Actual source code: ex5f90.F
1: ! "$Id: ex5f90.F,v 1.44 2001/09/11 18:47:20 bsmith Exp $";
2: !
3: ! Description: Solves a nonlinear system in parallel with SNES.
4: ! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
5: ! domain, using distributed arrays (DAs) to partition the parallel grid.
6: ! The command line options include:
7: ! -par <parameter>, where <parameter> indicates the nonlinearity of the problem
8: ! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)
9: !
10: !/*T
11: ! Concepts: SNES^parallel Bratu example
12: ! Concepts: DA^using distributed arrays;
13: ! Processors: n
14: !T*/
15: !
16: ! --------------------------------------------------------------------------
17: !
18: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
19: ! the partial differential equation
20: !
21: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
22: !
23: ! with boundary conditions
24: !
25: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
26: !
27: ! A finite difference approximation with the usual 5-point stencil
28: ! is used to discretize the boundary value problem to obtain a nonlinear
29: ! system of equations.
30: !
31: ! The uniprocessor version of this code is snes/examples/tutorials/ex4f.F
32: !
33: ! --------------------------------------------------------------------------
34: ! The following define must be used before including any PETSc include files
35: ! into a module or interface. This is because they can't handle declarations
36: ! in them
37: !
39: module f90module
40: type userctx
41: #define PETSC_AVOID_DECLARATIONS
42: #include include/finclude/petsc.h
43: #include include/finclude/petscvec.h
44: #include include/finclude/petscda.h
45: #undef PETSC_AVOID_DECLARATIONS
46: DA da
47: integer xs,xe,xm,gxs,gxe,gxm
48: integer ys,ye,ym,gys,gye,gym
49: integer mx,my,rank
50: double precision lambda
51: end type userctx
52: contains
53: ! ---------------------------------------------------------------------
54: !
55: ! FormFunction - Evaluates nonlinear function, F(x).
56: !
57: ! Input Parameters:
58: ! snes - the SNES context
59: ! X - input vector
60: ! dummy - optional user-defined context, as set by SNESSetFunction()
61: ! (not used here)
62: !
63: ! Output Parameter:
64: ! F - function vector
65: !
66: ! Notes:
67: ! This routine serves as a wrapper for the lower-level routine
68: ! "FormFunctionLocal", where the actual computations are
69: ! done using the standard Fortran style of treating the local
70: ! vector data as a multidimensional array over the local mesh.
71: ! This routine merely handles ghost point scatters and accesses
72: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
73: !
74: subroutine FormFunction(snes,X,F,user,ierr)
75: implicit none
77: #include include/finclude/petsc.h
78: #include include/finclude/petscvec.h
79: #include include/finclude/petscda.h
80: #include include/finclude/petscis.h
81: #include include/finclude/petscmat.h
82: #include include/finclude/petscksp.h
83: #include include/finclude/petscpc.h
84: #include include/finclude/petscsles.h
85: #include include/finclude/petscsnes.h
87: #include "include/finclude/petscvec.h90"
90: ! Input/output variables:
91: SNES snes
92: Vec X,F
93: integer ierr
94: type (userctx) user
96: ! Declarations for use with local arrays:
97: PetscScalar,pointer :: lx_v(:),lf_v(:)
98: Vec localX
100: ! Scatter ghost points to local vector, using the 2-step process
101: ! DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
102: ! By placing code between these two statements, computations can
103: ! be done while messages are in transition.
105: call DAGetLocalVector(user%da,localX,ierr)
106: call DAGlobalToLocalBegin(user%da,X,INSERT_VALUES, &
107: & localX,ierr)
108: call DAGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
110: ! Get a pointer to vector data.
111: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
112: ! the data array. Otherwise, the routine is implementation dependent.
113: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
114: ! the array.
115: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
116: ! and is useable from Fortran-90 Only.
