Actual source code: ex11f.F

      1: !
      2: !  Description: Solves a complex linear system in parallel with KSP (Fortran code).
      3: !
      4: !/*T
      5: !  Concepts: KSP^solving a Helmholtz equation
      6: !  Concepts: complex numbers
      7: !  Processors: n
      8: !T*/
      9: !
     10: !  The model problem:
     11: !     Solve Helmholtz equation on the unit square: (0,1) x (0,1)
     12: !          -delta u - sigma1*u + i*sigma2*u = f,
     13: !           where delta = Laplace operator
     14: !     Dirichlet b.c.'s on all sides
     15: !     Use the 2-D, five-point finite difference stencil.
     16: !
     17: !     Compiling the code:
     18: !      This code uses the complex numbers version of PETSc, so configure
     19: !      must be run to enable this
     20: !
     21: !
     22: ! -----------------------------------------------------------------------

     24:       program main
     25:       implicit none

     27: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     28: !                    Include files
     29: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     30: !
     31: !  The following include statements are required for KSP Fortran programs:
     32: !     petsc.h       - base PETSc routines
     33: !     petscvec.h    - vectors
     34: !     petscmat.h    - matrices
     35: !     petscpc.h     - preconditioners
     36: !     petscksp.h    - Krylov subspace methods
     37: !  Include the following to use PETSc random numbers:
     38: !     petscsys.h    - system routines
     39: !  Additional include statements may be needed if using other PETSc
     40: !  routines in a Fortran program, e.g.,
     41: !     petscviewer.h - viewers
     42: !     petscis.h     - index sets
     43: !
     44:  #include include/finclude/petsc.h
     45:  #include include/finclude/petscvec.h
     46:  #include include/finclude/petscmat.h
     47:  #include include/finclude/petscpc.h
     48:  #include include/finclude/petscksp.h
     49:  #include include/finclude/petscsys.h
     50: !
     51: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52: !                   Variable declarations
     53: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     54: !
     55: !  Variables:
     56: !     ksp     - linear solver context
     57: !     x, b, u  - approx solution, right-hand-side, exact solution vectors
     58: !     A        - matrix that defines linear system
     59: !     its      - iterations for convergence
     60: !     norm     - norm of error in solution
     61: !     rctx     - random number context
     62: !

     64:       KSP             ksp
     65:       Mat              A
     66:       Vec              x,b,u
     67:       PetscRandom      rctx
     68:       double precision norm,h2,sigma1
     69:       PetscScalar      none,sigma2,v,pfive
     70:       PetscInt          dim,its,n,Istart,Iend,i,j,II,JJ,one
     71:       PetscErrorCode ierr
     72:       PetscMPIInt rank
     73:       PetscTruth flg
     74:       logical          use_random

     76: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     77: !                 Beginning of program
     78: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     80:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
     81: #if !defined(PETSC_USE_COMPLEX)
     82:       write(6,*) "This example requires complex numbers."
     83:       goto 200
     84: #endif

     86:       none   = -1.0
     87:       n      = 6
     88:       sigma1 = 100.0
     89:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
     90:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-sigma1',sigma1,      &
     91:      &                       flg,ierr)
     92:       call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-n',n,flg,ierr)
     93:       dim    = n*n

     95: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     96: !      Compute the matrix and right-hand-side vector that define
     97: !      the linear system, Ax = b.
     98: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    100: !  Create parallel matrix, specifying only its global dimensions.
    101: !  When using MatCreate(), the matrix format can be specified at
    102: !  runtime. Also, the parallel partitioning of the matrix is
    103: !  determined by PETSc at runtime.

    105:       call MatCreate(PETSC_COMM_WORLD,A,ierr)
    106:       call MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim,ierr)
    107:       call MatSetFromOptions(A,ierr)

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

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

    115: !  Set matrix elements in parallel.
    116: !   - Each processor needs to insert only elements that it owns
    117: !     locally (but any non-local elements will be sent to the
    118: !     appropriate processor during matrix assembly).
    119: !   - Always specify global rows and columns of matrix entries.

