ! Input/output variables:
507: type (userctx) user
508: PetscScalar x(user%gxs:user%gxe, &
509: & user%gys:user%gye)
510: PetscScalar f(user%xs:user%xe, &
511: & user%ys:user%ye)
512: PetscErrorCode ierr
514: ! Local variables:
515: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
516: PetscScalar u,uxx,uyy
517: PetscInt i,j
519: one = 1.0
520: two = 2.0
521: hx = one/dble(user%mx-1)
522: hy = one/dble(user%my-1)
523: sc = hx*hy*user%lambda
524: hxdhy = hx/hy
525: hydhx = hy/hx
527: ! Compute function over the locally owned part of the grid
529: do 20 j=user%ys,user%ye
530: do 10 i=user%xs,user%xe
531: if (i .eq. 1 .or. j .eq. 1 &
532: & .or. i .eq. user%mx .or. j .eq. user%my) then
533: f(i,j) = x(i,j)
534: else
535: u = x(i,j)
536: uxx = hydhx * (two*u &
537: & - x(i-1,j) - x(i+1,j))
538: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
539: f(i,j) = uxx + uyy - sc*exp(u)
540: endif
541: 10 continue
542: 20 continue
544: return
545: end
547: ! ---------------------------------------------------------------------
548: !
549: ! FormJacobian - Evaluates Jacobian matrix.
550: !
551: ! Input Parameters:
552: ! snes - the SNES context
553: ! x - input vector
554: ! dummy - optional user-defined context, as set by SNESSetJacobian()
555: ! (not used here)
556: !
557: ! Output Parameters:
558: ! jac - Jacobian matrix
559: ! jac_prec - optionally different preconditioning matrix (not used here)
560: ! flag - flag indicating matrix structure
561: !
562: ! Notes:
563: ! This routine serves as a wrapper for the lower-level routine
564: ! "FormJacobianLocal", where the actual computations are
565: ! done using the standard Fortran style of treating the local
566: ! vector data as a multidimensional array over the local mesh.
567: ! This routine merely accesses the local vector data via
568: ! VecGetArrayF90() and VecRestoreArrayF90().
569: !
570: ! Notes:
571: ! Due to grid point reordering with DAs, we must always work
572: ! with the local grid points, and then transform them to the new
573: ! global numbering with the "ltog" mapping (via DAGetGlobalIndicesF90()).
574: ! We cannot work directly with the global numbers for the original
575: ! uniprocessor grid!
576: !
577: ! Two methods are available for imposing this transformation
578: ! when setting matrix entries:
579: ! (A) MatSetValuesLocal(), using the local ordering (including
580: ! ghost points!)
581: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
582: ! - Associate this map with the matrix by calling
583: ! MatSetLocalToGlobalMapping() once
584: ! - Set matrix entries using the local ordering
585: ! by calling MatSetValuesLocal()
586: ! (B) MatSetValues(), using the global ordering
587: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
588: ! - Then apply this map explicitly yourself
589: ! - Set matrix entries using the global ordering by calling
590: ! MatSetValues()
591: ! Option (A) seems cleaner/easier in many cases, and is the procedure
592: ! used in this example.
593: !
594: subroutine FormJacobian(snes,X,jac,jac_prec,flag,user,ierr)
595: use f90module
596: implicit none
598: #include finclude/petscsys.h
599: #include finclude/petscvec.h
600: #include finclude/petscda.h
601: #include finclude/petscis.h
602: #include finclude/petscmat.h
603: #include finclude/petscksp.h
604: #include finclude/petscpc.h
605: #include finclude/petscsnes.h
607: #include "finclude/petscvec.h90"
609: ! Input/output variables:
610: SNES snes
611: Vec X
612: Mat jac,jac_prec
613: MatStructure flag
614: type(userctx) user
615: PetscErrorCode ierr
617: ! Declarations for use with local arrays:
618: PetscScalar,pointer :: lx_v(:)
619: Vec localX
621: ! Scatter ghost points to local vector, using the 2-step process
622: ! DAGlobalToLocalBegin(), DAGlobalToLocalEnd()
623: ! Computations can be done while messages are in transition,
624: ! by placing code between these two statements.
626: call DAGetLocalVector(user%da,localX,ierr)
627: call DAGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX, &
628: & ierr)
629: call DAGlobalToLocalEnd(user%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 DARestoreLocalVector(user%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
652:
653: ! Set flag to indicate that the Jacobian matrix retains an identical
654: ! nonzero structure throughout all nonlinear iterations (although the
655: ! values of the entries change). Thus, we can save some work in setting
656: ! up the preconditioner (e.g., no need to redo symbolic factorization for
657: ! ILU/ICC preconditioners).
