Date: 2013-07-02T14:50:36+00:00

Actual source code: ex5f90.F
petsc-3.4.2 2013-07-02

      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: !
      9: !/*T
     10: !  Concepts: SNES^parallel Bratu example
     11: !  Concepts: DMDA^using distributed arrays;
     12: !  Processors: n
     13: !T*/
     14: !
     15: !  --------------------------------------------------------------------------
     16: !
     17: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
     18: !  the partial differential equation
     19: !
     20: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
     21: !
     22: !  with boundary conditions
     23: !
     24: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
     25: !
     26: !  A finite difference approximation with the usual 5-point stencil
     27: !  is used to discretize the boundary value problem to obtain a nonlinear
     28: !  system of equations.
     29: !
     30: !  The uniprocessor version of this code is snes/examples/tutorials/ex4f.F
     31: !
     32: !  --------------------------------------------------------------------------
     33: !  The following define must be used before including any PETSc include files
     34: !  into a module or interface. This is because they can't handle declarations
     35: !  in them
     36: !

     38:       module f90module
     39:       type userctx
     40: #include <finclude/petscsysdef.h>
     41: #include <finclude/petscvecdef.h>
     42: #include <finclude/petscdmdef.h>
     43:         PetscInt xs,xe,xm,gxs,gxe,gxm
     44:         PetscInt ys,ye,ym,gys,gye,gym
     45:         PetscInt mx,my
     46:         PetscMPIInt rank
     47:         double precision lambda
     48:       end type userctx

     50:       contains
     51: ! ---------------------------------------------------------------------
     52: !
     53: !  FormFunction - Evaluates nonlinear function, F(x).
     54: !
     55: !  Input Parameters:
     56: !  snes - the SNES context
     57: !  X - input vector
     58: !  dummy - optional user-defined context, as set by SNESSetFunction()
     59: !          (not used here)
     60: !
     61: !  Output Parameter:
     62: !  F - function vector
     63: !
     64: !  Notes:
     65: !  This routine serves as a wrapper for the lower-level routine
     66: !  "FormFunctionLocal", where the actual computations are
     67: !  done using the standard Fortran style of treating the local
     68: !  vector data as a multidimensional array over the local mesh.
     69: !  This routine merely handles ghost point scatters and accesses
     70: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
     71: !
     72:       subroutine FormFunction(snes,X,F,user,ierr)
     73:       implicit none

     75: #include <finclude/petscsys.h>
     76: #include <finclude/petscvec.h>
     77: #include <finclude/petscdmda.h>
     78: #include <finclude/petscis.h>
     79: #include <finclude/petscmat.h>
     80: #include <finclude/petscksp.h>
     81: #include <finclude/petscpc.h>
     82: #include <finclude/petscsnes.h>
     83: #include <finclude/petscvec.h90>
     84: #include <finclude/petscsnes.h90>

     86: !  Input/output variables:
     87:       SNES           snes
     88:       Vec            X,F
     89:       PetscErrorCode ierr
     90:       type (userctx) user
     91:       DM             da

     93: !  Declarations for use with local arrays:
     94:       PetscScalar,pointer :: lx_v(:),lf_v(:)
     95:       Vec            localX

     97: !  Scatter ghost points to local vector, using the 2-step process
     98: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
     99: !  By placing code between these two statements, computations can
    100: !  be done while messages are in transition.
    101:       call SNESGetDM(snes,da,ierr)
    102:       call DMGetLocalVector(da,localX,ierr)
    103:       call DMGlobalToLocalBegin(da,X,INSERT_VALUES,                     &
    104:      &     localX,ierr)
    105:       call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr)

    107: !  Get a pointer to vector data.
    108: !    - For default PETSc vectors, VecGetArray90() returns a pointer to
    109: !      the data array. Otherwise, the routine is implementation dependent.
    110: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
    111: !      the array.
    112: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
    113: !      and is useable from Fortran-90 Only.

