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: ! TODO: Need to update to latest API
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: #include <petsc/finclude/petscdm.h> 41: use petscdmdef
42: type userctx
43: type(tDM) 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: PetscReal 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(snesIn,X,F,user,ierr)
74: #include <petsc/finclude/petscsnes.h> 75: use petscsnes
77: ! Input/output variables:
78: type(tSNES) snesIn
79: type(tVec) X,F
80: PetscErrorCode ierr
81: type (userctx) user
83: ! Declarations for use with local arrays:
84: PetscScalar,pointer :: lx_v(:),lf_v(:)
85: type(tVec) localX
87: ! Scatter ghost points to local vector, using the 2-step process
88: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
89: ! By placing code between these two statements, computations can
90: ! be done while messages are in transition.
91: call DMGetLocalVector(user%da,localX,ierr);CHKERRQ(ierr)
92: call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
93: call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
95: ! Get a pointer to vector data.
96: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
97: ! the data array. Otherwise, the routine is implementation dependent.
98: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
99: ! the array.
100: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
101: ! and is useable from Fortran-90 Only.
103: call VecGetArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
104: call VecGetArrayF90(F,lf_v,ierr);CHKERRQ(ierr)
106: ! Compute function over the locally owned part of the grid
107: call FormFunctionLocal(lx_v,lf_v,user,ierr);CHKERRQ(ierr)
109: ! Restore vectors
110: call VecRestoreArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
111: call VecRestoreArrayF90(F,lf_v,ierr);CHKERRQ(ierr)
113: ! Insert values into global vector
115: call DMRestoreLocalVector(user%da,localX,ierr);CHKERRQ(ierr)
116: call PetscLogFlops(11.0d0*user%ym*user%xm,ierr)
118: ! call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
119: ! call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
120: return
121: end subroutine formfunction
122: end module f90module
124: module f90moduleinterfaces
125: use f90module
127: Interface SNESSetApplicationContext128: Subroutine SNESSetApplicationContext(snesIn,ctx,ierr)
129: #include <petsc/finclude/petscsnes.h>130: use petscsnes
131: use f90module
132: type(tSNES) snesIn
133: type(userctx) ctx
134: PetscErrorCode ierr
135: End Subroutine
136: End Interface SNESSetApplicationContext138: Interface SNESGetApplicationContext139: Subroutine SNESGetApplicationContext(snesIn,ctx,ierr)
140: #include <petsc/finclude/petscsnes.h>141: use petscsnes
142: use f90module
143: type(tSNES) snesIn
144: type(userctx), pointer :: ctx
145: PetscErrorCode ierr
146: End Subroutine
147: End Interface SNESGetApplicationContext148: end module f90moduleinterfaces
150: program main
151: #include <petsc/finclude/petscdm.h>152: #include <petsc/finclude/petscsnes.h>153: use petscdmda
154: use petscdm
155: use petscsnes
156: use f90module
157: use f90moduleinterfaces
158: implicit none
159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: ! Variable declarations
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: !
163: ! Variables:
164: ! mysnes - nonlinear solver
165: ! x, r - solution, residual vectors
166: ! J - Jacobian matrix
167: ! its - iterations for convergence
168: ! Nx, Ny - number of preocessors in x- and y- directions
169: ! matrix_free - flag - 1 indicates matrix-free version
170: !
171: type(tSNES) mysnes
172: type(tVec) x,r
173: type(tMat) J
174: PetscErrorCode ierr
175: PetscInt its
176: PetscBool flg,matrix_free,set
177: PetscInt ione,nfour
178: PetscReal lambda_max,lambda_min
179: type(userctx) user
180: type(userctx), pointer:: puser
181: type(tPetscOptions) :: options
183: ! Note: Any user-defined Fortran routines (such as FormJacobian)
184: ! MUST be declared as external.
185: external FormInitialGuess,FormJacobian
187: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: ! Initialize program
189: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
191: if (ierr .ne. 0) then
192: print*,'Unable to initialize PETSc'
193: stop
194: endif
195: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
197: ! Initialize problem parameters
198: options%v = 0
199: lambda_max = 6.81
200: lambda_min = 0.0
201: user%lambda = 6.0
202: ione = 1
203: nfour = 4
204: call PetscOptionsGetReal(options,PETSC_NULL_CHARACTER,'-par',user%lambda,flg,ierr);CHKERRA(ierr)
205: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) then
206: if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
207: SETERRA(PETSC_COMM_SELF,1,' ')
208: endif
210: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211: ! Create nonlinear solver context
212: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
213: call SNESCreate(PETSC_COMM_WORLD,mysnes,ierr);CHKERRA(ierr)
215: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
216: ! Create vector data structures; set function evaluation routine
217: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
219: ! Create distributed array (DMDA) to manage parallel grid and vectors
221: ! This really needs only the star-type stencil, but we use the box
222: ! stencil temporarily.
