Actual source code: ex5f90.F90
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: !
10: !
11: ! --------------------------------------------------------------------------
12: !
13: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
14: ! the partial differential equation
15: !
16: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
17: !
18: ! with boundary conditions
19: !
20: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
21: !
22: ! A finite difference approximation with the usual 5-point stencil
23: ! is used to discretize the boundary value problem to obtain a nonlinear
24: ! system of equations.
25: !
26: ! The uniprocessor version of this code is snes/tutorials/ex4f.F
27: !
28: ! --------------------------------------------------------------------------
29: ! The following define must be used before including any PETSc include files
30: ! into a module or interface. This is because they can't handle declarations
31: ! in them
32: !
34: module ex5f90module
35: use petscsnes
36: use petscdmda
37: #include <petsc/finclude/petscsnes.h>
38: type userctx
39: PetscInt xs,xe,xm,gxs,gxe,gxm
40: PetscInt ys,ye,ym,gys,gye,gym
41: PetscInt mx,my
42: PetscMPIInt rank
43: PetscReal lambda
44: end type userctx
46: contains
47: ! ---------------------------------------------------------------------
48: !
49: ! FormFunction - Evaluates nonlinear function, F(x).
50: !
51: ! Input Parameters:
52: ! snes - the SNES context
53: ! X - input vector
54: ! dummy - optional user-defined context, as set by SNESSetFunction()
55: ! (not used here)
56: !
57: ! Output Parameter:
58: ! F - function vector
59: !
60: ! Notes:
61: ! This routine serves as a wrapper for the lower-level routine
62: ! "FormFunctionLocal", where the actual computations are
63: ! done using the standard Fortran style of treating the local
64: ! vector data as a multidimensional array over the local mesh.
65: ! This routine merely handles ghost point scatters and accesses
66: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
67: !
68: subroutine FormFunction(snes,X,F,user,ierr)
69: implicit none
71: ! Input/output variables:
72: SNES snes
73: Vec X,F
74: PetscErrorCode ierr
75: type (userctx) user
76: DM da
78: ! Declarations for use with local arrays:
79: PetscScalar,pointer :: lx_v(:),lf_v(:)
80: Vec localX
82: ! Scatter ghost points to local vector, using the 2-step process
83: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
84: ! By placing code between these two statements, computations can
85: ! be done while messages are in transition.
86: PetscCall(SNESGetDM(snes,da,ierr))
87: PetscCall(DMGetLocalVector(da,localX,ierr))
88: PetscCall(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr))
89: PetscCall(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr))
91: ! Get a pointer to vector data.
92: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
93: ! the data array. Otherwise, the routine is implementation dependent.
94: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
95: ! the array.
96: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
97: ! and is useable from Fortran-90 Only.
99: PetscCall(VecGetArrayF90(localX,lx_v,ierr))
100: PetscCall(VecGetArrayF90(F,lf_v,ierr))
102: ! Compute function over the locally owned part of the grid
103: PetscCall(FormFunctionLocal(lx_v,lf_v,user,ierr))
105: ! Restore vectors
106: PetscCall(VecRestoreArrayF90(localX,lx_v,ierr))
107: PetscCall(VecRestoreArrayF90(F,lf_v,ierr))
109: ! Insert values into global vector
111: PetscCall(DMRestoreLocalVector(da,localX,ierr))
112: PetscCall(PetscLogFlops(11.0d0*user%ym*user%xm,ierr))
114: ! PetscCallA(VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr))
115: ! PetscCallA(VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr))
116: return
117: end subroutine formfunction
118: end module ex5f90module
120: module ex5f90moduleinterfaces
121: use ex5f90module
123: Interface SNESSetApplicationContext
124: Subroutine SNESSetApplicationContext(snes,ctx,ierr)
125: use ex5f90module
126: SNES snes
127: type(userctx) ctx
128: PetscErrorCode ierr
129: End Subroutine
130: End Interface SNESSetApplicationContext
132: Interface SNESGetApplicationContext
133: Subroutine SNESGetApplicationContext(snes,ctx,ierr)
134: use ex5f90module
135: SNES snes
136: type(userctx), pointer :: ctx
137: PetscErrorCode ierr
138: End Subroutine
139: End Interface SNESGetApplicationContext
140: end module ex5f90moduleinterfaces
142: program main
143: use ex5f90module
144: use ex5f90moduleinterfaces
145: implicit none
146: !
