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: #define PETSC_AVOID_DECLARATIONS
41: #include include/finclude/petsc.h
42: #include include/finclude/petscvec.h
43: #include include/finclude/petscda.h
44: #undef PETSC_AVOID_DECLARATIONS
45: DA da
46: PetscInt xs,xe,xm,gxs,gxe,gxm
47: PetscInt ys,ye,ym,gys,gye,gym
48: PetscInt mx,my
49: PetscMPIInt rank
50: double precision lambda
51: end type userctx
53: contains
54: ! ---------------------------------------------------------------------
55: !
56: ! FormFunction - Evaluates nonlinear function, F(x).
57: !
58: ! Input Parameters:
59: ! snes - the SNES context
60: ! X - input vector
61: ! dummy - optional user-defined context, as set by SNESSetFunction()
62: ! (not used here)
63: !
64: ! Output Parameter:
65: ! F - function vector
66: !
67: ! Notes:
68: ! This routine serves as a wrapper for the lower-level routine
69: ! "FormFunctionLocal", where the actual computations are
70: ! done using the standard Fortran style of treating the local
71: ! vector data as a multidimensional array over the local mesh.
72: ! This routine merely handles ghost point scatters and accesses
73: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
74: !
75: subroutine FormFunction(snes,X,F,user,ierr)
76: implicit none
78: #include include/finclude/petsc.h
79: #include include/finclude/petscvec.h
80: #include include/finclude/petscda.h
81: #include include/finclude/petscis.h
82: #include include/finclude/petscmat.h
83: #include include/finclude/petscksp.h
84: #include include/finclude/petscpc.h
85: #include include/finclude/petscsnes.h
86: #include "include/finclude/petscvec.h90"
88: ! Input/output variables:
89: SNES snes
90: Vec X,F
91: PetscErrorCode ierr
92: type (userctx) user
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: ! DAGlobalToLocalBegin(), DAGlobalToLocalEnd().
100: ! By placing code between these two statements, computations can
101: ! be done while messages are in transition.
102: call DAGetLocalVector(user%da,localX,ierr)
103: call DAGlobalToLocalBegin(user%da,X,INSERT_VALUES, &
104: & localX,ierr)
105: call DAGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
107: ! Get a pointer to vector data.
108: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
109: ! the data array. Otherwise, the routine is implementation dependent.
110: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
111: ! the array.
112: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
113: ! and is useable from Fortran-90 Only.
115: call VecGetArrayF90(localX,lx_v,ierr)
116: call VecGetArrayF90(F,lf_v,ierr)
118: ! Compute function over the locally owned part of the grid
119: call FormFunctionLocal(lx_v,lf_v,user,ierr)
121: ! Restore vectors
122: call VecRestoreArrayF90(localX,lx_v,ierr)
123: call VecRestoreArrayF90(F,lf_v,ierr)
125: ! Insert values into global vector
127: call DARestoreLocalVector(user%da,localX,ierr)
128: call PetscLogFlops(11*user%ym*user%xm,ierr)
130: ! call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
131: ! call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
132: return
133: end subroutine formfunction
134: end module f90module
136: module f90moduleinterfaces
137: use f90module
138:
139: Interface SNESSetApplicationContext
140: Subroutine SNESSetApplicationContext(snes,ctx,ierr)
141: use f90module
142: SNES snes
143: type(userctx) ctx
144: PetscErrorCode ierr
145: End Subroutine
146: End Interface SNESSetApplicationContext
148: Interface SNESGetApplicationContext
149: Subroutine SNESGetApplicationContext(snes,ctx,ierr)
150: use f90module
151: SNES snes
152: type(userctx), pointer :: ctx
153: PetscErrorCode ierr
154: End Subroutine
155: End Interface SNESGetApplicationContext
156: end module f90moduleinterfaces
158: program main
159: use f90module
160: use f90moduleinterfaces
161: implicit none
162: !
163: #include include/finclude/petsc.h
164: #include include/finclude/petscvec.h
165: #include include/finclude/petscda.h
166: #include include/finclude/petscis.h
167: #include include/finclude/petscmat.h
168: #include include/finclude/petscksp.h
169: #include include/finclude/petscpc.h
170: #include include/finclude/petscsnes.h
171: #include "include/finclude/petscvec.h90"
172: #include "include/finclude/petscda.h90"
174: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: ! Variable declarations
176: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: !
