Actual source code: ex21f.F90

petsc-3.11.2 2019-05-18
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  1: !
  2: !   Solves a linear system in parallel with KSP.  Also indicates
  3: !   use of a user-provided preconditioner.  Input parameters include:
  4: !
  5: !
  6: !!/*T
  7: !   Concepts: KSP^basic parallel example
  8: !   Concepts: PC^setting a user-defined shell preconditioner
  9: !   Processors: n
 10: !T*/


 13: !
 14: !  -------------------------------------------------------------------------
 15:       module mymoduleex21f
 16:  #include <petsc/finclude/petscksp.h>
 17:       use petscksp
 18:       PC jacobi,sor
 19:       Vec work
 20:       end module

 22:       program main
 23:       use mymoduleex21f
 24:       implicit none

 26: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 27: !                   Variable declarations
 28: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 29: !
 30: !  Variables:
 31: !     ksp     - linear solver context
 32: !     ksp      - Krylov subspace method context
 33: !     pc       - preconditioner context
 34: !     x, b, u  - approx solution, right-hand-side, exact solution vectors
 35: !     A        - matrix that defines linear system
 36: !     its      - iterations for convergence
 37: !     norm     - norm of solution error

 39:       Vec              x,b,u
 40:       Mat              A
 41:       PC               pc
 42:       KSP              ksp
 43:       PetscScalar      v,one,neg_one
 44:       PetscReal norm,tol
 45:       PetscInt i,j,II,JJ,Istart
 46:       PetscInt Iend,m,n,its,ione
 47:       PetscMPIInt rank
 48:       PetscBool  flg
 49:       PetscErrorCode ierr

 51: !  Note: Any user-defined Fortran routines MUST be declared as external.

 53:       external SampleShellPCSetUp,SampleShellPCApply

 55: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 56: !                 Beginning of program
 57: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 59:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 60:       if (ierr .ne. 0) then
 61:         print*,'Unable to initialize PETSc'
 62:         stop
 63:       endif
 64:       one     = 1.0
 65:       neg_one = -1.0
 66:       m       = 8
 67:       n       = 7
 68:       ione    = 1
 69:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr)
 70:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
 71:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)

 73: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 74: !      Compute the matrix and right-hand-side vector that define
 75: !      the linear system, Ax = b.
 76: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 78: !  Create parallel matrix, specifying only its global dimensions.
 79: !  When using MatCreate(), the matrix format can be specified at
 80: !  runtime. Also, the parallel partitioning of the matrix is
 81: !  determined by PETSc at runtime.

 83:       call MatCreate(PETSC_COMM_WORLD,A,ierr)
 84:       call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr)
 85:       call MatSetFromOptions(A,ierr)
 86:       call MatSetUp(A,ierr)

 88: !  Currently, all PETSc parallel matrix formats are partitioned by
 89: !  contiguous chunks of rows across the processors.  Determine which
 90: !  rows of the matrix are locally owned.

 92:       call MatGetOwnershipRange(A,Istart,Iend,ierr)

 94: !  Set matrix elements for the 2-D, five-point stencil in parallel.
 95: !   - Each processor needs to insert only elements that it owns
 96: !     locally (but any non-local elements will be sent to the
 97: !     appropriate processor during matrix assembly).
 98: !   - Always specify global row and columns of matrix entries.
 99: !   - Note that MatSetValues() uses 0-based row and column numbers
100: !     in Fortran as well as in C.

102:       do 10, II=Istart,Iend-1
103:         v = -1.0
104:         i = II/n
105:         j = II - i*n
106:         if (i.gt.0) then
107:           JJ = II - n
108:           call MatSetValues(A,ione,II,ione,JJ,v,ADD_VALUES,ierr)
109:         endif
110:         if (i.lt.m-1) then
111:           JJ = II + n
112:           call MatSetValues(A,ione,II,ione,JJ,v,ADD_VALUES,ierr)
113:         endif
114:         if (j.gt.0) then
115:           JJ = II - 1
116:           call MatSetValues(A,ione,II,ione,JJ,v,ADD_VALUES,ierr)
117:         endif
118:         if (j.lt.n-1) then
119:           JJ = II + 1
120:           call MatSetValues(A,ione,II,ione,JJ,v,ADD_VALUES,ierr)
121:         endif
122:         v = 4.0
123:         call  MatSetValues(A,ione,II,ione,II,v,ADD_VALUES,ierr)
124:  10   continue

126: !  Assemble matrix, using the 2-step process:
127: !       MatAssemblyBegin(), MatAssemblyEnd()
128: !  Computations can be done while messages are in transition,
129: !  by placing code between these two statements.

131:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
132:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)

134: !  Create parallel vectors.
135: !   - Here, the parallel partitioning of the vector is determined by
136: !     PETSc at runtime.  We could also specify the local dimensions
137: !     if desired -- or use the more general routine VecCreate().
138: !   - When solving a linear system, the vectors and matrices MUST
139: !     be partitioned accordingly.  PETSc automatically generates
140: !     appropriately partitioned matrices and vectors when MatCreate()
141: !     and VecCreate() are used with the same communicator.
142: !   - Note: We form 1 vector from scratch and then duplicate as needed.

144:       call VecCreateMPI(PETSC_COMM_WORLD,PETSC_DECIDE,m*n,u,ierr)
145:       call VecDuplicate(u,b,ierr)
146:       call VecDuplicate(b,x,ierr)

148: !  Set exact solution; then compute right-hand-side vector.

150:       call VecSet(u,one,ierr)
151:       call MatMult(A,u,b,ierr)

153: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
154: !         Create the linear solver and set various options
155: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

157: !  Create linear solver context

159:       call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)

161: !  Set operators. Here the matrix that defines the linear system
162: !  also serves as the preconditioning matrix.

