1: !
2: ! Description: Solves a nonlinear system in parallel with SNES.
3: ! We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
4: ! domain, using distributed arrays (DMDAs) to partition the parallel grid.
5: ! The command line options include:
6: ! -par <parameter>, where <parameter> indicates the nonlinearity of the problem
7: ! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)
8: !
9: !/*T
10: ! Concepts: SNES^parallel Bratu example
11: ! Concepts: DMDA^using distributed arrays;
12: ! Processors: n
13: !T*/
14: !
15: ! --------------------------------------------------------------------------
16: !
17: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
18: ! the partial differential equation
19: !
20: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
21: !
22: ! with boundary conditions
23: !
24: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
25: !
26: ! A finite difference approximation with the usual 5-point stencil
27: ! is used to discretize the boundary value problem to obtain a nonlinear
28: ! system of equations.
29: !
30: ! The uniprocessor version of this code is snes/examples/tutorials/ex4f.F
31: !
32: ! --------------------------------------------------------------------------
33: ! The following define must be used before including any PETSc include files
34: ! into a module or interface. This is because they can't handle declarations
35: ! in them
36: !
38: module f90module
39: use petscsys
40: use petscis
41: use petscvec
42: use petscdm
43: use petscdmda
44: use petscmat
45: use petscpc
46: use petscksp
47: use petscsnes
48: #include <petsc/finclude/petscsnes.h> 49: type userctx
50: PetscInt xs,xe,xm,gxs,gxe,gxm
51: PetscInt ys,ye,ym,gys,gye,gym
52: PetscInt mx,my
53: PetscMPIInt rank
54: PetscReal lambda
55: end type userctx
57: contains
58: ! ---------------------------------------------------------------------
59: !
60: ! FormFunction - Evaluates nonlinear function, F(x).
61: !
62: ! Input Parameters:
63: ! snes - the SNES context
64: ! X - input vector
65: ! dummy - optional user-defined context, as set by SNESSetFunction()
66: ! (not used here)
67: !
68: ! Output Parameter:
69: ! F - function vector
70: !
71: ! Notes:
72: ! This routine serves as a wrapper for the lower-level routine
73: ! "FormFunctionLocal", where the actual computations are
74: ! done using the standard Fortran style of treating the local
75: ! vector data as a multidimensional array over the local mesh.
76: ! This routine merely handles ghost point scatters and accesses
77: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
78: !
79: subroutine FormFunction(snes,X,F,user,ierr)
80: implicit none
82: ! Input/output variables:
83: SNES snes
84: Vec X,F
85: PetscErrorCode ierr
86: type (userctx) user
87: DM da
89: ! Declarations for use with local arrays:
90: PetscScalar,pointer :: lx_v(:),lf_v(:)
91: Vec localX
93: ! Scatter ghost points to local vector, using the 2-step process
94: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
95: ! By placing code between these two statements, computations can
96: ! be done while messages are in transition.
97: call SNESGetDM(snes,da,ierr);CHKERRQ(ierr)
98: call DMGetLocalVector(da,localX,ierr);CHKERRQ(ierr)
99: call DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
100: call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
102: ! Get a pointer to vector data.
103: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
104: ! the data array. Otherwise, the routine is implementation dependent.
105: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
106: ! the array.
107: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
108: ! and is useable from Fortran-90 Only.
110: call VecGetArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
111: call VecGetArrayF90(F,lf_v,ierr);CHKERRQ(ierr)
113: ! Compute function over the locally owned part of the grid
114: call FormFunctionLocal(lx_v,lf_v,user,ierr);CHKERRQ(ierr)
116: ! Restore vectors
117: call VecRestoreArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
118: call VecRestoreArrayF90(F,lf_v,ierr);CHKERRQ(ierr)
120: ! Insert values into global vector
122: call DMRestoreLocalVector(da,localX,ierr);CHKERRQ(ierr)
123: call PetscLogFlops(11.0d0*user%ym*user%xm,ierr)
125: ! call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
126: ! call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
127: return
128: end subroutine formfunction
129: end module f90module
131: module f90moduleinterfaces
132: use f90module
134: Interface SNESSetApplicationContext135: Subroutine SNESSetApplicationContext(snes,ctx,ierr)
136: use f90module
137: SNES snes
138: type(userctx) ctx
139: PetscErrorCode ierr
140: End Subroutine
141: End Interface SNESSetApplicationContext143: Interface SNESGetApplicationContext144: Subroutine SNESGetApplicationContext(snes,ctx,ierr)
145: use f90module
146: SNES snes
147: type(userctx), pointer :: ctx
148: PetscErrorCode ierr
149: End Subroutine
150: End Interface SNESGetApplicationContext151: end module f90moduleinterfaces
153: program main
154: use f90module
155: use f90moduleinterfaces
156: implicit none
157: !