178: ! Variables:
179: ! snes - nonlinear solver
180: ! x, r - solution, residual vectors
181: ! J - Jacobian matrix
182: ! its - iterations for convergence
183: ! Nx, Ny - number of preocessors in x- and y- directions
184: ! matrix_free - flag - 1 indicates matrix-free version
185: !
186: SNES snes
187: Vec x,r
188: Mat J
189: PetscErrorCode ierr
190: PetscInt its
191: PetscTruth flg,matrix_free
192: PetscInt ione,nfour
193: double precision lambda_max,lambda_min
194: type (userctx) user
195: type(userctx), pointer:: puser
197: ! Note: Any user-defined Fortran routines (such as FormJacobian)
198: ! MUST be declared as external.
199: external FormInitialGuess,FormJacobian
201: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202: ! Initialize program
203: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
205: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
207: ! Initialize problem parameters
208: lambda_max = 6.81
209: lambda_min = 0.0
210: user%lambda = 6.0
211: ione = 1
212: nfour = -4
213: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par', &
214: & user%lambda,flg,ierr)
215: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) &
216: & then
217: if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
218: SETERRQ(1,' ',ierr)
219: endif
221: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
222: ! Create nonlinear solver context
223: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
224: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
226: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
227: ! Create vector data structures; set function evaluation routine
228: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
230: ! Create distributed array (DA) to manage parallel grid and vectors
232: ! This really needs only the star-type stencil, but we use the box
233: ! stencil temporarily.
234: call DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_BOX, &
235: & nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,ione,ione, &
236: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr)
237: call DAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my, &
238: & PETSC_NULL_INTEGER, &
239: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
240: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
241: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
242: & PETSC_NULL_INTEGER,ierr)
243:
244: !
245: ! Visualize the distribution of the array across the processors
246: !
247: ! call DAView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)
249: ! Extract global and local vectors from DA; then duplicate for remaining
250: ! vectors that are the same types
251: call DACreateGlobalVector(user%da,x,ierr)
252: call VecDuplicate(x,r,ierr)
254: ! Get local grid boundaries (for 2-dimensional DA)
255: call DAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER, &
256: & user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
257: call DAGetGhostCorners(user%da,user%gxs,user%gys, &
258: & PETSC_NULL_INTEGER,user%gxm,user%gym, &
259: & PETSC_NULL_INTEGER,ierr)
261: ! Here we shift the starting indices up by one so that we can easily
262: ! use the Fortran convention of 1-based indices (rather 0-based indices).
263: user%xs = user%xs+1
264: user%ys = user%ys+1
265: user%gxs = user%gxs+1
266: user%gys = user%gys+1
268: user%ye = user%ys+user%ym-1
269: user%xe = user%xs+user%xm-1
270: user%gye = user%gys+user%gym-1
271: user%gxe = user%gxs+user%gxm-1
273: call SNESSetApplicationContext(snes,user,ierr)
275: ! Set function evaluation routine and vector
276: call SNESSetFunction(snes,r,FormFunction,user,ierr)
278: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
279: ! Create matrix data structure; set Jacobian evaluation routine
280: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
282: ! Set Jacobian matrix data structure and default Jacobian evaluation
283: ! routine. User can override with:
284: ! -snes_fd : default finite differencing approximation of Jacobian
285: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
286: ! (unless user explicitly sets preconditioner)
287: ! -snes_mf_operator : form preconditioning matrix as set by the user,
288: ! but use matrix-free approx for Jacobian-vector
289: ! products within Newton-Krylov method
290: !
291: ! Note: For the parallel case, vectors and matrices MUST be partitioned
292: ! accordingly. When using distributed arrays (DAs) to create vectors,
293: ! the DAs determine the problem partitioning. We must explicitly
294: ! specify the local matrix dimensions upon its creation for compatibility
295: ! with the vector distribution. Thus, the generic MatCreate() routine
296: ! is NOT sufficient when working with distributed arrays.
297: !
298: ! Note: Here we only approximately preallocate storage space for the
299: ! Jacobian. See the users manual for a discussion of better techniques
300: ! for preallocating matrix memory.