    115:       call VecGetArrayF90(localX,lx_v,ierr)
    116:       call VecGetArrayF90(F,lf_v,ierr)

    118: !  Compute function over the locally owned part of the grid
    119:       call FormFunctionLocal(lx_v,lf_v,user,ierr)

    121: !  Restore vectors
    122:       call VecRestoreArrayF90(localX,lx_v,ierr)
    123:       call VecRestoreArrayF90(F,lf_v,ierr)

    125: !  Insert values into global vector

    127:       call DMRestoreLocalVector(da,localX,ierr)
    128:       call PetscLogFlops(11.0d0*user%ym*user%xm,ierr)

    130: !      call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
    131: !      call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
    132:       return
    133:       end subroutine formfunction
    134:       end module f90module

    136:       module f90moduleinterfaces
    137:         use f90module

    139:       Interface SNESSetApplicationContext
    140:         Subroutine SNESSetApplicationContext(snes,ctx,ierr)
    141:         use f90module
    142:           SNES snes
    143:           type(userctx) ctx
    144:           PetscErrorCode ierr
    145:         End Subroutine
    146:       End Interface SNESSetApplicationContext

    148:       Interface SNESGetApplicationContext
    149:         Subroutine SNESGetApplicationContext(snes,ctx,ierr)
    150:         use f90module
    151:           SNES snes
    152:           type(userctx), pointer :: ctx
    153:           PetscErrorCode ierr
    154:         End Subroutine
    155:       End Interface SNESGetApplicationContext
    156:       end module f90moduleinterfaces

    158:       program main
    159:       use f90module
    160:       use f90moduleinterfaces
    161:       implicit none
    162: !
    163: #include <finclude/petscsys.h>
    164: #include <finclude/petscvec.h>
    165: #include <finclude/petscdmda.h>
    166: #include <finclude/petscis.h>
    167: #include <finclude/petscmat.h>
    168: #include <finclude/petscksp.h>
    169: #include <finclude/petscpc.h>
    170: #include <finclude/petscsnes.h>
    171: #include <finclude/petscvec.h90>
    172: #include <finclude/petscdmda.h90>

    174: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    175: !                   Variable declarations
    176: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    177: !
    178: !  Variables:
    179: !     snes        - nonlinear solver
    180: !     x, r        - solution, residual vectors
    181: !     J           - Jacobian matrix
    182: !     its         - iterations for convergence
    183: !     Nx, Ny      - number of preocessors in x- and y- directions
    184: !     matrix_free - flag - 1 indicates matrix-free version
    185: !
    186:       SNES             snes
    187:       Vec              x,r
    188:       Mat              J
    189:       PetscErrorCode   ierr
    190:       PetscInt         its
    191:       PetscBool        flg,matrix_free
    192:       PetscInt         ione,nfour
    193:       double precision lambda_max,lambda_min
    194:       type (userctx)   user
    195:       DM               da

    197: !  Note: Any user-defined Fortran routines (such as FormJacobian)
    198: !  MUST be declared as external.
    199:       external FormInitialGuess,FormJacobian

    201: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    202: !  Initialize program
    203: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    204:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
    205:       call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)

    207: !  Initialize problem parameters
    208:       lambda_max  = 6.81
    209:       lambda_min  = 0.0
    210:       user%lambda = 6.0
    211:       ione = 1
    212:       nfour = -4
    213:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par',             &
    214:      &     user%lambda,flg,ierr)
    215:       if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) &
    216:      &     then
    217:          if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
    218:          SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
    219:       endif

    221: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    222: !  Create nonlinear solver context
    223: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    224:       call SNESCreate(PETSC_COMM_WORLD,snes,ierr)

    226: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    227: !  Create vector data structures; set function evaluation routine
    228: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    230: !  Create distributed array (DMDA) to manage parallel grid and vectors

    232: ! This really needs only the star-type stencil, but we use the box
    233: ! stencil temporarily.
    234:       call DMDACreate2d(PETSC_COMM_WORLD,                               &
    235:      &     DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,                      &
    236:      &     DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,          &
    237:      &     ione,ione,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
    238:       call DMDAGetInfo(da,PETSC_NULL_INTEGER,user%mx,user%my,           &
    239:      &               PETSC_NULL_INTEGER,                                &
    240:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
    241:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
    242:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
    243:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
    244:      &               PETSC_NULL_INTEGER,ierr)