159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: ! Variable declarations
161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162: !
163: ! Variables:
164: ! snes - 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: SNES snes
172: Vec x,r
173: Mat J
174: PetscErrorCode ierr
175: PetscInt its
176: PetscBool flg,matrix_free
177: PetscInt ione,nfour
178: PetscReal lambda_max,lambda_min
179: type (userctx) user
180: DM da
182: ! Note: Any user-defined Fortran routines (such as FormJacobian)
183: ! MUST be declared as external.
184: external FormInitialGuess,FormJacobian
186: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187: ! Initialize program
188: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
189: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
190: if (ierr .ne. 0) then
191: print*,'Unable to initialize PETSc'
192: stop
193: endif
194: call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)
196: ! Initialize problem parameters
197: lambda_max = 6.81
198: lambda_min = 0.0
199: user%lambda = 6.0
200: ione = 1
201: nfour = 4
202: call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',user%lambda,flg,ierr);CHKERRA(ierr)
203: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) then
204: if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
205: SETERRA(PETSC_COMM_SELF,1,' ')
206: endif
208: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
209: ! Create nonlinear solver context
210: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
211: call SNESCreate(PETSC_COMM_WORLD,snes,ierr);CHKERRA(ierr)
213: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
214: ! Create vector data structures; set function evaluation routine
215: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
217: ! Create distributed array (DMDA) to manage parallel grid and vectors
219: ! This really needs only the star-type stencil, but we use the box
220: ! stencil temporarily.
221: call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,ione,ione, &
222: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr);CHKERRA(ierr)
223: call DMSetFromOptions(da,ierr)
224: call DMSetUp(da,ierr)
226: call DMDAGetInfo(da,PETSC_NULL_INTEGER,user%mx,user%my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
227: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
229: !
230: ! Visualize the distribution of the array across the processors
231: !
232: ! call DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr)
234: ! Extract global and local vectors from DMDA; then duplicate for remaining
235: ! vectors that are the same types
236: call DMCreateGlobalVector(da,x,ierr);CHKERRA(ierr)
237: call VecDuplicate(x,r,ierr);CHKERRA(ierr)
239: ! Get local grid boundaries (for 2-dimensional DMDA)
240: call DMDAGetCorners(da,user%xs,user%ys,PETSC_NULL_INTEGER,user%xm,user%ym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
241: call DMDAGetGhostCorners(da,user%gxs,user%gys,PETSC_NULL_INTEGER,user%gxm,user%gym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
243: ! Here we shift the starting indices up by one so that we can easily
244: ! use the Fortran convention of 1-based indices (rather 0-based indices).
245: user%xs = user%xs+1
246: user%ys = user%ys+1
247: user%gxs = user%gxs+1
248: user%gys = user%gys+1
250: user%ye = user%ys+user%ym-1
251: user%xe = user%xs+user%xm-1
252: user%gye = user%gys+user%gym-1
253: user%gxe = user%gxs+user%gxm-1
255: call SNESSetApplicationContext(snes,user,ierr);CHKERRA(ierr)
257: ! Set function evaluation routine and vector
258: call SNESSetFunction(snes,r,FormFunction,user,ierr);CHKERRA(ierr)
260: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
261: ! Create matrix data structure; set Jacobian evaluation routine
262: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
264: ! Set Jacobian matrix data structure and default Jacobian evaluation
265: ! routine. User can override with:
266: ! -snes_fd : default finite differencing approximation of Jacobian
267: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
268: ! (unless user explicitly sets preconditioner)
269: ! -snes_mf_operator : form preconditioning matrix as set by the user,
270: ! but use matrix-free approx for Jacobian-vector
271: ! products within Newton-Krylov method
272: !
273: ! Note: For the parallel case, vectors and matrices MUST be partitioned
274: ! accordingly. When using distributed arrays (DMDAs) to create vectors,
275: ! the DMDAs determine the problem partitioning. We must explicitly
276: ! specify the local matrix dimensions upon its creation for compatibility
277: ! with the vector distribution. Thus, the generic MatCreate() routine
278: ! is NOT sufficient when working with distributed arrays.
279: !
280: ! Note: Here we only approximately preallocate storage space for the
281: ! Jacobian. See the users manual for a discussion of better techniques
282: ! for preallocating matrix memory.
