Actual source code: ex5f.F90
petsc-3.13.6 2020-09-29
1: !
2: ! Description: This example 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 <param>, where <param> indicates the nonlinearity of the problem
7: ! problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)
8: !
9: !
10: !!/*T
11: ! Concepts: SNES^parallel Bratu example
12: ! Concepts: DMDA^using distributed arrays;
13: ! Processors: n
14: !T*/
17: !
18: ! --------------------------------------------------------------------------
19: !
20: ! Solid Fuel Ignition (SFI) problem. This problem is modeled by
21: ! the partial differential equation
22: !
23: ! -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1,
24: !
25: ! with boundary conditions
26: !
27: ! u = 0 for x = 0, x = 1, y = 0, y = 1.
28: !
29: ! A finite difference approximation with the usual 5-point stencil
30: ! is used to discretize the boundary value problem to obtain a nonlinear
31: ! system of equations.
32: !
33: ! --------------------------------------------------------------------------
35: program main
36: #include <petsc/finclude/petscsnes.h>
37: use petscdmda
38: use petscsnes
39: implicit none
40: !
41: ! We place common blocks, variable declarations, and other include files
42: ! needed for this code in the single file ex5f.h. We then need to include
43: ! only this file throughout the various routines in this program. See
44: ! additional comments in the file ex5f.h.
45: !
46: #include "ex5f.h"
48: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
49: ! Variable declarations
50: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: !
52: ! Variables:
53: ! snes - nonlinear solver
54: ! x, r - solution, residual vectors
55: ! its - iterations for convergence
56: !
57: ! See additional variable declarations in the file ex5f.h
58: !
59: SNES snes
60: Vec x,r
61: PetscInt its,i1,i4
62: PetscErrorCode ierr
63: PetscReal lambda_max,lambda_min
64: PetscBool flg
65: DM da
67: ! Note: Any user-defined Fortran routines (such as FormJacobianLocal)
68: ! MUST be declared as external.
70: external FormInitialGuess
71: external FormFunctionLocal,FormJacobianLocal
72: external MySNESConverged
74: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
75: ! Initialize program
76: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
78: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
79: if (ierr .ne. 0) then
80: print*,'Unable to initialize PETSc'
81: stop
82: endif
83: call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
84: call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
86: ! Initialize problem parameters
88: i1 = 1
89: i4 = 4
90: lambda_max = 6.81
91: lambda_min = 0.0
92: lambda = 6.0
93: call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,PETSC_NULL_BOOL,ierr)
94: ! this statement is split into multiple-lines to keep lines under 132 char limit - required by 'make check'
95: if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
96: PETSC_ERR_ARG_OUTOFRANGE; SETERRA(PETSC_COMM_WORLD,ierr,'Lambda')
97: endif
99: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100: ! Create nonlinear solver context
101: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103: call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
105: ! Set convergence test routine if desired
107: call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_snes_convergence',flg,ierr)
108: if (flg) then
109: call SNESSetConvergenceTest(snes,MySNESConverged,0,PETSC_NULL_FUNCTION,ierr)
110: endif
112: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113: ! Create vector data structures; set function evaluation routine
114: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116: ! Create distributed array (DMDA) to manage parallel grid and vectors
118: ! This really needs only the star-type stencil, but we use the box
119: ! stencil temporarily.
120: call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE, &
121: & DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE,i1,i1, &
122: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
123: call DMSetFromOptions(da,ierr)
124: call DMSetUp(da,ierr)
126: ! Extract global and local vectors from DMDA; then duplicate for remaining
127: ! vectors that are the same types
129: call DMCreateGlobalVector(da,x,ierr)
130: call VecDuplicate(x,r,ierr)
132: ! Get local grid boundaries (for 2-dimensional DMDA)
134: call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER, &
135: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
136: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
137: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
138: & PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
139: & PETSC_NULL_INTEGER,ierr)
140: call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr)
141: call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr)
143: ! Here we shift the starting indices up by one so that we can easily
144: ! use the Fortran convention of 1-based indices (rather 0-based indices).