223: call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,ione,ione, &
224: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr);CHKERRA(ierr)
225: call DMSetFromOptions(user%da,ierr);CHKERRA(ierr)
226: call DMSetUp(user%da,ierr);CHKERRA(ierr)
227: call DMDAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
228: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
230: !
231: ! Visualize the distribution of the array across the processors
232: !
233: ! call DMView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)
235: ! Extract global and local vectors from DMDA; then duplicate for remaining
236: ! vectors that are the same types
237: call DMCreateGlobalVector(user%da,x,ierr);CHKERRA(ierr)
238: call VecDuplicate(x,r,ierr);CHKERRA(ierr)
240: ! Get local grid boundaries (for 2-dimensional DMDA)
241: call DMDAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER,user%xm,user%ym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
242: call DMDAGetGhostCorners(user%da,user%gxs,user%gys,PETSC_NULL_INTEGER,user%gxm,user%gym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
244: ! Here we shift the starting indices up by one so that we can easily
245: ! use the Fortran convention of 1-based indices (rather 0-based indices).
246: user%xs = user%xs+1
247: user%ys = user%ys+1
248: user%gxs = user%gxs+1
249: user%gys = user%gys+1
251: user%ye = user%ys+user%ym-1
252: user%xe = user%xs+user%xm-1
253: user%gye = user%gys+user%gym-1
254: user%gxe = user%gxs+user%gxm-1
256: call SNESSetApplicationContext(mysnes,user,ierr);CHKERRA(ierr)
258: ! Set function evaluation routine and vector
259: call SNESSetFunction(mysnes,r,FormFunction,user,ierr);CHKERRA(ierr)
261: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
262: ! Create matrix data structure; set Jacobian evaluation routine
263: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
265: ! Set Jacobian matrix data structure and default Jacobian evaluation
266: ! routine. User can override with:
267: ! -snes_fd : default finite differencing approximation of Jacobian
268: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
269: ! (unless user explicitly sets preconditioner)
270: ! -snes_mf_operator : form preconditioning matrix as set by the user,
271: ! but use matrix-free approx for Jacobian-vector
272: ! products within Newton-Krylov method
273: !
274: ! Note: For the parallel case, vectors and matrices MUST be partitioned
275: ! accordingly. When using distributed arrays (DMDAs) to create vectors,
276: ! the DMDAs determine the problem partitioning. We must explicitly
277: ! specify the local matrix dimensions upon its creation for compatibility
278: ! with the vector distribution. Thus, the generic MatCreate() routine
279: ! is NOT sufficient when working with distributed arrays.
280: !
281: ! Note: Here we only approximately preallocate storage space for the
282: ! Jacobian. See the users manual for a discussion of better techniques
283: ! for preallocating matrix memory.
285: call PetscOptionsHasName(options,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr);CHKERRA(ierr)
286: if (.not. matrix_free) then
287: call DMSetMatType(user%da,MATAIJ,ierr);CHKERRA(ierr)
288: call DMCreateMatrix(user%da,J,ierr);CHKERRA(ierr)
289: call SNESSetJacobian(mysnes,J,J,FormJacobian,user,ierr);CHKERRA(ierr)
290: endif
292: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
293: ! Customize nonlinear solver; set runtime options
294: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
295: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
296: call SNESSetFromOptions(mysnes,ierr);CHKERRA(ierr)
298: ! Test Fortran90 wrapper for SNESSet/Get ApplicationContext()
299: call PetscOptionsGetBool(options,PETSC_NULL_CHARACTER,'-test_appctx',flg,set,ierr);CHKERRA(ierr)
300: if (flg) then
301: call SNESGetApplicationContext(mysnes,puser,ierr);CHKERRA(ierr)
302: endif
304: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
305: ! Evaluate initial guess; then solve nonlinear system.