148: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: ! Variable declarations
150: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151: !
152: ! Variables:
153: ! snes - nonlinear solver
154: ! x, r - solution, residual vectors
155: ! J - Jacobian matrix
156: ! its - iterations for convergence
157: ! Nx, Ny - number of preocessors in x- and y- directions
158: ! matrix_free - flag - 1 indicates matrix-free version
159: !
160: SNES snes
161: Vec x,r
162: Mat J
163: PetscErrorCode ierr
164: PetscInt its
165: PetscBool flg,matrix_free
166: PetscInt ione,nfour
167: PetscReal lambda_max,lambda_min
168: type (userctx) user
169: DM da
171: ! Note: Any user-defined Fortran routines (such as FormJacobian)
172: ! MUST be declared as external.
173: external FormInitialGuess,FormJacobian
175: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176: ! Initialize program
177: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: PetscCallA(PetscInitialize(ierr))
179: PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr))
181: ! Initialize problem parameters
182: lambda_max = 6.81
183: lambda_min = 0.0
184: user%lambda = 6.0
185: ione = 1
186: nfour = 4
187: PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',user%lambda,flg,ierr))
188: if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) then
189: SETERRA(PETSC_COMM_SELF,PETSC_ERR_USER,'Lambda provided with -par is out of range ')
190: endif
192: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: ! Create nonlinear solver context
194: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195: PetscCallA(SNESCreate(PETSC_COMM_WORLD,snes,ierr))
197: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198: ! Create vector data structures; set function evaluation routine
199: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201: ! Create distributed array (DMDA) to manage parallel grid and vectors
203: ! This really needs only the star-type stencil, but we use the box
204: ! stencil temporarily.
205: PetscCallA(DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,ione,ione,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr))
206: PetscCallA(DMSetFromOptions(da,ierr))
207: PetscCallA(DMSetUp(da,ierr))
209: PetscCallA(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,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr))
211: !
212: ! Visualize the distribution of the array across the processors
213: !
214: ! PetscCallA(DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr))
216: ! Extract global and local vectors from DMDA; then duplicate for remaining
217: ! vectors that are the same types
218: PetscCallA(DMCreateGlobalVector(da,x,ierr))
219: PetscCallA(VecDuplicate(x,r,ierr))
221: ! Get local grid boundaries (for 2-dimensional DMDA)
222: PetscCallA(DMDAGetCorners(da,user%xs,user%ys,PETSC_NULL_INTEGER,user%xm,user%ym,PETSC_NULL_INTEGER,ierr))
223: PetscCallA(DMDAGetGhostCorners(da,user%gxs,user%gys,PETSC_NULL_INTEGER,user%gxm,user%gym,PETSC_NULL_INTEGER,ierr))
225: ! Here we shift the starting indices up by one so that we can easily
226: ! use the Fortran convention of 1-based indices (rather 0-based indices).