146: xs = xs+1
147: ys = ys+1
148: gxs = gxs+1
149: gys = gys+1
151: ye = ys+ym-1
152: xe = xs+xm-1
153: gye = gys+gym-1
154: gxe = gxs+gxm-1
156: ! Set function evaluation routine and vector
158: call DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal,da,ierr)
159: call DMDASNESSetJacobianLocal(da,FormJacobianLocal,da,ierr)
160: call SNESSetDM(snes,da,ierr)
162: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: ! Customize nonlinear solver; set runtime options
164: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166: ! Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
168: call SNESSetFromOptions(snes,ierr)
169: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170: ! Evaluate initial guess; then solve nonlinear system.
171: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
173: ! Note: The user should initialize the vector, x, with the initial guess
174: ! for the nonlinear solver prior to calling SNESSolve(). In particular,
175: ! to employ an initial guess of zero, the user should explicitly set
176: ! this vector to zero by calling VecSet().
178: call FormInitialGuess(x,ierr)
179: call SNESSolve(snes,PETSC_NULL_VEC,x,ierr)
180: call SNESGetIterationNumber(snes,its,ierr)
181: if (rank .eq. 0) then
182: write(6,100) its
183: endif
184: 100 format('Number of SNES iterations = ',i5)
187: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
188: ! Free work space. All PETSc objects should be destroyed when they
189: ! are no longer needed.
190: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
192: call VecDestroy(x,ierr)
193: call VecDestroy(r,ierr)
194: call SNESDestroy(snes,ierr)
195: call DMDestroy(da,ierr)
196: call PetscFinalize(ierr)
197: end
199: ! ---------------------------------------------------------------------
200: !
201: ! FormInitialGuess - Forms initial approximation.
202: !
203: ! Input Parameters:
204: ! X - vector
205: !
206: ! Output Parameter:
207: ! X - vector
208: !
209: ! Notes:
210: ! This routine serves as a wrapper for the lower-level routine
211: ! "ApplicationInitialGuess", where the actual computations are
212: ! done using the standard Fortran style of treating the local
213: ! vector data as a multidimensional array over the local mesh.
214: ! This routine merely handles ghost point scatters and accesses
215: ! the local vector data via VecGetArray() and VecRestoreArray().
216: !
217: subroutine FormInitialGuess(X,ierr)
218: use petscsnes
219: implicit none
221: #include "ex5f.h"
223: ! Input/output variables:
224: Vec X
225: PetscErrorCode ierr
227: ! Declarations for use with local arrays:
228: PetscScalar lx_v(0:1)
229: PetscOffset lx_i
231: 0
233: ! Get a pointer to vector data.
234: ! - For default PETSc vectors, VecGetArray() returns a pointer to
235: ! the data array. Otherwise, the routine is implementation dependent.
236: ! - You MUST call VecRestoreArray() when you no longer need access to
237: ! the array.
238: ! - Note that the Fortran interface to VecGetArray() differs from the
239: ! C version. See the users manual for details.
241: call VecGetArray(X,lx_v,lx_i,ierr)
243: ! Compute initial guess over the locally owned part of the grid
245: call InitialGuessLocal(lx_v(lx_i),ierr)
247: ! Restore vector
249: call VecRestoreArray(X,lx_v,lx_i,ierr)
251: return
252: end
254: ! ---------------------------------------------------------------------
255: !
256: ! InitialGuessLocal - Computes initial approximation, called by
257: ! the higher level routine FormInitialGuess().
258: !
259: ! Input Parameter:
260: ! x - local vector data
261: !
262: ! Output Parameters:
263: ! x - local vector data
264: ! ierr - error code
265: !
266: ! Notes:
267: ! This routine uses standard Fortran-style computations over a 2-dim array.
268: !