    246: !
    247: !   Visualize the distribution of the array across the processors
    248: !
    249: !     call DMView(da,PETSC_VIEWER_DRAW_WORLD,ierr)

    251: !  Extract global and local vectors from DMDA; then duplicate for remaining
    252: !  vectors that are the same types
    253:       call DMCreateGlobalVector(da,x,ierr)
    254:       call VecDuplicate(x,r,ierr)

    256: !  Get local grid boundaries (for 2-dimensional DMDA)
    257:       call DMDAGetCorners(da,user%xs,user%ys,PETSC_NULL_INTEGER,        &
    258:      &     user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
    259:       call DMDAGetGhostCorners(da,user%gxs,user%gys,                    &
    260:      &     PETSC_NULL_INTEGER,user%gxm,user%gym,                        &
    261:      &     PETSC_NULL_INTEGER,ierr)

    263: !  Here we shift the starting indices up by one so that we can easily
    264: !  use the Fortran convention of 1-based indices (rather 0-based indices).
    265:       user%xs  = user%xs+1
    266:       user%ys  = user%ys+1
    267:       user%gxs = user%gxs+1
    268:       user%gys = user%gys+1

    270:       user%ye  = user%ys+user%ym-1
    271:       user%xe  = user%xs+user%xm-1
    272:       user%gye = user%gys+user%gym-1
    273:       user%gxe = user%gxs+user%gxm-1

    275:       call SNESSetApplicationContext(snes,user,ierr)

    277: !  Set function evaluation routine and vector
    278:       call SNESSetFunction(snes,r,FormFunction,user,ierr)

    280: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    281: !  Create matrix data structure; set Jacobian evaluation routine
    282: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    284: !  Set Jacobian matrix data structure and default Jacobian evaluation
    285: !  routine. User can override with:
    286: !     -snes_fd : default finite differencing approximation of Jacobian
    287: !     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
    288: !                (unless user explicitly sets preconditioner)
    289: !     -snes_mf_operator : form preconditioning matrix as set by the user,
    290: !                         but use matrix-free approx for Jacobian-vector
    291: !                         products within Newton-Krylov method
    292: !
    293: !  Note:  For the parallel case, vectors and matrices MUST be partitioned
    294: !     accordingly.  When using distributed arrays (DMDAs) to create vectors,
    295: !     the DMDAs determine the problem partitioning.  We must explicitly
    296: !     specify the local matrix dimensions upon its creation for compatibility
    297: !     with the vector distribution.  Thus, the generic MatCreate() routine
    298: !     is NOT sufficient when working with distributed arrays.
    299: !
    300: !     Note: Here we only approximately preallocate storage space for the
    301: !     Jacobian.  See the users manual for a discussion of better techniques
    302: !     for preallocating matrix memory.

    304:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf',         &
    305:      &     matrix_free,ierr)
    306:       if (.not. matrix_free) then
    307:         call DMCreateMatrix(da,MATAIJ,J,ierr)
    308:         call SNESSetJacobian(snes,J,J,FormJacobian,user,ierr)
    309:       endif

    311: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    312: !  Customize nonlinear solver; set runtime options
    313: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    314: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
    315:       call SNESSetDM(snes,da,ierr)
    316:       call SNESSetFromOptions(snes,ierr)

    319: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    320: !  Evaluate initial guess; then solve nonlinear system.
    321: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    322: !  Note: The user should initialize the vector, x, with the initial guess
    323: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
    324: !  to employ an initial guess of zero, the user should explicitly set
    325: !  this vector to zero by calling VecSet().