118: call VecGetArrayF90(localX,lx_v,ierr)
119: call VecGetArrayF90(F,lf_v,ierr)
121: ! Compute function over the locally owned part of the grid
123: call FormFunctionLocal(lx_v,lf_v,user,ierr)
125: ! Restore vectors
127: call VecRestoreArrayF90(localX,lx_v,ierr)
128: call VecRestoreArrayF90(F,lf_v,ierr)
130: ! Insert values into global vector
132: call DARestoreLocalVector(user%da,localX,ierr)
133: call PetscLogFlops(11*user%ym*user%xm,ierr)
135: ! call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
136: ! call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
138: return
139: end subroutine formfunction
140: end module f90module
144: program main
145: use f90module
146: implicit none
147: !
148: !
149: #include include/finclude/petsc.h
150: #include include/finclude/petscvec.h
151: #include include/finclude/petscda.h
152: #include include/finclude/petscis.h
153: #include include/finclude/petscmat.h
154: #include include/finclude/petscksp.h
155: #include include/finclude/petscpc.h
156: #include include/finclude/petscsles.h
157: #include include/finclude/petscsnes.h
158: #include "include/finclude/petscvec.h90"
159: #include "include/finclude/petscda.h90"
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: ! Variable declarations
163: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
164: !
165: ! Variables:
166: ! snes - nonlinear solver
167: ! x, r - solution, residual vectors
168: ! J - Jacobian matrix
169: ! its - iterations for convergence
170: ! Nx, Ny - number of preocessors in x- and y- directions
171: ! matrix_free - flag - 1 indicates matrix-free version
172: !
173: !
174: SNES snes
175: Vec x,r
176: Mat J
177: integer its,matrix_free,flg,ierr
178: double precision lambda_max,lambda_min
179: type (userctx) user
181: ! Note: Any user-defined Fortran routines (such as FormJacobian)
182: ! MUST be declared as external.
184: external FormInitialGuess,FormJacobian
186: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187: ! Initialize program
188: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
191: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
193: ! Initialize problem parameters
195: lambda_max = 6.81
196: lambda_min = 0.0
197: user%lambda = 6.0
198: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par', &
199: & user%lambda,flg,ierr)
200: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) &
201: & then
202: if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
203: SETERRQ(1,' ',ierr)
204: endif
207: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208: ! Create nonlinear solver context
209: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211: call SNESCreate(PETSC_COMM_WORLD,SNES_NONLINEAR_EQUATIONS, &
212: & snes,ierr)
214: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
215: ! Create vector data structures; set function evaluation routine
216: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
218: ! Create distributed array (DA) to manage parallel grid and vectors
220: ! This really needs only the star-type stencil, but we use the box
221: ! stencil temporarily.
222: call DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX, &
223: & -4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1, &
224: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr)
225: call DAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my, &
226: & PETSC_NULL_INTEGER, &
227: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
228: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
229: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
230: & PETSC_NULL_INTEGER,ierr)
231:
232: !
233: ! Visualize the distribution of the array across the processors
234: !
235: ! call DAView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)
237: ! Extract global and local vectors from DA; then duplicate for remaining
238: ! vectors that are the same types
240: call DACreateGlobalVector(user%da,x,ierr)
241: call VecDuplicate(x,r,ierr)
243: ! Get local grid boundaries (for 2-dimensional DA)
245: call DAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER, &
246: & user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
247: call DAGetGhostCorners(user%da,user%gxs,user%gys, &
248: & PETSC_NULL_INTEGER,user%gxm,user%gym, &
249: & PETSC_NULL_INTEGER,ierr)
251: ! Here we shift the starting indices up by one so that we can easily
252: ! use the Fortran convention of 1-based indices (rather 0-based indices).
254: user%xs = user%xs+1
255: user%ys = user%ys+1
256: user%gxs = user%gxs+1
257: user%gys = user%gys+1
259: user%ye = user%ys+user%ym-1
260: user%xe = user%xs+user%xm-1
261: user%gye = user%gys+user%gym-1
262: user%gxe = user%gxs+user%gxm-1
264: ! Set function evaluation routine and vector
266: call SNESSetFunction(snes,r,FormFunction,user,ierr)
268: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
269: ! Create matrix data structure; set Jacobian evaluation routine
270: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
272: ! Set Jacobian matrix data structure and default Jacobian evaluation
273: ! routine. User can override with:
274: ! -snes_fd : default finite differencing approximation of Jacobian
275: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
276: ! (unless user explicitly sets preconditioner)
277: ! -snes_mf_operator : form preconditioning matrix as set by the user,
278: ! but use matrix-free approx for Jacobian-vector
279: ! products within Newton-Krylov method
280: !