301:
302: call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf', &
303: & matrix_free,ierr)
304: if (.not. matrix_free) then
305: call DAGetMatrix(user%da,MATAIJ,J,ierr)
306: call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)
307: endif
309: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
310: ! Customize nonlinear solver; set runtime options
311: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
312: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
313: call SNESSetFromOptions(snes,ierr)
315: ! Test Fortran90 wrapper for SNESSet/Get ApplicationContext()
316: call PetscOptionsGetTruth(PETSC_NULL_CHARACTER,'-test_appctx', &
317: & flg,PETSC_NULL_CHARACTER,ierr)
318: if (flg) then
319: call SNESGetApplicationContext(snes,puser,ierr)
320: if (user%da .ne. puser%da) then
321: write(*,*) "Error: uesr != puesr"
322: write(*,*) "user: ", user
323: write(*,*) "puesr: ", puser
324: endif
325: endif
327: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
328: ! Evaluate initial guess; then solve nonlinear system.
329: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
330: ! Note: The user should initialize the vector, x, with the initial guess
331: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
332: ! to employ an initial guess of zero, the user should explicitly set
333: ! this vector to zero by calling VecSet().
335: call FormInitialGuess(snes,x,ierr)
336: call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
337: call SNESGetIterationNumber(snes,its,ierr);
338: if (user%rank .eq. 0) then
339: write(6,100) its
340: endif
341: 100 format('Number of Newton iterations = ',i5)
343: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
344: ! Free work space. All PETSc objects should be destroyed when they
345: ! are no longer needed.
346: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
347: if (.not. matrix_free) call MatDestroy(J,ierr)
348: call VecDestroy(x,ierr)
349: call VecDestroy(r,ierr)
350: call SNESDestroy(snes,ierr)
351: call DADestroy(user%da,ierr)
353: call PetscFinalize(ierr)
354: end
356: ! ---------------------------------------------------------------------
357: !
358: ! FormInitialGuess - Forms initial approximation.
359: !
360: ! Input Parameters:
361: ! X - vector
362: !
363: ! Output Parameter:
364: ! X - vector
365: !
366: ! Notes:
367: ! This routine serves as a wrapper for the lower-level routine
368: ! "InitialGuessLocal", where the actual computations are
369: ! done using the standard Fortran style of treating the local
370: ! vector data as a multidimensional array over the local mesh.
371: ! This routine merely handles ghost point scatters and accesses
372: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
373: !
374: subroutine FormInitialGuess(snes,X,ierr)
375: use f90module
376: use f90moduleinterfaces
377: implicit none
379: #include "include/finclude/petscvec.h90"
380: #include include/finclude/petsc.h
381: #include include/finclude/petscvec.h
382: #include include/finclude/petscda.h
383: #include include/finclude/petscis.h
384: #include include/finclude/petscmat.h
385: #include include/finclude/petscksp.h
386: #include include/finclude/petscpc.h
387: #include include/finclude/petscsnes.h
389: ! Input/output variables:
390: SNES snes
391: type(userctx), pointer:: puser
392: Vec X
393: PetscErrorCode ierr
394:
395: ! Declarations for use with local arrays:
396: PetscScalar,pointer :: lx_v(:)
397: Vec localX
399: 0
400: call SNESGetApplicationContext(snes,puser,ierr)
401: ! Get a pointer to vector data.
402: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
403: ! the data array. Otherwise, the routine is implementation dependent.
404: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
405: ! the array.
406: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
407: ! and is useable from Fortran-90 Only.
409: call DAGetLocalVector(puser%da,localX,ierr)
410: call VecGetArrayF90(localX,lx_v,ierr)
412: ! Compute initial guess over the locally owned part of the grid
413: call InitialGuessLocal(puser,lx_v,ierr)
415: ! Restore vector
416: call VecRestoreArrayF90(localX,lx_v,ierr)
418: ! Insert values into global vector
419: call DALocalToGlobal(puser%da,localX,INSERT_VALUES,X,ierr)
420: call DARestoreLocalVector(puser%da,localX,ierr)
422: return
423: end
425: ! ---------------------------------------------------------------------
426: !
427: ! InitialGuessLocal - Computes initial approximation, called by
428: ! the higher level routine FormInitialGuess().
429: !
430: ! Input Parameter:
431: ! x - local vector data
432: !
433: ! Output Parameters:
434: ! x - local vector data
435: ! ierr - error code
436: !