284: call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr);CHKERRA(ierr)
285: if (.not. matrix_free) then
286: call DMSetMatType(da,MATAIJ,ierr);CHKERRA(ierr)
287: call DMCreateMatrix(da,J,ierr);CHKERRA(ierr)
288: call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr);CHKERRA(ierr)
289: endif
291: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
292: ! Customize nonlinear solver; set runtime options
293: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
294: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
295: call SNESSetDM(snes,da,ierr);CHKERRA(ierr)
296: call SNESSetFromOptions(snes,ierr);CHKERRA(ierr)
299: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
300: ! Evaluate initial guess; then solve nonlinear system.
301: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
302: ! Note: The user should initialize the vector, x, with the initial guess
303: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
304: ! to employ an initial guess of zero, the user should explicitly set
305: ! this vector to zero by calling VecSet().
307: call FormInitialGuess(snes,x,ierr);CHKERRA(ierr)
308: call SNESSolve(snes,PETSC_NULL_VEC,x,ierr);CHKERRA(ierr)
309: call SNESGetIterationNumber(snes,its,ierr);;CHKERRA(ierr)
310: if (user%rank .eq. 0) then
311: write(6,100) its
312: endif
313: 100 format('Number of SNES iterations = ',i5)
315: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
316: ! Free work space. All PETSc objects should be destroyed when they
317: ! are no longer needed.
318: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
319: if (.not. matrix_free) call MatDestroy(J,ierr);CHKERRA(ierr)
320: call VecDestroy(x,ierr);CHKERRA(ierr)
321: call VecDestroy(r,ierr);CHKERRA(ierr)
322: call SNESDestroy(snes,ierr);CHKERRA(ierr)
323: call DMDestroy(da,ierr);CHKERRA(ierr)
325: call PetscFinalize(ierr)
326: end
328: ! ---------------------------------------------------------------------
329: !
330: ! FormInitialGuess - Forms initial approximation.
331: !
332: ! Input Parameters:
333: ! X - vector
334: !
335: ! Output Parameter:
336: ! X - vector
337: !
338: ! Notes:
339: ! This routine serves as a wrapper for the lower-level routine
340: ! "InitialGuessLocal", where the actual computations are
341: ! done using the standard Fortran style of treating the local
342: ! vector data as a multidimensional array over the local mesh.
343: ! This routine merely handles ghost point scatters and accesses
344: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
345: !
346: subroutine FormInitialGuess(snes,X,ierr)
347: use f90module
348: use f90moduleinterfaces
349: implicit none
351: ! Input/output variables:
352: SNES snes
353: type(userctx), pointer:: puser
354: Vec X
355: PetscErrorCode ierr
356: DM da
358: ! Declarations for use with local arrays:
359: PetscScalar,pointer :: lx_v(:)
361: 0
362: call SNESGetDM(snes,da,ierr);CHKERRQ(ierr)
363: call SNESGetApplicationContext(snes,puser,ierr);CHKERRQ(ierr)
364: ! Get a pointer to vector data.
365: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
366: ! the data array. Otherwise, the routine is implementation dependent.
367: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
368: ! the array.
369: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
370: ! and is useable from Fortran-90 Only.
372: call VecGetArrayF90(X,lx_v,ierr);CHKERRQ(ierr)
374: ! Compute initial guess over the locally owned part of the grid
375: call InitialGuessLocal(puser,lx_v,ierr);CHKERRQ(ierr)
377: ! Restore vector
378: call VecRestoreArrayF90(X,lx_v,ierr);CHKERRQ(ierr)
380: ! Insert values into global vector
382: return
383: end
385: ! ---------------------------------------------------------------------
386: !
387: ! InitialGuessLocal - Computes initial approximation, called by
388: ! the higher level routine FormInitialGuess().
389: !
390: ! Input Parameter:
391: ! x - local vector data
392: !
393: ! Output Parameters:
394: ! x - local vector data
395: ! ierr - error code
396: !
397: ! Notes:
398: ! This routine uses standard Fortran-style computations over a 2-dim array.
399: !