269: subroutine InitialGuessLocal(x,ierr)
270: use petscsnes
271: implicit none
273: #include "ex5f.h"
275: ! Input/output variables:
276: PetscScalar x(xs:xe,ys:ye)
277: PetscErrorCode ierr
279: ! Local variables:
280: PetscInt i,j
281: PetscReal temp1,temp,one,hx,hy
283: ! Set parameters
285: 0
286: one = 1.0
287: hx = one/((mx-1))
288: hy = one/((my-1))
289: temp1 = lambda/(lambda + one)
291: do 20 j=ys,ye
292: temp = (min(j-1,my-j))*hy
293: do 10 i=xs,xe
294: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
295: x(i,j) = 0.0
296: else
297: x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,(temp)))
298: endif
299: 10 continue
300: 20 continue
302: return
303: end
305: ! ---------------------------------------------------------------------
306: !
307: ! FormFunctionLocal - Computes nonlinear function, called by
308: ! the higher level routine FormFunction().
309: !
310: ! Input Parameter:
311: ! x - local vector data
312: !
313: ! Output Parameters:
314: ! f - local vector data, f(x)
315: ! ierr - error code
316: !
317: ! Notes:
318: ! This routine uses standard Fortran-style computations over a 2-dim array.
319: !
320: !
321: subroutine FormFunctionLocal(info,x,f,da,ierr)
322: #include <petsc/finclude/petscdmda.h>
323: use petscsnes
324: implicit none
326: #include "ex5f.h"
327: DM da
329: ! Input/output variables:
330: DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
331: PetscScalar x(gxs:gxe,gys:gye)
332: PetscScalar f(xs:xe,ys:ye)
333: PetscErrorCode ierr
335: ! Local variables:
336: PetscScalar two,one,hx,hy
337: PetscScalar hxdhy,hydhx,sc
338: PetscScalar u,uxx,uyy
339: PetscInt i,j
341: xs = info(DMDA_LOCAL_INFO_XS)+1
342: xe = xs+info(DMDA_LOCAL_INFO_XM)-1
343: ys = info(DMDA_LOCAL_INFO_YS)+1
344: ye = ys+info(DMDA_LOCAL_INFO_YM)-1
345: mx = info(DMDA_LOCAL_INFO_MX)
346: my = info(DMDA_LOCAL_INFO_MY)
348: one = 1.0
349: two = 2.0
350: hx = one/(mx-1)
351: hy = one/(my-1)
352: sc = hx*hy*lambda
353: hxdhy = hx/hy
354: hydhx = hy/hx
356: ! Compute function over the locally owned part of the grid
358: do 20 j=ys,ye
359: do 10 i=xs,xe
360: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
361: f(i,j) = x(i,j)
362: else
363: u = x(i,j)
364: uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
365: uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
366: f(i,j) = uxx + uyy - sc*exp(u)
367: endif
368: 10 continue
369: 20 continue
371: call PetscLogFlops(11.0d0*ym*xm,ierr)
373: return
374: end
376: ! ---------------------------------------------------------------------
377: !
378: ! FormJacobianLocal - Computes Jacobian matrix, called by
379: ! the higher level routine FormJacobian().
380: !
381: ! Input Parameters:
382: ! x - local vector data
383: !
384: ! Output Parameters:
385: ! jac - Jacobian matrix
386: ! jac_prec - optionally different preconditioning matrix (not used here)
387: ! ierr - error code
388: !
389: ! Notes:
390: ! This routine uses standard Fortran-style computations over a 2-dim array.
391: !
392: ! Notes:
393: ! Due to grid point reordering with DMDAs, we must always work
394: ! with the local grid points, and then transform them to the new
395: ! global numbering with the "ltog" mapping
396: ! We cannot work directly with the global numbers for the original
397: ! uniprocessor grid!
398: !
399: ! Two methods are available for imposing this transformation
400: ! when setting matrix entries:
401: ! (A) MatSetValuesLocal(), using the local ordering (including
402: ! ghost points!)