437: ! Notes:
438: ! This routine uses standard Fortran-style computations over a 2-dim array.
439: !
440: subroutine InitialGuessLocal(user,x,ierr)
441: use f90module
442: implicit none
444: #include include/finclude/petsc.h
445: #include include/finclude/petscvec.h
446: #include include/finclude/petscda.h
447: #include include/finclude/petscis.h
448: #include include/finclude/petscmat.h
449: #include include/finclude/petscksp.h
450: #include include/finclude/petscpc.h
451: #include 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 DAs, we must always work
574: ! with the local grid points, and then transform them to the new
575: ! global numbering with the "ltog" mapping (via DAGetGlobalIndicesF90()).
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: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
584: ! - Associate this map with the matrix by calling
585: ! MatSetLocalToGlobalMapping() once
586: ! - Set matrix entries using the local ordering
587: ! by calling MatSetValuesLocal()
588: ! (B) MatSetValues(), using the global ordering
589: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
590: ! - Then apply this map explicitly yourself
591: ! - Set matrix entries using the global ordering by calling
592: ! MatSetValues()
593: ! Option (A) seems cleaner/easier in many cases, and is the procedure
594: ! used in this example.
595: !
596: subroutine FormJacobian(snes,X,jac,jac_prec,flag,user,ierr)
597: use f90module
598: implicit none
600: #include include/finclude/petsc.h
601: #include include/finclude/petscvec.h
602: #include include/finclude/petscda.h
603: #include include/finclude/petscis.h
604: #include include/finclude/petscmat.h
605: #include include/finclude/petscksp.h
606: #include include/finclude/petscpc.h
607: #include include/finclude/petscsnes.h
609: #include "include/finclude/petscvec.h90"
611: ! Input/output variables:
612: SNES snes
613: Vec X
614: Mat jac,jac_prec
615: MatStructure flag
616: type(userctx) user
617: PetscErrorCode ierr
619: ! Declarations for use with local arrays:
620: PetscScalar,pointer :: lx_v(:)
621: Vec localX
623: ! Scatter ghost points to local vector, using the 2-step process
624: ! DAGlobalToLocalBegin(), DAGlobalToLocalEnd()
625: ! Computations can be done while messages are in transition,
626: ! by placing code between these two statements.
628: call DAGetLocalVector(user%da,localX,ierr)
629: call DAGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX, &
630: & ierr)
631: call DAGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
633: ! Get a pointer to vector data
634: call VecGetArrayF90(localX,lx_v,ierr)
636: ! Compute entries for the locally owned part of the Jacobian preconditioner.
637: call FormJacobianLocal(lx_v,jac_prec,user,ierr)
639: ! Assemble matrix, using the 2-step process:
640: ! MatAssemblyBegin(), MatAssemblyEnd()
641: ! Computations can be done while messages are in transition,
642: ! by placing code between these two statements.
644: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
645: if (jac .ne. jac_prec) then
646: call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
647: endif
648: call VecRestoreArrayF90(localX,lx_v,ierr)
649: call DARestoreLocalVector(user%da,localX,ierr)
650: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
651: if (jac .ne. jac_prec) then
652: call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
653: endif
654:
655: ! Set flag to indicate that the Jacobian matrix retains an identical
656: ! nonzero structure throughout all nonlinear iterations (although the
657: ! values of the entries change). Thus, we can save some work in setting
658: ! up the preconditioner (e.g., no need to redo symbolic factorization for
659: ! ILU/ICC preconditioners).
660: ! - If the nonzero structure of the matrix is different during
661: ! successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
662: ! must be used instead. If you are unsure whether the matrix
663: ! structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
664: ! - Caution: If you specify SAME_NONZERO_PATTERN, PETSc
665: ! believes your assertion and does not check the structure
666: ! of the matrix. If you erroneously claim that the structure
667: ! is the same when it actually is not, the new preconditioner
668: ! will not function correctly. Thus, use this optimization
669: ! feature with caution!
671: flag = SAME_NONZERO_PATTERN
673: ! Tell the matrix we will never add a new nonzero location to the
674: ! matrix. If we do it will generate an error.
676: call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE, &
677: & ierr)
679: return
680: end
682: ! ---------------------------------------------------------------------
683: !