306: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
307: ! Note: The user should initialize the vector, x, with the initial guess
308: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
309: ! to employ an initial guess of zero, the user should explicitly set
310: ! this vector to zero by calling VecSet().
312: call FormInitialGuess(mysnes,x,ierr);CHKERRA(ierr)
313: call SNESSolve(mysnes,PETSC_NULL_VEC,x,ierr);CHKERRA(ierr)
314: call SNESGetIterationNumber(mysnes,its,ierr);CHKERRA(ierr)
315: if (user%rank .eq. 0) then
316: write(6,100) its
317: endif
318: 100 format('Number of SNES iterations = ',i5)
320: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
321: ! Free work space. All PETSc objects should be destroyed when they
322: ! are no longer needed.
323: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
324: if (.not. matrix_free) call MatDestroy(J,ierr);CHKERRA(ierr)
325: call VecDestroy(x,ierr);CHKERRA(ierr)
326: call VecDestroy(r,ierr);CHKERRA(ierr)
327: call SNESDestroy(mysnes,ierr);CHKERRA(ierr)
328: call DMDestroy(user%da,ierr);CHKERRA(ierr)
330: call PetscFinalize(ierr)
331: end
333: ! ---------------------------------------------------------------------
334: !
335: ! FormInitialGuess - Forms initial approximation.
336: !
337: ! Input Parameters:
338: ! X - vector
339: !
340: ! Output Parameter:
341: ! X - vector
342: !
343: ! Notes:
344: ! This routine serves as a wrapper for the lower-level routine
345: ! "InitialGuessLocal", where the actual computations are
346: ! done using the standard Fortran style of treating the local
347: ! vector data as a multidimensional array over the local mesh.
348: ! This routine merely handles ghost point scatters and accesses
349: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
350: !
351: subroutine FormInitialGuess(mysnes,X,ierr)
352: #include <petsc/finclude/petscsnes.h>353: use petscsnes
354: use f90module
355: use f90moduleinterfaces
356: ! Input/output variables:
357: type(tSNES) mysnes
358: type(userctx), pointer:: puser
359: type(tVec) X
360: PetscErrorCode ierr
362: ! Declarations for use with local arrays:
363: PetscScalar,pointer :: lx_v(:)
365: 0
366: call SNESGetApplicationContext(mysnes,puser,ierr)
367: ! Get a pointer to vector data.
368: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
369: ! the data array. Otherwise, the routine is implementation dependent.
370: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
371: ! the array.
372: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
373: ! and is useable from Fortran-90 Only.
375: call VecGetArrayF90(X,lx_v,ierr)
377: ! Compute initial guess over the locally owned part of the grid
378: call InitialGuessLocal(puser,lx_v,ierr)
380: ! Restore vector
381: call VecRestoreArrayF90(X,lx_v,ierr)
383: ! Insert values into global vector
385: return
386: end
388: ! ---------------------------------------------------------------------
389: !
390: ! InitialGuessLocal - Computes initial approximation, called by
391: ! the higher level routine FormInitialGuess().
392: !
393: ! Input Parameter:
394: ! x - local vector data
395: !
396: ! Output Parameters:
397: ! x - local vector data
398: ! ierr - error code
399: !
400: ! Notes:
401: ! This routine uses standard Fortran-style computations over a 2-dim array.
402: !
403: subroutine InitialGuessLocal(user,x,ierr)
404: #include <petsc/finclude/petscsys.h>405: use petscsys
406: use f90module
407: ! Input/output variables:
408: type (userctx) user
409: PetscScalar x(user%xs:user%xe,user%ys:user%ye)
410: PetscErrorCode ierr
412: ! Local variables:
413: PetscInt i,j
414: PetscScalar temp1,temp,hx,hy
415: PetscScalar one
417: ! Set parameters
419: 0
420: one = 1.0
421: hx = one/(PetscIntToReal(user%mx-1))
422: hy = one/(PetscIntToReal(user%my-1))
423: temp1 = user%lambda/(user%lambda + one)
425: do 20 j=user%ys,user%ye
426: temp = PetscIntToReal(min(j-1,user%my-j))*hy
427: do 10 i=user%xs,user%xe
428: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
429: x(i,j) = 0.0
430: else
431: x(i,j) = temp1 * sqrt(min(PetscIntToReal(min(i-1,user%mx-i)*hx),PetscIntToReal(temp)))
432: endif
433: 10 continue
434: 20 continue
436: return
437: end
439: ! ---------------------------------------------------------------------
440: !