281: ! Note: For the parallel case, vectors and matrices MUST be partitioned
282: ! accordingly. When using distributed arrays (DAs) to create vectors,
283: ! the DAs determine the problem partitioning. We must explicitly
284: ! specify the local matrix dimensions upon its creation for compatibility
285: ! with the vector distribution. Thus, the generic MatCreate() routine
286: ! is NOT sufficient when working with distributed arrays.
287: !
288: ! Note: Here we only approximately preallocate storage space for the
289: ! Jacobian. See the users manual for a discussion of better techniques
290: ! for preallocating matrix memory.
292: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf', &
293: & matrix_free,ierr)
294: if (matrix_free .eq. 0) then
295: call DAGetMatrix(user%da,MATMPIAIJ,J,ierr)
296: call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)
297: endif
299: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
300: ! Customize nonlinear solver; set runtime options
301: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
303: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
305: call SNESSetFromOptions(snes,ierr)
307: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
308: ! Evaluate initial guess; then solve nonlinear system.
309: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
311: ! Note: The user should initialize the vector, x, with the initial guess
312: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
313: ! to employ an initial guess of zero, the user should explicitly set
314: ! this vector to zero by calling VecSet().
316: call FormInitialGuess(user,x,ierr)
317: call SNESSolve(snes,x,its,ierr)
318: if (user%rank .eq. 0) then
319: write(6,100) its
320: endif
321: 100 format('Number of Newton iterations = ',i5)
323: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
324: ! Free work space. All PETSc objects should be destroyed when they
325: ! are no longer needed.
326: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
328: if (matrix_free .eq. 0) call MatDestroy(J,ierr)
329: call VecDestroy(x,ierr)
330: call VecDestroy(r,ierr)
331: call SNESDestroy(snes,ierr)
332: call DADestroy(user%da,ierr)
333: call PetscFinalize(ierr)
334: end
336: ! ---------------------------------------------------------------------
337: !
338: ! FormInitialGuess - Forms initial approximation.
339: !
340: ! Input Parameters:
341: ! X - vector
342: !
343: ! Output Parameter:
344: ! X - vector
345: !
346: ! Notes:
347: ! This routine serves as a wrapper for the lower-level routine
348: ! "InitialGuessLocal", where the actual computations are
349: ! done using the standard Fortran style of treating the local
350: ! vector data as a multidimensional array over the local mesh.
351: ! This routine merely handles ghost point scatters and accesses
352: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
353: !
354: subroutine FormInitialGuess(user,X,ierr)
355: use f90module
356: implicit none
358: #include "include/finclude/petscvec.h90"
359: #include include/finclude/petsc.h
360: #include include/finclude/petscvec.h
361: #include include/finclude/petscda.h
362: #include include/finclude/petscis.h
363: #include include/finclude/petscmat.h
364: #include include/finclude/petscksp.h
365: #include include/finclude/petscpc.h
366: #include include/finclude/petscsles.h
367: #include include/finclude/petscsnes.h
369: ! Input/output variables:
370: type (userctx) user
371: Vec X
372: integer ierr
373:
374: ! Declarations for use with local arrays:
375: PetscScalar,pointer :: lx_v(:)
376: Vec localX
378: 0
380: ! Get a pointer to vector data.
381: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
382: ! the data array. Otherwise, the routine is implementation dependent.
383: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
384: ! the array.
385: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
386: ! and is useable from Fortran-90 Only.
388: call DAGetLocalVector(user%da,localX,ierr)
389: call VecGetArrayF90(localX,lx_v,ierr)
391: ! Compute initial guess over the locally owned part of the grid
393: call InitialGuessLocal(user,lx_v,ierr)
395: ! Restore vector
397: call VecRestoreArrayF90(localX,lx_v,ierr)
399: ! Insert values into global vector
401: call DALocalToGlobal(user%da,localX,INSERT_VALUES,X,ierr)
402: call DARestoreLocalVector(user%da,localX,ierr)
404: return
405: end
407: ! ---------------------------------------------------------------------
408: !