400: subroutine InitialGuessLocal(user,x,ierr)
401: use f90module
402: implicit none
404: ! Input/output variables:
405: type (userctx) user
406: PetscScalar x(user%xs:user%xe,user%ys:user%ye)
407: PetscErrorCode ierr
409: ! Local variables:
410: PetscInt i,j
411: PetscReal temp1,temp,hx,hy
412: PetscReal one
414: ! Set parameters
416: 0
417: one = 1.0
418: hx = one/(user%mx-1)
419: hy = one/(user%my-1)
420: temp1 = user%lambda/(user%lambda + one)
422: do 20 j=user%ys,user%ye
423: temp = min(j-1,user%my-j)*hy
424: do 10 i=user%xs,user%xe
425: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
426: x(i,j) = 0.0
427: else
428: x(i,j) = temp1 * sqrt(min(hx*min(i-1,user%mx-i),temp))
429: endif
430: 10 continue
431: 20 continue
433: return
434: end
436: ! ---------------------------------------------------------------------
437: !
438: ! FormFunctionLocal - Computes nonlinear function, called by
439: ! the higher level routine FormFunction().
440: !
441: ! Input Parameter:
442: ! x - local vector data
443: !
444: ! Output Parameters:
445: ! f - local vector data, f(x)
446: ! ierr - error code
447: !
448: ! Notes:
449: ! This routine uses standard Fortran-style computations over a 2-dim array.
450: !
451: subroutine FormFunctionLocal(x,f,user,ierr)
452: use f90module
454: implicit none
456: ! Input/output variables:
457: type (userctx) user
458: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
459: PetscScalar f(user%xs:user%xe,user%ys:user%ye)
460: PetscErrorCode ierr
462: ! Local variables:
463: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
464: PetscScalar u,uxx,uyy
465: PetscInt i,j
467: one = 1.0
468: two = 2.0
469: hx = one/(user%mx-1)
470: hy = one/(user%my-1)
471: sc = hx*hy*user%lambda
472: hxdhy = hx/hy
473: hydhx = hy/hx
475: ! Compute function over the locally owned part of the grid
477: do 20 j=user%ys,user%ye
478: do 10 i=user%xs,user%xe
479: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
480: f(i,j) = x(i,j)
481: else
482: u = x(i,j)
483: uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
484: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
485: f(i,j) = uxx + uyy - sc*exp(u)
486: endif
487: 10 continue
488: 20 continue
490: return
491: end
493: ! ---------------------------------------------------------------------
494: !
495: ! FormJacobian - Evaluates Jacobian matrix.
496: !
497: ! Input Parameters:
498: ! snes - the SNES context
499: ! x - input vector
500: ! dummy - optional user-defined context, as set by SNESSetJacobian()
501: ! (not used here)
502: !
503: ! Output Parameters:
504: ! jac - Jacobian matrix
505: ! jac_prec - optionally different preconditioning matrix (not used here)
506: ! flag - flag indicating matrix structure
507: !
508: ! Notes:
509: ! This routine serves as a wrapper for the lower-level routine
510: ! "FormJacobianLocal", where the actual computations are
511: ! done using the standard Fortran style of treating the local
512: ! vector data as a multidimensional array over the local mesh.
513: ! This routine merely accesses the local vector data via
514: ! VecGetArrayF90() and VecRestoreArrayF90().
515: !
516: ! Notes:
517: ! Due to grid point reordering with DMDAs, we must always work
518: ! with the local grid points, and then transform them to the new
519: ! global numbering with the "ltog" mapping
520: ! We cannot work directly with the global numbers for the original
521: ! uniprocessor grid!
522: !
523: ! Two methods are available for imposing this transformation
524: ! when setting matrix entries:
525: ! (A) MatSetValuesLocal(), using the local ordering (including
526: ! ghost points!)
527: ! - Set matrix entries using the local ordering
528: ! by calling MatSetValuesLocal()
529: ! (B) MatSetValues(), using the global ordering
531: ! - Set matrix entries using the global ordering by calling
532: ! MatSetValues()
533: ! Option (A) seems cleaner/easier in many cases, and is the procedure
534: ! used in this example.
535: !
536: subroutine FormJacobian(snes,X,jac,jac_prec,user,ierr)
537: use f90module
538: implicit none
540: ! Input/output variables:
541: SNES snes
542: Vec X
543: Mat jac,jac_prec
544: type(userctx) user
545: PetscErrorCode ierr
546: DM da
548: ! Declarations for use with local arrays:
549: PetscScalar,pointer :: lx_v(:)
550: Vec localX
552: ! Scatter ghost points to local vector, using the 2-step process
553: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
554: ! Computations can be done while messages are in transition,
555: ! by placing code between these two statements.
557: call SNESGetDM(snes,da,ierr);CHKERRQ(ierr)
558: call DMGetLocalVector(da,localX,ierr);CHKERRQ(ierr)
559: call DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
560: call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
562: ! Get a pointer to vector data
563: call VecGetArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
565: ! Compute entries for the locally owned part of the Jacobian preconditioner.
