Date: 2025-03-28T21:10:54+00:00

Actual source code: ex15f.F90

      1: !
      2: !   Solves a linear system in parallel with KSP.  Also indicates
      3: !   use of a user-provided preconditioner.  Input parameters include:
      4: !      -user_defined_pc : Activate a user-defined preconditioner
      5: !
      6: !     -------------------------------------------------------------------------
      7: !
      8: !     Module contains diag needed by shell preconditioner
      9: !
     10:       module ex15fmodule
     11: #include <petsc/finclude/petscksp.h>
     12:       use petscksp
     13:       Vec    diag
     14:       end module

     16:       program main
     17:       use ex15fmodule
     18:       implicit none

     20: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     21: !                   Variable declarations
     22: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     23: !
     24: !  Variables:
     25: !     ksp     - linear solver context
     26: !     ksp      - Krylov subspace method context
     27: !     pc       - preconditioner context
     28: !     x, b, u  - approx solution, right-hand side, exact solution vectors
     29: !     A        - matrix that defines linear system
     30: !     its      - iterations for convergence
     31: !     norm     - norm of solution error

     33:       Vec              x,b,u
     34:       Mat              A
     35:       PC               pc
     36:       KSP              ksp
     37:       PetscScalar      v,one,neg_one
     38:       PetscReal norm,tol
     39:       PetscErrorCode ierr
     40:       PetscInt   i,j,II,JJ,Istart
     41:       PetscInt   Iend,m,n,i1,its,five
     42:       PetscMPIInt rank
     43:       PetscBool  user_defined_pc,flg

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

     47:       external SampleShellPCSetUp, SampleShellPCApply
     48:       external  SampleShellPCDestroy

     50: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     51: !                 Beginning of program
     52: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     54:       PetscCallA(PetscInitialize(ierr))
     55:       one     = 1.0
     56:       neg_one = -1.0
     57:       i1 = 1
     58:       m       = 8
     59:       n       = 7
     60:       five    = 5
     61:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-m',m,flg,ierr))
     62:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr))
     63:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))

     65: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     66: !      Compute the matrix and right-hand-side vector that define
     67: !      the linear system, Ax = b.
     68: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     70: !  Create parallel matrix, specifying only its global dimensions.
     71: !  When using MatCreate(), the matrix format can be specified at
     72: !  runtime. Also, the parallel partitioning of the matrix is
     73: !  determined by PETSc at runtime.

     75:       PetscCallA(MatCreate(PETSC_COMM_WORLD,A,ierr))
     76:       PetscCallA(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,ierr))
     77:       PetscCallA(MatSetType(A, MATAIJ,ierr))
     78:       PetscCallA(MatSetFromOptions(A,ierr))
     79:       PetscCallA(MatMPIAIJSetPreallocation(A,five,PETSC_NULL_INTEGER_ARRAY,five,PETSC_NULL_INTEGER_ARRAY,ierr))
     80:       PetscCallA(MatSeqAIJSetPreallocation(A,five,PETSC_NULL_INTEGER_ARRAY,ierr))

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

     86:       PetscCallA(MatGetOwnershipRange(A,Istart,Iend,ierr))

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

     96:       do 10, II=Istart,Iend-1
     97:         v = -1.0
     98:         i = II/n
     99:         j = II - i*n
    100:         if (i.gt.0) then
    101:           JJ = II - n
    102:           PetscCallA(MatSetValues(A,i1,[II],i1,[JJ],[v],ADD_VALUES,ierr))
    103:         endif
    104:         if (i.lt.m-1) then
    105:           JJ = II + n
    106:           PetscCallA(MatSetValues(A,i1,[II],i1,[JJ],[v],ADD_VALUES,ierr))
    107:         endif
    108:         if (j.gt.0) then
    109:           JJ = II - 1
    110:           PetscCallA(MatSetValues(A,i1,[II],i1,[JJ],[v],ADD_VALUES,ierr))
    111:         endif
    112:         if (j.lt.n-1) then
    113:           JJ = II + 1
    114:           PetscCallA(MatSetValues(A,i1,[II],i1,[JJ],[v],ADD_VALUES,ierr))
    115:         endif
    116:         v = 4.0
    117:         PetscCallA( MatSetValues(A,i1,[II],i1,[II],[v],ADD_VALUES,ierr))
    118:  10   continue

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

    125:       PetscCallA(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr))
    126:       PetscCallA(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr))

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

    138:       PetscCallA(VecCreateFromOptions(PETSC_COMM_WORLD,PETSC_NULL_CHARACTER,i1,PETSC_DECIDE,m*n,u,ierr))
    139:       PetscCallA(VecDuplicate(u,b,ierr))
    140:       PetscCallA(VecDuplicate(b,x,ierr))

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

    144:       PetscCallA(VecSet(u,one,ierr))
    145:       PetscCallA(MatMult(A,u,b,ierr))

    147: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    148: !         Create the linear solver and set various options
    149: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    151: !  Create linear solver context

    153:       PetscCallA(KSPCreate(PETSC_COMM_WORLD,ksp,ierr))

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

    158:       PetscCallA(KSPSetOperators(ksp,A,A,ierr))

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

    165:       PetscCallA(KSPGetPC(ksp,pc,ierr))
    166:       tol = 1.e-7
    167:       PetscCallA(KSPSetTolerances(ksp,tol,PETSC_CURRENT_REAL,PETSC_CURRENT_REAL,PETSC_CURRENT_INTEGER,ierr))