409: ! InitialGuessLocal - Computes initial approximation, called by
410: ! the higher level routine FormInitialGuess().
411: !
412: ! Input Parameter:
413: ! x - local vector data
414: !
415: ! Output Parameters:
416: ! x - local vector data
417: ! ierr - error code
418: !
419: ! Notes:
420: ! This routine uses standard Fortran-style computations over a 2-dim array.
421: !
422: subroutine InitialGuessLocal(user,x,ierr)
423: use f90module
424: implicit none
426: #include include/finclude/petsc.h
427: #include include/finclude/petscvec.h
428: #include include/finclude/petscda.h
429: #include include/finclude/petscis.h
430: #include include/finclude/petscmat.h
431: #include include/finclude/petscksp.h
432: #include include/finclude/petscpc.h
433: #include include/finclude/petscsles.h
434: #include include/finclude/petscsnes.h
436: ! Input/output variables:
437: type (userctx) user
438: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
439: integer ierr
441: ! Local variables:
442: integer i,j,hxdhy,hydhx
443: PetscScalar temp1,temp,hx,hy,sc,one
445: ! Set parameters
447: ierr = 0
448: one = 1.0
449: hx = one/(dble(user%mx-1))
450: hy = one/(dble(user%my-1))
451: sc = hx*hy*user%lambda
452: hxdhy = hx/hy
453: hydhx = hy/hx
454: temp1 = user%lambda/(user%lambda + one)
456: do 20 j=user%ys,user%ye
457: temp = dble(min(j-1,user%my-j))*hy
458: do 10 i=user%xs,user%xe
459: if (i .eq. 1 .or. j .eq. 1 &
460: & .or. i .eq. user%mx .or. j .eq. user%my) then
461: x(i,j) = 0.0
462: else
463: x(i,j) = temp1 * &
464: & sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
465: endif
466: 10 continue
467: 20 continue
469: return
470: end
472: ! ---------------------------------------------------------------------
473: !
474: ! FormFunctionLocal - Computes nonlinear function, called by
475: ! the higher level routine FormFunction().
476: !
477: ! Input Parameter:
478: ! x - local vector data
479: !
480: ! Output Parameters:
481: ! f - local vector data, f(x)
482: ! ierr - error code
483: !
484: ! Notes:
485: ! This routine uses standard Fortran-style computations over a 2-dim array.
486: !
487: subroutine FormFunctionLocal(x,f,user,ierr)
488: use f90module
490: implicit none
492: ! Input/output variables:
493: type (userctx) user
494: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
495: PetscScalar f(user%xs:user%xe,user%ys:user%ye)
496: integer ierr
498: ! Local variables:
499: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
500: PetscScalar u,uxx,uyy
501: integer i,j
503: one = 1.0
504: two = 2.0
505: hx = one/dble(user%mx-1)
506: hy = one/dble(user%my-1)
507: sc = hx*hy*user%lambda
508: hxdhy = hx/hy
509: hydhx = hy/hx
511: ! Compute function over the locally owned part of the grid
513: do 20 j=user%ys,user%ye
514: do 10 i=user%xs,user%xe
515: if (i .eq. 1 .or. j .eq. 1 &
516: & .or. i .eq. user%mx .or. j .eq. user%my) then
517: f(i,j) = x(i,j)
518: else
519: u = x(i,j)
520: uxx = hydhx * (two*u &
521: & - x(i-1,j) - x(i+1,j))
522: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
523: f(i,j) = uxx + uyy - sc*exp(u)
524: endif
525: 10 continue
526: 20 continue
528: return
529: end
531: ! ---------------------------------------------------------------------
532: !
533: ! FormJacobian - Evaluates Jacobian matrix.
534: !
535: ! Input Parameters:
536: ! snes - the SNES context
537: ! x - input vector
538: ! dummy - optional user-defined context, as set by SNESSetJacobian()
539: ! (not used here)
540: !
541: ! Output Parameters:
542: ! jac - Jacobian matrix
543: ! jac_prec - optionally different preconditioning matrix (not used here)
544: ! flag - flag indicating matrix structure
545: !