684: ! FormJacobianLocal - Computes Jacobian preconditioner matrix,
685: ! called by the higher level routine FormJacobian().
686: !
687: ! Input Parameters:
688: ! x - local vector data
689: !
690: ! Output Parameters:
691: ! jac_prec - Jacobian preconditioner matrix
692: ! ierr - error code
693: !
694: ! Notes:
695: ! This routine uses standard Fortran-style computations over a 2-dim array.
696: !
697: ! Notes:
698: ! Due to grid point reordering with DAs, we must always work
699: ! with the local grid points, and then transform them to the new
700: ! global numbering with the "ltog" mapping (via DAGetGlobalIndicesF90()).
701: ! We cannot work directly with the global numbers for the original
702: ! uniprocessor grid!
703: !
704: ! Two methods are available for imposing this transformation
705: ! when setting matrix entries:
706: ! (A) MatSetValuesLocal(), using the local ordering (including
707: ! ghost points!)
708: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
709: ! - Associate this map with the matrix by calling
710: ! MatSetLocalToGlobalMapping() once
711: ! - Set matrix entries using the local ordering
712: ! by calling MatSetValuesLocal()
713: ! (B) MatSetValues(), using the global ordering
714: ! - Use DAGetGlobalIndicesF90() to extract the local-to-global map
715: ! - Then apply this map explicitly yourself
716: ! - Set matrix entries using the global ordering by calling
717: ! MatSetValues()
718: ! Option (A) seems cleaner/easier in many cases, and is the procedure
719: ! used in this example.
720: !
721: subroutine FormJacobianLocal(x,jac_prec,user,ierr)
722: use f90module
723: implicit none
725: #include include/finclude/petsc.h
726: #include include/finclude/petscvec.h
727: #include include/finclude/petscda.h
728: #include include/finclude/petscis.h
729: #include include/finclude/petscmat.h
730: #include include/finclude/petscksp.h
731: #include include/finclude/petscpc.h
732: #include include/finclude/petscsnes.h
734: ! Input/output variables:
735: type (userctx) user
736: PetscScalar x(user%gxs:user%gxe, &
737: & user%gys:user%gye)
738: Mat jac_prec
739: PetscErrorCode ierr
741: ! Local variables:
742: PetscInt row,col(5),i,j
743: PetscInt ione,ifive
744: PetscScalar two,one,hx,hy,hxdhy
745: PetscScalar hydhx,sc,v(5)
747: ! Set parameters
748: ione = 1
749: ifive = 5
750: one = 1.0
751: two = 2.0
752: hx = one/dble(user%mx-1)
753: hy = one/dble(user%my-1)
754: sc = hx*hy
755: hxdhy = hx/hy
756: hydhx = hy/hx
758: ! Compute entries for the locally owned part of the Jacobian.
759: ! - Currently, all PETSc parallel matrix formats are partitioned by
760: ! contiguous chunks of rows across the processors.
761: ! - Each processor needs to insert only elements that it owns
762: ! locally (but any non-local elements will be sent to the
763: ! appropriate processor during matrix assembly).
764: ! - Here, we set all entries for a particular row at once.
765: ! - We can set matrix entries either using either
766: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
767: ! - Note that MatSetValues() uses 0-based row and column numbers
768: ! in Fortran as well as in C.
770: do 20 j=user%ys,user%ye
771: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
772: do 10 i=user%xs,user%xe
773: row = row + 1
774: ! boundary points
775: if (i .eq. 1 .or. j .eq. 1 &
776: & .or. i .eq. user%mx .or. j .eq. user%my) then
777: col(1) = row
778: v(1) = one
779: call MatSetValuesLocal(jac_prec,ione,row,ione,col,v, &
780: & INSERT_VALUES,ierr)
781: ! interior grid points
782: else
783: v(1) = -hxdhy
784: v(2) = -hydhx
785: v(3) = two*(hydhx + hxdhy) &
786: & - sc*user%lambda*exp(x(i,j))
787: v(4) = -hydhx
788: v(5) = -hxdhy
789: col(1) = row - user%gxm
790: col(2) = row - 1
791: col(3) = row
792: col(4) = row + 1
793: col(5) = row + user%gxm
794: call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v, &
795: & INSERT_VALUES,ierr)
796: endif
797: 10 continue
798: 20 continue
800: return
801: end