403: ! by calling MatSetValuesLocal()
404: ! (B) MatSetValues(), using the global ordering
405: ! - Use DMDAGetGlobalIndices() to extract the local-to-global map
406: ! - Then apply this map explicitly yourself
407: ! - Set matrix entries using the global ordering by calling
408: ! MatSetValues()
409: ! Option (A) seems cleaner/easier in many cases, and is the procedure
410: ! used in this example.
411: !
412: subroutine FormJacobianLocal(info,x,A,jac,da,ierr)
413: use petscsnes
414: implicit none
416: #include "ex5f.h"
417: DM da
418:
419: ! Input/output variables:
420: PetscScalar x(gxs:gxe,gys:gye)
421: Mat A,jac
422: PetscErrorCode ierr
423: DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
426: ! Local variables:
427: PetscInt row,col(5),i,j,i1,i5
428: PetscScalar two,one,hx,hy,v(5)
429: PetscScalar hxdhy,hydhx,sc
431: ! Set parameters
433: i1 = 1
434: i5 = 5
435: one = 1.0
436: two = 2.0
437: hx = one/(mx-1)
438: hy = one/(my-1)
439: sc = hx*hy
440: hxdhy = hx/hy
441: hydhx = hy/hx
443: ! Compute entries for the locally owned part of the Jacobian.
444: ! - Currently, all PETSc parallel matrix formats are partitioned by
445: ! contiguous chunks of rows across the processors.
446: ! - Each processor needs to insert only elements that it owns
447: ! locally (but any non-local elements will be sent to the
448: ! appropriate processor during matrix assembly).
449: ! - Here, we set all entries for a particular row at once.
450: ! - We can set matrix entries either using either
451: ! MatSetValuesLocal() or MatSetValues(), as discussed above.
452: ! - Note that MatSetValues() uses 0-based row and column numbers
453: ! in Fortran as well as in C.
455: do 20 j=ys,ye
456: row = (j - gys)*gxm + xs - gxs - 1
457: do 10 i=xs,xe
458: row = row + 1
459: ! boundary points
460: if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
461: ! Some f90 compilers need 4th arg to be of same type in both calls
462: col(1) = row
463: v(1) = one
464: call MatSetValuesLocal(jac,i1,row,i1,col,v,INSERT_VALUES,ierr)
465: ! interior grid points
466: else
467: v(1) = -hxdhy
468: v(2) = -hydhx
469: v(3) = two*(hydhx + hxdhy) - sc*lambda*exp(x(i,j))
470: v(4) = -hydhx
471: v(5) = -hxdhy
472: col(1) = row - gxm
473: col(2) = row - 1
474: col(3) = row
475: col(4) = row + 1
476: col(5) = row + gxm
477: call MatSetValuesLocal(jac,i1,row,i5,col,v, INSERT_VALUES,ierr)
478: endif
479: 10 continue
480: 20 continue
481: call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
482: call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
483: if (A .ne. jac) then
484: call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
485: call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
486: endif
487: return
488: end
490: !
491: ! Simple convergence test based on the infinity norm of the residual being small
492: !
493: subroutine MySNESConverged(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr)
494: use petscsnes
495: implicit none
497: SNES snes
498: PetscInt it,dummy
499: PetscReal xnorm,snorm,fnorm,nrm
500: SNESConvergedReason reason
501: Vec f
502: PetscErrorCode ierr
504: call SNESGetFunction(snes,f,PETSC_NULL_FUNCTION,dummy,ierr)
505: call VecNorm(f,NORM_INFINITY,nrm,ierr)
506: if (nrm .le. 1.e-5) reason = SNES_CONVERGED_FNORM_ABS
508: end
510: !/*TEST
511: !
512: ! build:
513: ! requires: !complex !single
514: !
515: ! test:
516: ! nsize: 4
517: ! args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
518: !
519: ! test:
520: ! suffix: 2
521: ! nsize: 4
522: ! args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
523: !
524: ! test:
525: ! suffix: 3
526: ! nsize: 3
527: ! args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
528: !
529: ! test:
530: ! suffix: 6
531: ! nsize: 1
532: ! args: -snes_monitor_short -my_snes_convergence
533: !
534: !TEST*/