546: ! Notes:
547: ! This routine serves as a wrapper for the lower-level routine
548: ! "FormJacobianLocal", where the actual computations are
549: ! done using the standard Fortran style of treating the local
550: ! vector data as a multidimensional array over the local mesh.
551: ! This routine merely accesses the local vector data via
552: ! VecGetArrayF90() and VecRestoreArrayF90().
553: !
554: ! Notes:
555: ! Due to grid point reordering with DAs, we must always work
556: ! with the local grid points, and then transform them to the new
557: ! global numbering with the "ltog" mapping (via DAGetGlobalIndicesF90()).
558: ! We cannot work directly with the global numbers for the original
559: ! uniprocessor grid!
560: !
561: ! Two methods are available for imposing this transformation
562: ! when setting matrix entries:
563: ! (A) MatSetValuesLocal(), using the local ordering (including
564: ! ghost points!)
565: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
566: ! - Associate this map with the matrix by calling
567: ! MatSetLocalToGlobalMapping() once
568: ! - Set matrix entries using the local ordering
569: ! by calling MatSetValuesLocal()
570: ! (B) MatSetValues(), using the global ordering
571: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
572: ! - Then apply this map explicitly yourself
573: ! - Set matrix entries using the global ordering by calling
574: ! MatSetValues()
575: ! Option (A) seems cleaner/easier in many cases, and is the procedure
576: ! used in this example.
577: !
578: subroutine FormJacobian(snes,X,jac,jac_prec,flag,user,ierr)
579: use f90module
580: implicit none
582: #include include/finclude/petsc.h
583: #include include/finclude/petscvec.h
584: #include include/finclude/petscda.h
585: #include include/finclude/petscis.h
586: #include include/finclude/petscmat.h
587: #include include/finclude/petscksp.h
588: #include include/finclude/petscpc.h
589: #include include/finclude/petscsles.h
590: #include include/finclude/petscsnes.h
592: #include "include/finclude/petscvec.h90"
594: ! Input/output variables:
595: SNES snes
596: Vec X
597: Mat jac,jac_prec
598: MatStructure flag
599: type(userctx) user
600: integer ierr
602: ! Declarations for use with local arrays:
603: PetscScalar,pointer :: lx_v(:)
604: Vec localX
606: ! Scatter ghost points to local vector, using the 2-step process
607: ! DAGlobalToLocalBegin(), DAGlobalToLocalEnd()
608: ! Computations can be done while messages are in transition,
609: ! by placing code between these two statements.
611: call DAGetLocalVector(user%da,localX,ierr)
612: call DAGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX, &
613: & ierr)
614: call DAGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
616: ! Get a pointer to vector data
618: call VecGetArrayF90(localX,lx_v,ierr)
620: ! Compute entries for the locally owned part of the Jacobian.
622: call FormJacobianLocal(lx_v,jac,jac_prec,user,ierr)
624: ! Assemble matrix, using the 2-step process:
625: ! MatAssemblyBegin(), MatAssemblyEnd()
626: ! Computations can be done while messages are in transition,
627: ! by placing code between these two statements.
629: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
630: call VecRestoreArrayF90(localX,lx_v,ierr)
631: call DARestoreLocalVector(user%da,localX,ierr)
632: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
634: ! Set flag to indicate that the Jacobian matrix retains an identical
635: ! nonzero structure throughout all nonlinear iterations (although the
636: ! values of the entries change). Thus, we can save some work in setting
637: ! up the preconditioner (e.g., no need to redo symbolic factorization for
638: ! ILU/ICC preconditioners).
639: ! - If the nonzero structure of the matrix is different during
640: ! successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
641: ! must be used instead. If you are unsure whether the matrix
642: ! structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
643: ! - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
644: ! believes your assertion and does not check the structure
645: ! of the matrix. If you erroneously claim that the structure
646: ! is the same when it actually is not, the new preconditioner
647: ! will not function correctly. Thus, use this optimization
648: ! feature with caution!
650: flag = SAME_NONZERO_PATTERN
652: ! Tell the matrix we will never add a new nonzero location to the
653: ! matrix. If we do it will generate an error.