164:       call KSPSetOperators(ksp,A,A,ierr)

166: !  Set linear solver defaults for this problem (optional).
167: !   - By extracting the KSP and PC contexts from the KSP context,
168: !     we can then directly directly call any KSP and PC routines
169: !     to set various options.

171:       call KSPGetPC(ksp,pc,ierr)
172:       tol = 1.e-7
173:       call KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr)

175: !
176: !  Set a user-defined shell preconditioner
177: !

179: !  (Required) Indicate to PETSc that we are using a shell preconditioner
180:       call PCSetType(pc,PCSHELL,ierr)

182: !  (Required) Set the user-defined routine for applying the preconditioner
183:       call PCShellSetApply(pc,SampleShellPCApply,ierr)

185: !  (Optional) Do any setup required for the preconditioner
186: !     Note: if you use PCShellSetSetUp, this will be done for your
187:       call SampleShellPCSetUp(pc,x,ierr)


190: !  Set runtime options, e.g.,
191: !      -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
192: !  These options will override those specified above as long as
193: !  KSPSetFromOptions() is called _after_ any other customization
194: !  routines.

196:       call KSPSetFromOptions(ksp,ierr)

198: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: !                      Solve the linear system
200: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

202:       call KSPSolve(ksp,b,x,ierr)

204: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
205: !                     Check solution and clean up
206: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

208: !  Check the error

210:       call VecAXPY(x,neg_one,u,ierr)
211:       call VecNorm(x,NORM_2,norm,ierr)
212:       call KSPGetIterationNumber(ksp,its,ierr)

214:       if (rank .eq. 0) then
215:         if (norm .gt. 1.e-12) then
216:            write(6,100) norm,its
217:         else
218:            write(6,110) its
219:         endif
220:       endif
221:   100 format('Norm of error ',1pe11.4,' iterations ',i5)
222:   110 format('Norm of error < 1.e-12,iterations ',i5)


225: !  Free work space.  All PETSc objects should be destroyed when they
226: !  are no longer needed.

228:       call KSPDestroy(ksp,ierr)
229:       call VecDestroy(u,ierr)
230:       call VecDestroy(x,ierr)
231:       call VecDestroy(b,ierr)
232:       call MatDestroy(A,ierr)

234: ! Free up PCShell data
235:       call PCDestroy(sor,ierr)
236:       call PCDestroy(jacobi,ierr)
237:       call VecDestroy(work,ierr)


240: !  Always call PetscFinalize() before exiting a program.

242:       call PetscFinalize(ierr)
243:       end

245: !/***********************************************************************/
246: !/*          Routines for a user-defined shell preconditioner           */
247: !/***********************************************************************/

249: !
250: !   SampleShellPCSetUp - This routine sets up a user-defined
251: !   preconditioner context.
252: !
253: !   Input Parameters:
254: !   pc    - preconditioner object
255: !   x     - vector
256: !
257: !   Output Parameter:
258: !   ierr  - error code (nonzero if error has been detected)
259: !
260: !   Notes:
261: !   In this example, we define the shell preconditioner to be Jacobi
262: !   method.  Thus, here we create a work vector for storing the reciprocal
263: !   of the diagonal of the preconditioner matrix; this vector is then
264: !   used within the routine SampleShellPCApply().
265: !
266:       subroutine SampleShellPCSetUp(pc,x,ierr)
267:       use mymoduleex21f
268:       implicit none

270:       PC      pc
271:       Vec     x
272:       Mat     pmat
273:       PetscErrorCode ierr

275:       call PCGetOperators(pc,PETSC_NULL_MAT,pmat,ierr)
276:       call PCCreate(PETSC_COMM_WORLD,jacobi,ierr)
277:       call PCSetType(jacobi,PCJACOBI,ierr)
278:       call PCSetOperators(jacobi,pmat,pmat,ierr)
279:       call PCSetUp(jacobi,ierr)

281:       call PCCreate(PETSC_COMM_WORLD,sor,ierr)
282:       call PCSetType(sor,PCSOR,ierr)
283:       call PCSetOperators(sor,pmat,pmat,ierr)
284: !      call PCSORSetSymmetric(sor,SOR_LOCAL_SYMMETRIC_SWEEP,ierr)
285:       call PCSetUp(sor,ierr)

287:       call VecDuplicate(x,work,ierr)

289:       end

291: ! -------------------------------------------------------------------
292: !
293: !   SampleShellPCApply - This routine demonstrates the use of a
294: !   user-provided preconditioner.
295: !
296: !   Input Parameters:
297: !   pc - preconditioner object
298: !   x - input vector
299: !
300: !   Output Parameters:
301: !   y - preconditioned vector
302: !   ierr  - error code (nonzero if error has been detected)
303: !
304: !   Notes:
305: !   This code implements the Jacobi preconditioner plus the
306: !   SOR preconditioner
307: !
308: ! YOU CAN GET THE EXACT SAME EFFECT WITH THE PCCOMPOSITE preconditioner using
309: ! mpiexec -n 1 ex21f -ksp_monitor -pc_type composite -pc_composite_pcs jacobi,sor -pc_composite_type additive
310: !
311:       subroutine SampleShellPCApply(pc,x,y,ierr)
312:       use mymoduleex21f
313:       implicit none

315:       PC      pc
316:       Vec     x,y
317:       PetscErrorCode ierr
318:       PetscScalar  one

320:       one = 1.0
321:       call PCApply(jacobi,x,y,ierr)
322:       call PCApply(sor,x,work,ierr)
323:       call VecAXPY(y,one,work,ierr)

325:       end

327: !/*TEST
328: !
329: !   test:
330: !     requires: !single
331: !
332: !TEST*/