    327:       call FormInitialGuess(snes,x,ierr)
    328:       call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr)
    329:       call SNESGetIterationNumber(snes,its,ierr);
    330:       if (user%rank .eq. 0) then
    331:          write(6,100) its
    332:       endif
    333:   100 format('Number of SNES iterations = ',i5)

    335: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    336: !  Free work space.  All PETSc objects should be destroyed when they
    337: !  are no longer needed.
    338: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    339:       if (.not. matrix_free) call MatDestroy(J,ierr)
    340:       call VecDestroy(x,ierr)
    341:       call VecDestroy(r,ierr)
    342:       call SNESDestroy(snes,ierr)
    343:       call DMDestroy(da,ierr)

    345:       call PetscFinalize(ierr)
    346:       end

    348: ! ---------------------------------------------------------------------
    349: !
    350: !  FormInitialGuess - Forms initial approximation.
    351: !
    352: !  Input Parameters:
    353: !  X - vector
    354: !
    355: !  Output Parameter:
    356: !  X - vector
    357: !
    358: !  Notes:
    359: !  This routine serves as a wrapper for the lower-level routine
    360: !  "InitialGuessLocal", where the actual computations are
    361: !  done using the standard Fortran style of treating the local
    362: !  vector data as a multidimensional array over the local mesh.
    363: !  This routine merely handles ghost point scatters and accesses
    364: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
    365: !
    366:       subroutine FormInitialGuess(snes,X,ierr)
    367:       use f90module
    368:       use f90moduleinterfaces
    369:       implicit none

    371: #include <finclude/petscvec.h90>
    372: #include <finclude/petscsys.h>
    373: #include <finclude/petscvec.h>
    374: #include <finclude/petscdmda.h>
    375: #include <finclude/petscis.h>
    376: #include <finclude/petscmat.h>
    377: #include <finclude/petscksp.h>
    378: #include <finclude/petscpc.h>
    379: #include <finclude/petscsnes.h>

    381: !  Input/output variables:
    382:       SNES           snes
    383:       type(userctx), pointer:: puser
    384:       Vec            X
    385:       PetscErrorCode ierr
    386:       DM             da

    388: !  Declarations for use with local arrays:
    389:       PetscScalar,pointer :: lx_v(:)
    390:       Vec               localX

    392:       0
    393:       call SNESGetDM(snes,da,ierr)
    394:       call SNESGetApplicationContext(snes,puser,ierr)
    395: !  Get a pointer to vector data.
    396: !    - For default PETSc vectors, VecGetArray90() returns a pointer to
    397: !      the data array. Otherwise, the routine is implementation dependent.
    398: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
    399: !      the array.
    400: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
    401: !      and is useable from Fortran-90 Only.

    403:       call DMGetLocalVector(da,localX,ierr)
    404:       call VecGetArrayF90(localX,lx_v,ierr)

    406: !  Compute initial guess over the locally owned part of the grid
    407:       call InitialGuessLocal(puser,lx_v,ierr)

    409: !  Restore vector
    410:       call VecRestoreArrayF90(localX,lx_v,ierr)

    412: !  Insert values into global vector
    413:       call DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X,ierr)
    414:       call DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X,ierr)
    415:       call DMRestoreLocalVector(da,localX,ierr)

    417:       return
    418:       end

    420: ! ---------------------------------------------------------------------
    421: !
    422: !  InitialGuessLocal - Computes initial approximation, called by
    423: !  the higher level routine FormInitialGuess().
    424: !
    425: !  Input Parameter:
    426: !  x - local vector data
    427: !
    428: !  Output Parameters:
    429: !  x - local vector data
    430: !  ierr - error code
    431: !
    432: !  Notes:
    433: !  This routine uses standard Fortran-style computations over a 2-dim array.
    434: !
    435:       subroutine InitialGuessLocal(user,x,ierr)
    436:       use f90module
    437:       implicit none

    439: #include <finclude/petscsys.h>
    440: #include <finclude/petscvec.h>
    441: #include <finclude/petscdmda.h>
    442: #include <finclude/petscis.h>
    443: #include <finclude/petscmat.h>
    444: #include <finclude/petscksp.h>
    445: #include <finclude/petscpc.h>
    446: #include <finclude/petscsnes.h>