227: user%xs = user%xs+1
228: user%ys = user%ys+1
229: user%gxs = user%gxs+1
230: user%gys = user%gys+1
232: user%ye = user%ys+user%ym-1
233: user%xe = user%xs+user%xm-1
234: user%gye = user%gys+user%gym-1
235: user%gxe = user%gxs+user%gxm-1
237: PetscCallA(SNESSetApplicationContext(snes,user,ierr))
239: ! Set function evaluation routine and vector
240: PetscCallA(SNESSetFunction(snes,r,FormFunction,user,ierr))
242: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
243: ! Create matrix data structure; set Jacobian evaluation routine
244: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
246: ! Set Jacobian matrix data structure and default Jacobian evaluation
247: ! routine. User can override with:
248: ! -snes_fd : default finite differencing approximation of Jacobian
249: ! -snes_mf : matrix-free Newton-Krylov method with no preconditioning
250: ! (unless user explicitly sets preconditioner)
251: ! -snes_mf_operator : form preconditioning matrix as set by the user,
252: ! but use matrix-free approx for Jacobian-vector
253: ! products within Newton-Krylov method
254: !
255: ! Note: For the parallel case, vectors and matrices MUST be partitioned
256: ! accordingly. When using distributed arrays (DMDAs) to create vectors,
257: ! the DMDAs determine the problem partitioning. We must explicitly
258: ! specify the local matrix dimensions upon its creation for compatibility
259: ! with the vector distribution. Thus, the generic MatCreate() routine
260: ! is NOT sufficient when working with distributed arrays.
261: !
262: ! Note: Here we only approximately preallocate storage space for the
263: ! Jacobian. See the users manual for a discussion of better techniques
264: ! for preallocating matrix memory.
266: PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr))
267: if (.not. matrix_free) then
268: PetscCallA(DMSetMatType(da,MATAIJ,ierr))
269: PetscCallA(DMCreateMatrix(da,J,ierr))
270: PetscCallA(SNESSetJacobian(snes,J,J,FormJacobian,user,ierr))
271: endif
273: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
274: ! Customize nonlinear solver; set runtime options
275: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
276: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
277: PetscCallA(SNESSetDM(snes,da,ierr))
278: PetscCallA(SNESSetFromOptions(snes,ierr))
280: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
281: ! Evaluate initial guess; then solve nonlinear system.
282: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
283: ! Note: The user should initialize the vector, x, with the initial guess
284: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
285: ! to employ an initial guess of zero, the user should explicitly set
286: ! this vector to zero by calling VecSet().
288: PetscCallA(FormInitialGuess(snes,x,ierr))
289: PetscCallA(SNESSolve(snes,PETSC_NULL_VEC,x,ierr))
290: PetscCallA(SNESGetIterationNumber(snes,its,ierr))
291: if (user%rank .eq. 0) then
292: write(6,100) its
293: endif
294: 100 format('Number of SNES iterations = ',i5)
296: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
297: ! Free work space. All PETSc objects should be destroyed when they
298: ! are no longer needed.
299: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
300: if (.not. matrix_free) PetscCallA(MatDestroy(J,ierr))
301: PetscCallA(VecDestroy(x,ierr))
302: PetscCallA(VecDestroy(r,ierr))
303: PetscCallA(SNESDestroy(snes,ierr))
304: PetscCallA(DMDestroy(da,ierr))
306: PetscCallA(PetscFinalize(ierr))
307: end
309: ! ---------------------------------------------------------------------
310: !
311: ! FormInitialGuess - Forms initial approximation.
312: !
313: ! Input Parameters:
314: ! X - vector
315: !
316: ! Output Parameter:
317: ! X - vector
318: !
319: ! Notes:
320: ! This routine serves as a wrapper for the lower-level routine
321: ! "InitialGuessLocal", where the actual computations are
322: ! done using the standard Fortran style of treating the local
323: ! vector data as a multidimensional array over the local mesh.
324: ! This routine merely handles ghost point scatters and accesses
325: ! the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
326: !
327: subroutine FormInitialGuess(snes,X,ierr)
328: use ex5f90module
329: use ex5f90moduleinterfaces
330: implicit none
332: ! Input/output variables:
333: SNES snes
334: type(userctx), pointer:: puser
335: Vec X
336: PetscErrorCode ierr
337: DM da
339: ! Declarations for use with local arrays:
340: PetscScalar,pointer :: lx_v(:)
342: 0
343: PetscCallA(SNESGetDM(snes,da,ierr))
344: PetscCallA(SNESGetApplicationContext(snes,puser,ierr))
345: ! Get a pointer to vector data.