658: ! - If the nonzero structure of the matrix is different during
659: ! successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
660: ! must be used instead. If you are unsure whether the matrix
661: ! structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
662: ! - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
663: ! believes your assertion and does not check the structure
664: ! of the matrix. If you erroneously claim that the structure
665: ! is the same when it actually is not, the new preconditioner
666: ! will not function correctly. Thus, use this optimization
667: ! feature with caution!
669: flag = SAME_NONZERO_PATTERN
671: ! Tell the matrix we will never add a new nonzero location to the
672: ! matrix. If we do it will generate an error.
674: call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE, &
675: & ierr)
677: return
678: end
680: ! ---------------------------------------------------------------------
681: !
682: ! FormJacobianLocal - Computes Jacobian preconditioner matrix,
683: ! called by the higher level routine FormJacobian().
684: !
685: ! Input Parameters:
686: ! x - local vector data
687: !
688: ! Output Parameters:
689: ! jac_prec - Jacobian preconditioner matrix
690: ! ierr - error code
691: !
692: ! Notes:
693: ! This routine uses standard Fortran-style computations over a 2-dim array.
694: !
695: ! Notes:
696: ! Due to grid point reordering with DAs, we must always work
697: ! with the local grid points, and then transform them to the new
698: ! global numbering with the "ltog" mapping (via DAGetGlobalIndicesF90()).
699: ! We cannot work directly with the global numbers for the original
700: ! uniprocessor grid!
701: !
702: ! Two methods are available for imposing this transformation
703: ! when setting matrix entries:
704: ! (A) MatSetValuesLocal(), using the local ordering (including
705: ! ghost points!)
706: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
707: ! - Associate this map with the matrix by calling
708: ! MatSetLocalToGlobalMapping() once
709: ! - Set matrix entries using the local ordering
710: ! by calling MatSetValuesLocal()
711: ! (B) MatSetValues(), using the global ordering
712: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
713: ! - Then apply this map explicitly yourself
714: ! - Set matrix entries using the global ordering by calling
715: ! MatSetValues()
716: ! Option (A) seems cleaner/easier in many cases, and is the procedure
717: ! used in this example.
718: !
719: subroutine FormJacobianLocal(x,jac_prec,user,ierr)
720: use f90module
721: implicit none
723: #include finclude/petscsys.h
724: #include finclude/petscvec.h
725: #include finclude/petscda.h
726: #include finclude/petscis.h
727: #include finclude/petscmat.h
728: #include finclude/petscksp.h
729: #include finclude/petscpc.h
730: #include finclude/petscsnes.h
732: ! Input/output variables:
733: type (userctx) user
734: PetscScalar x(user%gxs:user%gxe, &
735: & user%gys:user%gye)
736: Mat jac_prec
737: PetscErrorCode ierr
739: ! Local variables:
740: PetscInt row,col(5),i,j
741: PetscInt ione,ifive
742: PetscScalar two,one,hx,hy,hxdhy
743: PetscScalar hydhx,sc,v(5)
745: ! Set parameters
746: ione = 1
747: ifive = 5
748: one = 1.0
749: two = 2.0
750: hx = one/dble(user%mx-1)
751: hy = one/dble(user%my-1)
752: sc = hx*hy
753: hxdhy = hx/hy
754: hydhx = hy/hx
756: ! Compute entries for the locally owned part of the Jacobian.
757: ! - Currently, all PETSc parallel matrix formats are partitioned by
758: ! contiguous chunks of rows across the processors.
759: ! - Each processor needs to insert only elements that it owns
760: ! locally (but any non-local elements will be sent to the
761: ! appropriate processor during matrix assembly).
762: ! - Here, we set all entries for a particular row at once.
763: ! - We can set matrix entries either using either
764: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
765: ! - Note that MatSetValues() uses 0-based row and column numbers
766: ! in Fortran as well as in C.
768: do 20 j=user%ys,user%ye
769: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
770: do 10 i=user%xs,user%xe
771: row = row + 1
772: ! boundary points
773: if (i .eq. 1 .or. j .eq. 1 &
774: & .or. i .eq. user%mx .or. j .eq. user%my) then
775: col(1) = row
776: v(1) = one
777: call MatSetValuesLocal(jac_prec,ione,row,ione,col,v, &
778: & INSERT_VALUES,ierr)
779: ! interior grid points
780: else
781: v(1) = -hxdhy
782: v(2) = -hydhx
783: v(3) = two*(hydhx + hxdhy) &
784: & - sc*user%lambda*exp(x(i,j))
785: v(4) = -hydhx
786: v(5) = -hxdhy
787: col(1) = row - user%gxm
788: col(2) = row - 1
789: col(3) = row
790: col(4) = row + 1
791: col(5) = row + user%gxm
792: call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v, &
793: & INSERT_VALUES,ierr)
794: endif
795: 10 continue
796: 20 continue
798: return
799: end