441: ! FormFunctionLocal - Computes nonlinear function, called by
442: ! the higher level routine FormFunction().
443: !
444: ! Input Parameter:
445: ! x - local vector data
446: !
447: ! Output Parameters:
448: ! f - local vector data, f(x)
449: ! ierr - error code
450: !
451: ! Notes:
452: ! This routine uses standard Fortran-style computations over a 2-dim array.
453: !
454: subroutine FormFunctionLocal(x,f,user,ierr)
455: #include <petsc/finclude/petscsys.h>456: use petscsys
457: use f90module
458: ! Input/output variables:
459: type (userctx) user
460: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
461: PetscScalar f(user%xs:user%xe,user%ys:user%ye)
462: PetscErrorCode ierr
464: ! Local variables:
465: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
466: PetscScalar u,uxx,uyy
467: PetscInt i,j
469: one = 1.0
470: two = 2.0
471: hx = one/PetscIntToReal(user%mx-1)
472: hy = one/PetscIntToReal(user%my-1)
473: sc = hx*hy*user%lambda
474: hxdhy = hx/hy
475: hydhx = hy/hx
477: ! Compute function over the locally owned part of the grid
479: do 20 j=user%ys,user%ye
480: do 10 i=user%xs,user%xe
481: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
482: f(i,j) = x(i,j)
483: else
484: u = x(i,j)
485: uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
486: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
487: f(i,j) = uxx + uyy - sc*exp(u)
488: endif
489: 10 continue
490: 20 continue
491: 0
492: return
493: end
495: ! ---------------------------------------------------------------------
496: !
497: ! FormJacobian - Evaluates Jacobian matrix.
498: !
499: ! Input Parameters:
500: ! snes - the SNES context
501: ! x - input vector
502: ! dummy - optional user-defined context, as set by SNESSetJacobian()
503: ! (not used here)
504: !
505: ! Output Parameters:
506: ! jac - Jacobian matrix
507: ! jac_prec - optionally different preconditioning matrix (not used here)
508: ! flag - flag indicating matrix structure
509: !
510: ! Notes:
511: ! This routine serves as a wrapper for the lower-level routine
512: ! "FormJacobianLocal", where the actual computations are
513: ! done using the standard Fortran style of treating the local
514: ! vector data as a multidimensional array over the local mesh.
515: ! This routine merely accesses the local vector data via
516: ! VecGetArrayF90() and VecRestoreArrayF90().
517: !
518: ! Notes:
519: ! Due to grid point reordering with DMDAs, we must always work
520: ! with the local grid points, and then transform them to the new
521: ! global numbering with the "ltog" mapping
522: ! We cannot work directly with the global numbers for the original
523: ! uniprocessor grid!
524: !
525: ! Two methods are available for imposing this transformation
526: ! when setting matrix entries:
527: ! (A) MatSetValuesLocal(), using the local ordering (including
528: ! ghost points!)
529: ! - Set matrix entries using the local ordering
530: ! by calling MatSetValuesLocal()
531: ! (B) MatSetValues(), using the global ordering
532: ! - Use DMGetLocalToGlobalMapping() then
533: ! ISLocalToGlobalMappingGetIndicesF90() to extract the local-to-global map
534: ! - Then apply this map explicitly yourself
535: ! - Set matrix entries using the global ordering by calling
536: ! MatSetValues()
537: ! Option (A) seems cleaner/easier in many cases, and is the procedure
538: ! used in this example.
539: !
540: subroutine FormJacobian(mysnes,X,jac,jac_prec,user,ierr)
541: #include <petsc/finclude/petscsnes.h>542: use petscsnes
543: use f90module
544: ! Input/output variables:
545: type(tSNES) mysnes
546: type(tVec) X
547: type(tMat) jac,jac_prec
548: type(userctx) user
549: PetscErrorCode ierr
551: ! Declarations for use with local arrays:
552: PetscScalar,pointer :: lx_v(:)
553: type(tVec) localX
555: ! Scatter ghost points to local vector, using the 2-step process
556: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
557: ! Computations can be done while messages are in transition,
558: ! by placing code between these two statements.
560: call DMGetLocalVector(user%da,localX,ierr)
561: call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,ierr)
562: call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)
564: ! Get a pointer to vector data
565: call VecGetArrayF90(localX,lx_v,ierr)
567: ! Compute entries for the locally owned part of the Jacobian preconditioner.