346: ! - For default PETSc vectors, VecGetArray90() returns a pointer to
347: ! the data array. Otherwise, the routine is implementation dependent.
348: ! - You MUST call VecRestoreArrayF90() when you no longer need access to
349: ! the array.
350: ! - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
351: ! and is useable from Fortran-90 Only.
353: PetscCallA(VecGetArrayF90(X,lx_v,ierr))
355: ! Compute initial guess over the locally owned part of the grid
356: PetscCallA(InitialGuessLocal(puser,lx_v,ierr))
358: ! Restore vector
359: PetscCallA(VecRestoreArrayF90(X,lx_v,ierr))
361: ! Insert values into global vector
363: return
364: end
366: ! ---------------------------------------------------------------------
367: !
368: ! InitialGuessLocal - Computes initial approximation, called by
369: ! the higher level routine FormInitialGuess().
370: !
371: ! Input Parameter:
372: ! x - local vector data
373: !
374: ! Output Parameters:
375: ! x - local vector data
376: ! ierr - error code
377: !
378: ! Notes:
379: ! This routine uses standard Fortran-style computations over a 2-dim array.
380: !
381: subroutine InitialGuessLocal(user,x,ierr)
382: use ex5f90module
383: implicit none
385: ! Input/output variables:
386: type (userctx) user
387: PetscScalar x(user%xs:user%xe,user%ys:user%ye)
388: PetscErrorCode ierr
390: ! Local variables:
391: PetscInt i,j
392: PetscReal temp1,temp,hx,hy
393: PetscReal one
395: ! Set parameters
397: 0
398: one = 1.0
399: hx = one/(user%mx-1)
400: hy = one/(user%my-1)
401: temp1 = user%lambda/(user%lambda + one)
403: do 20 j=user%ys,user%ye
404: temp = min(j-1,user%my-j)*hy
405: do 10 i=user%xs,user%xe
406: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
407: x(i,j) = 0.0
408: else
409: x(i,j) = temp1 * sqrt(min(hx*min(i-1,user%mx-i),temp))
410: endif
411: 10 continue
412: 20 continue
414: return
415: end
417: ! ---------------------------------------------------------------------
418: !
419: ! FormFunctionLocal - Computes nonlinear function, called by
420: ! the higher level routine FormFunction().
421: !
422: ! Input Parameter:
423: ! x - local vector data
424: !
425: ! Output Parameters:
426: ! f - local vector data, f(x)
427: ! ierr - error code
428: !
429: ! Notes:
430: ! This routine uses standard Fortran-style computations over a 2-dim array.
431: !
432: subroutine FormFunctionLocal(x,f,user,ierr)
433: use ex5f90module
435: implicit none
437: ! Input/output variables:
438: type (userctx) user
439: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
440: PetscScalar f(user%xs:user%xe,user%ys:user%ye)
441: PetscErrorCode ierr
443: ! Local variables:
444: PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
445: PetscScalar u,uxx,uyy
446: PetscInt i,j
448: one = 1.0
449: two = 2.0
450: hx = one/(user%mx-1)
451: hy = one/(user%my-1)
452: sc = hx*hy*user%lambda
453: hxdhy = hx/hy
454: hydhx = hy/hx
456: ! Compute function over the locally owned part of the grid
458: do 20 j=user%ys,user%ye
459: do 10 i=user%xs,user%xe
460: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
461: f(i,j) = x(i,j)
462: else
463: u = x(i,j)
464: uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
465: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
466: f(i,j) = uxx + uyy - sc*exp(u)
467: endif
468: 10 continue
469: 20 continue
471: return
472: end
474: ! ---------------------------------------------------------------------
475: !
476: ! FormJacobian - Evaluates Jacobian matrix.