    169: !
    170: !  Set a user-defined shell preconditioner if desired
    171: !
    172:       PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-user_defined_pc',user_defined_pc,ierr))

    174:       if (user_defined_pc) then

    176: !  (Required) Indicate to PETSc that we are using a shell preconditioner
    177:          PetscCallA(PCSetType(pc,PCSHELL,ierr))

    179: !  (Required) Set the user-defined routine for applying the preconditioner
    180:          PetscCallA(PCShellSetApply(pc,SampleShellPCApply,ierr))

    182: !  (Optional) Do any setup required for the preconditioner
    183:          PetscCallA(PCShellSetSetUp(pc,SampleShellPCSetUp,ierr))

    185: !  (Optional) Frees any objects we created for the preconditioner
    186:          PetscCallA(PCShellSetDestroy(pc,SampleShellPCDestroy,ierr))

    188:       else
    189:          PetscCallA(PCSetType(pc,PCJACOBI,ierr))
    190:       endif

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

    198:       PetscCallA(KSPSetFromOptions(ksp,ierr))

    200: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    201: !                      Solve the linear system
    202: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    204:       PetscCallA(KSPSolve(ksp,b,x,ierr))

    206: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    207: !                     Check solution and clean up
    208: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    210: !  Check the error

    212:       PetscCallA(VecAXPY(x,neg_one,u,ierr))
    213:       PetscCallA(VecNorm(x,NORM_2,norm,ierr))
    214:       PetscCallA(KSPGetIterationNumber(ksp,its,ierr))

    216:       if (rank .eq. 0) then
    217:         if (norm .gt. 1.e-12) then
    218:            write(6,100) norm,its
    219:         else
    220:            write(6,110) its
    221:         endif
    222:       endif
    223:   100 format('Norm of error ',1pe11.4,' iterations ',i5)
    224:   110 format('Norm of error < 1.e-12,iterations ',i5)

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

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

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

    237:       PetscCallA(PetscFinalize(ierr))
    238:       end

    240: !/***********************************************************************/
    241: !/*          Routines for a user-defined shell preconditioner           */
    242: !/***********************************************************************/

    244: !
    245: !   SampleShellPCSetUp - This routine sets up a user-defined
    246: !   preconditioner context.
    247: !
    248: !   Input Parameters:
    249: !   pc - preconditioner object
    250: !
    251: !   Output Parameter:
    252: !   ierr  - error code (nonzero if error has been detected)
    253: !
    254: !   Notes:
    255: !   In this example, we define the shell preconditioner to be Jacobi
    256: !   method.  Thus, here we create a work vector for storing the reciprocal
    257: !   of the diagonal of the preconditioner matrix; this vector is then
    258: !   used within the routine SampleShellPCApply().
    259: !
    260:       subroutine SampleShellPCSetUp(pc,ierr)
    261:       use ex15fmodule
    262:       implicit none

    264:       PC      pc
    265:       Mat     pmat
    266:       PetscErrorCode ierr

    268:       PetscCallA(PCGetOperators(pc,PETSC_NULL_MAT,pmat,ierr))
    269:       PetscCallA(MatCreateVecs(pmat,diag,PETSC_NULL_VEC,ierr))
    270:       PetscCallA(MatGetDiagonal(pmat,diag,ierr))
    271:       PetscCallA(VecReciprocal(diag,ierr))

    273:       end

    275: ! -------------------------------------------------------------------
    276: !
    277: !   SampleShellPCApply - This routine demonstrates the use of a
    278: !   user-provided preconditioner.
    279: !
    280: !   Input Parameters:
    281: !   pc - preconditioner object
    282: !   x - input vector
    283: !
    284: !   Output Parameters:
    285: !   y - preconditioned vector
    286: !   ierr  - error code (nonzero if error has been detected)
    287: !
    288: !   Notes:
    289: !   This code implements the Jacobi preconditioner, merely as an
    290: !   example of working with a PCSHELL.  Note that the Jacobi method
    291: !   is already provided within PETSc.
    292: !
    293:       subroutine SampleShellPCApply(pc,x,y,ierr)
    294:       use ex15fmodule
    295:       implicit none

    297:       PC      pc
    298:       Vec     x,y
    299:       PetscErrorCode ierr

    301:       PetscCallA(VecPointwiseMult(y,x,diag,ierr))

    303:       end

    305: !/***********************************************************************/
    306: !/*          Routines for a user-defined shell preconditioner           */
    307: !/***********************************************************************/

    309: !
    310: !   SampleShellPCDestroy - This routine destroys (frees the memory of) any
    311: !      objects we made for the preconditioner
    312: !
    313: !   Input Parameters:
    314: !   pc - for this example we use the actual PC as our shell context
    315: !
    316: !   Output Parameter:
    317: !   ierr  - error code (nonzero if error has been detected)
    318: !

    320:       subroutine SampleShellPCDestroy(pc,ierr)
    321:       use ex15fmodule
    322:       implicit none

    324:       PC      pc
    325:       PetscErrorCode ierr

    327: !  Normally we would recommend storing all the work data (like diag) in
    328: !  the context set with PCShellSetContext()

    330:       PetscCallA(VecDestroy(diag,ierr))

    332:       end

    334: !
    335: !/*TEST
    336: !
    337: !   test:
    338: !      nsize: 2
    339: !      args: -ksp_view -user_defined_pc -ksp_gmres_cgs_refinement_type refine_always
    340: !
    341: !TEST*/