    121:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-norandom',        &
    122:      &     flg,ierr)
    123:       if (flg .eq. 1) then
    124:          use_random = .false.
    125:          sigma2 = 10.0*PETSC_i
    126:       else
    127:          use_random = .true.
    128:          call PetscRandomCreate(PETSC_COMM_WORLD,                       &
    129:      &        RANDOM_DEFAULT_IMAGINARY,rctx,ierr)
    130:       endif
    131:       h2 = 1.0/((n+1)*(n+1))

    133:       one = 1
    134:       do 10, II=Istart,Iend-1
    135:         v = -1.0
    136:         i = II/n
    137:         j = II - i*n
    138:         if (i.gt.0) then
    139:           JJ = II - n
    140:           call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
    141:         endif
    142:         if (i.lt.n-1) then
    143:           JJ = II + n
    144:           call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
    145:         endif
    146:         if (j.gt.0) then
    147:           JJ = II - 1
    148:           call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
    149:         endif
    150:         if (j.lt.n-1) then
    151:           JJ = II + 1
    152:           call MatSetValues(A,one,II,one,JJ,v,ADD_VALUES,ierr)
    153:         endif
    154:         if (use_random) call PetscRandomGetValue(rctx,sigma2,ierr)
    155:         v = 4.0 - sigma1*h2 + sigma2*h2
    156:         call  MatSetValues(A,one,II,one,II,v,ADD_VALUES,ierr)
    157:  10   continue
    158:       if (use_random) call PetscRandomDestroy(rctx,ierr)

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

    165:       call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
    166:       call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)

    168: !  Create parallel vectors.
    169: !   - Here, the parallel partitioning of the vector is determined by
    170: !     PETSc at runtime.  We could also specify the local dimensions
    171: !     if desired.
    172: !   - Note: We form 1 vector from scratch and then duplicate as needed.

    174:       call VecCreate(PETSC_COMM_WORLD,u,ierr)
    175:       call VecSetSizes(u,PETSC_DECIDE,dim,ierr)
    176:       call VecSetFromOptions(u,ierr)
    177:       call VecDuplicate(u,b,ierr)
    178:       call VecDuplicate(b,x,ierr)

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

    182:       if (use_random) then
    183:          call PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,        &
    184:      &                          rctx,ierr)
    185:          call VecSetRandom(rctx,u,ierr)
    186:       else
    187:          pfive = 0.5
    188:          call VecSet(u,pfive,ierr)
    189:       endif
    190:       call MatMult(A,u,b,ierr)

    192: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    193: !         Create the linear solver and set various options
    194: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    196: !  Create linear solver context

    198:       call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)

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

    203:       call KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN,ierr)

    205: !  Set runtime options, e.g.,
    206: !      -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>

    208:       call KSPSetFromOptions(ksp,ierr)

    210: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    211: !                      Solve the linear system
    212: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    216: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    217: !                     Check solution and clean up
    218: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    220: !  Check the error

    222:       call VecAXPY(x,none,u,ierr)
    223:       call VecNorm(x,NORM_2,norm,ierr)
    224:       call KSPGetIterationNumber(ksp,its,ierr)
    225:       if (rank .eq. 0) then
    226:         if (norm .gt. 1.e-12) then
    227:            write(6,100) norm,its
    228:         else
    229:            write(6,110) its
    230:         endif
    231:       endif
    232:   100 format('Norm of error ',e10.4,',iterations ',i5)
    233:   110 format('Norm of error < 1.e-12,iterations ',i5)

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

    238:       if (use_random) call PetscRandomDestroy(rctx,ierr)
    239:       call KSPDestroy(ksp,ierr)
    240:       call VecDestroy(u,ierr)
    241:       call VecDestroy(x,ierr)
    242:       call VecDestroy(b,ierr)
    243:       call MatDestroy(A,ierr)

    245:  200  continue
    246:       call PetscFinalize(ierr)
    247:       end