477: !
478: ! Input Parameters:
479: ! snes - the SNES context
480: ! x - input vector
481: ! dummy - optional user-defined context, as set by SNESSetJacobian()
482: ! (not used here)
483: !
484: ! Output Parameters:
485: ! jac - Jacobian matrix
486: ! jac_prec - optionally different preconditioning matrix (not used here)
487: ! flag - flag indicating matrix structure
488: !
489: ! Notes:
490: ! This routine serves as a wrapper for the lower-level routine
491: ! "FormJacobianLocal", where the actual computations are
492: ! done using the standard Fortran style of treating the local
493: ! vector data as a multidimensional array over the local mesh.
494: ! This routine merely accesses the local vector data via
495: ! VecGetArrayF90() and VecRestoreArrayF90().
496: !
497: ! Notes:
498: ! Due to grid point reordering with DMDAs, we must always work
499: ! with the local grid points, and then transform them to the new
500: ! global numbering with the "ltog" mapping
501: ! We cannot work directly with the global numbers for the original
502: ! uniprocessor grid!
503: !
504: ! Two methods are available for imposing this transformation
505: ! when setting matrix entries:
506: ! (A) MatSetValuesLocal(), using the local ordering (including
507: ! ghost points!)
508: ! - Set matrix entries using the local ordering
509: ! by calling MatSetValuesLocal()
510: ! (B) MatSetValues(), using the global ordering
512: ! - Set matrix entries using the global ordering by calling
513: ! MatSetValues()
514: ! Option (A) seems cleaner/easier in many cases, and is the procedure
515: ! used in this example.
516: !
517: subroutine FormJacobian(snes,X,jac,jac_prec,user,ierr)
518: use ex5f90module
519: implicit none
521: ! Input/output variables:
522: SNES snes
523: Vec X
524: Mat jac,jac_prec
525: type(userctx) user
526: PetscErrorCode ierr
527: DM da
529: ! Declarations for use with local arrays:
530: PetscScalar,pointer :: lx_v(:)
531: Vec localX
533: ! Scatter ghost points to local vector, using the 2-step process
534: ! DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
535: ! Computations can be done while messages are in transition,
536: ! by placing code between these two statements.
538: PetscCallA(SNESGetDM(snes,da,ierr))
539: PetscCallA(DMGetLocalVector(da,localX,ierr))
540: PetscCallA(DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,ierr))
541: PetscCallA(DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr))
543: ! Get a pointer to vector data
544: PetscCallA(VecGetArrayF90(localX,lx_v,ierr))
546: ! Compute entries for the locally owned part of the Jacobian preconditioner.
547: PetscCallA(FormJacobianLocal(lx_v,jac_prec,user,ierr))
549: ! Assemble matrix, using the 2-step process:
550: ! MatAssemblyBegin(), MatAssemblyEnd()
551: ! Computations can be done while messages are in transition,
552: ! by placing code between these two statements.
554: PetscCallA(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr))
555: if (jac .ne. jac_prec) then
556: PetscCallA(MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr))
557: endif
558: PetscCallA(VecRestoreArrayF90(localX,lx_v,ierr))
559: PetscCallA(DMRestoreLocalVector(da,localX,ierr))
560: PetscCallA(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr))
561: if (jac .ne. jac_prec) then
562: PetscCallA(MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr))
563: endif
565: ! Tell the matrix we will never add a new nonzero location to the
566: ! matrix. If we do it will generate an error.
568: PetscCallA(MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr))
570: return
571: end
573: ! ---------------------------------------------------------------------
574: !
575: ! FormJacobianLocal - Computes Jacobian preconditioner matrix,
576: ! called by the higher level routine FormJacobian().
577: !
578: ! Input Parameters:
579: ! x - local vector data
580: !
581: ! Output Parameters:
582: ! jac_prec - Jacobian preconditioner matrix
583: ! ierr - error code
584: !