568: call FormJacobianLocal(lx_v,jac_prec,user,ierr)
570: ! Assemble matrix, using the 2-step process:
571: ! MatAssemblyBegin(), MatAssemblyEnd()
572: ! Computations can be done while messages are in transition,
573: ! by placing code between these two statements.
575: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
576: ! if (jac .ne. jac_prec) then
577: call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
578: ! endif
579: call VecRestoreArrayF90(localX,lx_v,ierr)
580: call DMRestoreLocalVector(user%da,localX,ierr)
581: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
582: ! if (jac .ne. jac_prec) then
583: call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
584: ! endif
586: ! Tell the matrix we will never add a new nonzero location to the
587: ! matrix. If we do it will generate an error.
589: call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr)
591: return
592: end
594: ! ---------------------------------------------------------------------
595: !
596: ! FormJacobianLocal - Computes Jacobian preconditioner matrix,
597: ! called by the higher level routine FormJacobian().
598: !
599: ! Input Parameters:
600: ! x - local vector data
601: !
602: ! Output Parameters:
603: ! jac_prec - Jacobian preconditioner matrix
604: ! ierr - error code
605: !
606: ! Notes:
607: ! This routine uses standard Fortran-style computations over a 2-dim array.
608: !
609: ! Notes:
610: ! Due to grid point reordering with DMDAs, we must always work
611: ! with the local grid points, and then transform them to the new
612: ! global numbering with the "ltog" mapping
613: ! We cannot work directly with the global numbers for the original
614: ! uniprocessor grid!
615: !
616: ! Two methods are available for imposing this transformation
617: ! when setting matrix entries:
618: ! (A) MatSetValuesLocal(), using the local ordering (including
619: ! ghost points!)
620: ! - Set matrix entries using the local ordering
621: ! by calling MatSetValuesLocal()
622: ! (B) MatSetValues(), using the global ordering
623: ! - Set matrix entries using the global ordering by calling
624: ! MatSetValues()
625: ! Option (A) seems cleaner/easier in many cases, and is the procedure
626: ! used in this example.
627: !
628: subroutine FormJacobianLocal(x,jac_prec,user,ierr)
629: #include <petsc/finclude/petscmat.h>630: use petscmat
631: use f90module
632: ! Input/output variables:
633: type (userctx) user
634: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
635: type(tMat) jac_prec
636: PetscErrorCode ierr
638: ! Local variables:
639: PetscInt row,col(5),i,j
640: PetscInt ione,ifive
641: PetscScalar two,one,hx,hy,hxdhy
642: PetscScalar hydhx,sc,v(5)
644: ! Set parameters
645: ione = 1
646: ifive = 5
647: one = 1.0
648: two = 2.0
649: hx = one/PetscIntToReal(user%mx-1)
650: hy = one/PetscIntToReal(user%my-1)
651: sc = hx*hy
652: hxdhy = hx/hy
653: hydhx = hy/hx
655: ! Compute entries for the locally owned part of the Jacobian.
656: ! - Currently, all PETSc parallel matrix formats are partitioned by
657: ! contiguous chunks of rows across the processors.
658: ! - Each processor needs to insert only elements that it owns
659: ! locally (but any non-local elements will be sent to the
660: ! appropriate processor during matrix assembly).
661: ! - Here, we set all entries for a particular row at once.
662: ! - We can set matrix entries either using either
663: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
664: ! - Note that MatSetValues() uses 0-based row and column numbers
665: ! in Fortran as well as in C.
667: do 20 j=user%ys,user%ye
668: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
669: do 10 i=user%xs,user%xe
670: row = row + 1
671: ! boundary points
672: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
673: col(1) = row
674: v(1) = one
675: call MatSetValuesLocal(jac_prec,ione,row,ione,col,v,INSERT_VALUES,ierr)
676: ! interior grid points
677: else
678: v(1) = -hxdhy
679: v(2) = -hydhx
680: v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i,j))
681: v(4) = -hydhx
682: v(5) = -hxdhy
683: col(1) = row - user%gxm
684: col(2) = row - 1
685: col(3) = row
686: col(4) = row + 1
687: col(5) = row + user%gxm
688: call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v,INSERT_VALUES,ierr)
689: endif
690: 10 continue
691: 20 continue
692: return
693: end