566: call FormJacobianLocal(lx_v,jac_prec,user,ierr);CHKERRQ(ierr)
568: ! Assemble matrix, using the 2-step process:
569: ! MatAssemblyBegin(), MatAssemblyEnd()
570: ! Computations can be done while messages are in transition,
571: ! by placing code between these two statements.
573: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(ierr)
574: if (jac .ne. jac_prec) then
575: call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(ierr)
576: endif
577: call VecRestoreArrayF90(localX,lx_v,ierr);CHKERRQ(ierr)
578: call DMRestoreLocalVector(da,localX,ierr);CHKERRQ(ierr)
579: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(ierr)
580: if (jac .ne. jac_prec) then
581: call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(ierr)
582: endif
584: ! Tell the matrix we will never add a new nonzero location to the
585: ! matrix. If we do it will generate an error.
587: call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr);CHKERRQ(ierr)
589: return
590: end
592: ! ---------------------------------------------------------------------
593: !
594: ! FormJacobianLocal - Computes Jacobian preconditioner matrix,
595: ! called by the higher level routine FormJacobian().
596: !
597: ! Input Parameters:
598: ! x - local vector data
599: !
600: ! Output Parameters:
601: ! jac_prec - Jacobian preconditioner matrix
602: ! ierr - error code
603: !
604: ! Notes:
605: ! This routine uses standard Fortran-style computations over a 2-dim array.
606: !
607: ! Notes:
608: ! Due to grid point reordering with DMDAs, we must always work
609: ! with the local grid points, and then transform them to the new
610: ! global numbering with the "ltog" mapping
611: ! We cannot work directly with the global numbers for the original
612: ! uniprocessor grid!
613: !
614: ! Two methods are available for imposing this transformation
615: ! when setting matrix entries:
616: ! (A) MatSetValuesLocal(), using the local ordering (including
617: ! ghost points!)
618: ! - Set matrix entries using the local ordering
619: ! by calling MatSetValuesLocal()
620: ! (B) MatSetValues(), using the global ordering
621: ! - Then apply this map explicitly yourself
622: ! - Set matrix entries using the global ordering by calling
623: ! MatSetValues()
624: ! Option (A) seems cleaner/easier in many cases, and is the procedure
625: ! used in this example.
626: !
627: subroutine FormJacobianLocal(x,jac_prec,user,ierr)
628: use f90module
629: implicit none
633: ! Input/output variables:
634: type (userctx) user
635: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
636: Mat jac_prec
637: PetscErrorCode ierr
639: ! Local variables:
640: PetscInt row,col(5),i,j
641: PetscInt ione,ifive
642: PetscScalar two,one,hx,hy,hxdhy
643: PetscScalar hydhx,sc,v(5)
645: ! Set parameters
646: ione = 1
647: ifive = 5
648: one = 1.0
649: two = 2.0
650: hx = one/(user%mx-1)
651: hy = one/(user%my-1)
652: sc = hx*hy
653: hxdhy = hx/hy
654: hydhx = hy/hx
656: ! Compute entries for the locally owned part of the Jacobian.
657: ! - Currently, all PETSc parallel matrix formats are partitioned by
658: ! contiguous chunks of rows across the processors.
659: ! - Each processor needs to insert only elements that it owns
660: ! locally (but any non-local elements will be sent to the
661: ! appropriate processor during matrix assembly).
662: ! - Here, we set all entries for a particular row at once.
663: ! - We can set matrix entries either using either
664: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
665: ! - Note that MatSetValues() uses 0-based row and column numbers
666: ! in Fortran as well as in C.
668: do 20 j=user%ys,user%ye
669: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
670: do 10 i=user%xs,user%xe
671: row = row + 1
672: ! boundary points
673: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
674: col(1) = row
675: v(1) = one
676: call MatSetValuesLocal(jac_prec,ione,row,ione,col,v,INSERT_VALUES,ierr);CHKERRQ(ierr)
677: ! interior grid points
678: else
679: v(1) = -hxdhy
680: v(2) = -hydhx
681: v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i,j))
682: v(4) = -hydhx
683: v(5) = -hxdhy
684: col(1) = row - user%gxm
685: col(2) = row - 1
686: col(3) = row
687: col(4) = row + 1
688: col(5) = row + user%gxm
689: call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v,INSERT_VALUES,ierr);CHKERRQ(ierr)
690: endif
691: 10 continue
692: 20 continue
694: return
695: end