585: ! Notes:
586: ! This routine uses standard Fortran-style computations over a 2-dim array.
587: !
588: ! Notes:
589: ! Due to grid point reordering with DMDAs, we must always work
590: ! with the local grid points, and then transform them to the new
591: ! global numbering with the "ltog" mapping
592: ! We cannot work directly with the global numbers for the original
593: ! uniprocessor grid!
594: !
595: ! Two methods are available for imposing this transformation
596: ! when setting matrix entries:
597: ! (A) MatSetValuesLocal(), using the local ordering (including
598: ! ghost points!)
599: ! - Set matrix entries using the local ordering
600: ! by calling MatSetValuesLocal()
601: ! (B) MatSetValues(), using the global ordering
602: ! - Then apply this map explicitly yourself
603: ! - Set matrix entries using the global ordering by calling
604: ! MatSetValues()
605: ! Option (A) seems cleaner/easier in many cases, and is the procedure
606: ! used in this example.
607: !
608: subroutine FormJacobianLocal(x,jac_prec,user,ierr)
609: use ex5f90module
610: implicit none
612: ! Input/output variables:
613: type (userctx) user
614: PetscScalar x(user%gxs:user%gxe,user%gys:user%gye)
615: Mat jac_prec
616: PetscErrorCode ierr
618: ! Local variables:
619: PetscInt row,col(5),i,j
620: PetscInt ione,ifive
621: PetscScalar two,one,hx,hy,hxdhy
622: PetscScalar hydhx,sc,v(5)
624: ! Set parameters
625: ione = 1
626: ifive = 5
627: one = 1.0
628: two = 2.0
629: hx = one/(user%mx-1)
630: hy = one/(user%my-1)
631: sc = hx*hy
632: hxdhy = hx/hy
633: hydhx = hy/hx
635: ! Compute entries for the locally owned part of the Jacobian.
636: ! - Currently, all PETSc parallel matrix formats are partitioned by
637: ! contiguous chunks of rows across the processors.
638: ! - Each processor needs to insert only elements that it owns
639: ! locally (but any non-local elements will be sent to the
640: ! appropriate processor during matrix assembly).
641: ! - Here, we set all entries for a particular row at once.
642: ! - We can set matrix entries either using either
643: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
644: ! - Note that MatSetValues() uses 0-based row and column numbers
645: ! in Fortran as well as in C.
647: do 20 j=user%ys,user%ye
648: row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
649: do 10 i=user%xs,user%xe
650: row = row + 1
651: ! boundary points
652: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
653: col(1) = row
654: v(1) = one
655: PetscCallA(MatSetValuesLocal(jac_prec,ione,row,ione,col,v,INSERT_VALUES,ierr))
656: ! interior grid points
657: else
658: v(1) = -hxdhy
659: v(2) = -hydhx
660: v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i,j))
661: v(4) = -hydhx
662: v(5) = -hxdhy
663: col(1) = row - user%gxm
664: col(2) = row - 1
665: col(3) = row
666: col(4) = row + 1
667: col(5) = row + user%gxm
668: PetscCallA(MatSetValuesLocal(jac_prec,ione,row,ifive,col,v,INSERT_VALUES,ierr))
669: endif
670: 10 continue
671: 20 continue
673: return
674: end
676: !
677: !/*TEST
678: !
679: ! test:
680: ! nsize: 4
681: ! args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
682: ! requires: !single
683: !
684: ! test:
685: ! suffix: 2
686: ! nsize: 4
687: ! args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
688: ! requires: !single
689: !
690: ! test:
691: ! suffix: 3
692: ! nsize: 3
693: ! args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
694: ! requires: !single
695: !
696: ! test:
697: ! suffix: 4
698: ! nsize: 3
699: ! args: -snes_mf_operator -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
700: ! requires: !single
701: !
702: ! test:
703: ! suffix: 5
704: ! requires: !single
705: !
706: !TEST*/