655: call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,ierr)
657: return
658: end
660: ! ---------------------------------------------------------------------
661: !
662: ! FormJacobianLocal - Computes Jacobian matrix, called by
663: ! the higher level routine FormJacobian().
664: !
665: ! Input Parameters:
666: ! x - local vector data
667: !
668: ! Output Parameters:
669: ! jac - Jacobian matrix
670: ! jac_prec - optionally different preconditioning matrix (not used here)
671: ! ierr - error code
672: !
673: ! Notes:
674: ! This routine uses standard Fortran-style computations over a 2-dim array.
675: !
676: ! Notes:
677: ! Due to grid point reordering with DAs, we must always work
678: ! with the local grid points, and then transform them to the new
679: ! global numbering with the "ltog" mapping (via DAGetGlobalIndicesF90()).
680: ! We cannot work directly with the global numbers for the original
681: ! uniprocessor grid!
682: !
683: ! Two methods are available for imposing this transformation
684: ! when setting matrix entries:
685: ! (A) MatSetValuesLocal(), using the local ordering (including
686: ! ghost points!)
687: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
688: ! - Associate this map with the matrix by calling
689: ! MatSetLocalToGlobalMapping() once
690: ! - Set matrix entries using the local ordering
691: ! by calling MatSetValuesLocal()
692: ! (B) MatSetValues(), using the global ordering
693: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
694: ! - Then apply this map explicitly yourself
695: ! - Set matrix entries using the global ordering by calling
696: ! MatSetValues()
697: ! Option (A) seems cleaner/easier in many cases, and is the procedure
698: ! used in this example.
699: !
700: subroutine FormJacobianLocal(x,jac,jac_prec,user,ierr)
701: use f90module
702: implicit none
704: #include include/finclude/petsc.h
705: #include include/finclude/petscvec.h
706: #include include/finclude/petscda.h
707: #include include/finclude/petscis.h
708: #include include/finclude/petscmat.h
709: #include include/finclude/petscksp.h
710: #include include/finclude/petscpc.h
711: #include include/finclude/petscsles.h
712: #include include/finclude/petscsnes.h
714: ! Input/output variables:
715: type (userctx) user
716: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
717: Mat jac,jac_prec
718: integer ierr
720: ! Local variables:
721: integer row,col(5),i,j
722: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc,v(5)
724: ! Set parameters
726: one = 1.0
727: two = 2.0
728: hx = one/dble(user%mx-1)
729: hy = one/dble(user%my-1)
730: sc = hx*hy
731: hxdhy = hx/hy
732: hydhx = hy/hx
734: ! Compute entries for the locally owned part of the Jacobian.
735: ! - Currently, all PETSc parallel matrix formats are partitioned by
736: ! contiguous chunks of rows across the processors.
737: ! - Each processor needs to insert only elements that it owns
738: ! locally (but any non-local elements will be sent to the
739: ! appropriate processor during matrix assembly).
740: ! - Here, we set all entries for a particular row at once.
741: ! - We can set matrix entries either using either
742: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
743: ! - Note that MatSetValues() uses 0-based row and column numbers
744: ! in Fortran as well as in C.
746: do 20 j=user%ys,user%ye
747: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
748: do 10 i=user%xs,user%xe
749: row = row + 1
750: ! boundary points
751: if (i .eq. 1 .or. j .eq. 1 &
752: & .or. i .eq. user%mx .or. j .eq. user%my) then
753: call MatSetValuesLocal(jac,1,row,1,row,one, &
754: & INSERT_VALUES,ierr)
755: ! interior grid points
756: else
757: v(1) = -hxdhy
758: v(2) = -hydhx
759: v(3) = two*(hydhx + hxdhy) &
760: & - sc*user%lambda*exp(x(i,j))
761: v(4) = -hydhx
762: v(5) = -hxdhy
763: col(1) = row - user%gxm
764: col(2) = row - 1
765: col(3) = row
766: col(4) = row + 1
767: col(5) = row + user%gxm
768: call MatSetValuesLocal(jac,1,row,5,col,v, &
769: & INSERT_VALUES,ierr)
770: endif
771: 10 continue
772: 20 continue
774: return
775: end