    448: !  Input/output variables:
    449:       type (userctx)         user
    450:       PetscScalar  x(user%gxs:user%gxe,                                 &
    451:      &              user%gys:user%gye)
    452:       PetscErrorCode ierr

    454: !  Local variables:
    455:       PetscInt  i,j
    456:       PetscScalar   temp1,temp,hx,hy
    457:       PetscScalar   one

    459: !  Set parameters

    461:       0
    462:       one    = 1.0
    463:       hx     = one/(dble(user%mx-1))
    464:       hy     = one/(dble(user%my-1))
    465:       temp1  = user%lambda/(user%lambda + one)

    467:       do 20 j=user%ys,user%ye
    468:          temp = dble(min(j-1,user%my-j))*hy
    469:          do 10 i=user%xs,user%xe
    470:             if (i .eq. 1 .or. j .eq. 1                                  &
    471:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
    472:               x(i,j) = 0.0
    473:             else
    474:               x(i,j) = temp1 *                                          &
    475:      &          sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
    476:             endif
    477:  10      continue
    478:  20   continue

    480:       return
    481:       end

    483: ! ---------------------------------------------------------------------
    484: !
    485: !  FormFunctionLocal - Computes nonlinear function, called by
    486: !  the higher level routine FormFunction().
    487: !
    488: !  Input Parameter:
    489: !  x - local vector data
    490: !
    491: !  Output Parameters:
    492: !  f - local vector data, f(x)
    493: !  ierr - error code
    494: !
    495: !  Notes:
    496: !  This routine uses standard Fortran-style computations over a 2-dim array.
    497: !
    498:       subroutine FormFunctionLocal(x,f,user,ierr)
    499:       use f90module

    501:       implicit none

    503: !  Input/output variables:
    504:       type (userctx) user
    505:       PetscScalar  x(user%gxs:user%gxe,                                         &
    506:      &              user%gys:user%gye)
    507:       PetscScalar  f(user%xs:user%xe,                                           &
    508:      &              user%ys:user%ye)
    509:       PetscErrorCode ierr

    511: !  Local variables:
    512:       PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
    513:       PetscScalar u,uxx,uyy
    514:       PetscInt  i,j

    516:       one    = 1.0
    517:       two    = 2.0
    518:       hx     = one/dble(user%mx-1)
    519:       hy     = one/dble(user%my-1)
    520:       sc     = hx*hy*user%lambda
    521:       hxdhy  = hx/hy
    522:       hydhx  = hy/hx

    524: !  Compute function over the locally owned part of the grid

    526:       do 20 j=user%ys,user%ye
    527:          do 10 i=user%xs,user%xe
    528:             if (i .eq. 1 .or. j .eq. 1                                  &
    529:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
    530:                f(i,j) = x(i,j)
    531:             else
    532:                u = x(i,j)
    533:                uxx = hydhx * (two*u                                     &
    534:      &                - x(i-1,j) - x(i+1,j))
    535:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
    536:                f(i,j) = uxx + uyy - sc*exp(u)
    537:             endif
    538:  10      continue
    539:  20   continue

    541:       return
    542:       end

    544: ! ---------------------------------------------------------------------
    545: !
    546: !  FormJacobian - Evaluates Jacobian matrix.
    547: !
    548: !  Input Parameters:
    549: !  snes     - the SNES context
    550: !  x        - input vector
    551: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
    552: !             (not used here)
    553: !
    554: !  Output Parameters:
    555: !  jac      - Jacobian matrix
    556: !  jac_prec - optionally different preconditioning matrix (not used here)
    557: !  flag     - flag indicating matrix structure
    558: !
    559: !  Notes:
    560: !  This routine serves as a wrapper for the lower-level routine
    561: !  "FormJacobianLocal", where the actual computations are
    562: !  done using the standard Fortran style of treating the local
    563: !  vector data as a multidimensional array over the local mesh.
    564: !  This routine merely accesses the local vector data via
    565: !  VecGetArrayF90() and VecRestoreArrayF90().
    566: !
    567: !  Notes:
    568: !  Due to grid point reordering with DMDAs, we must always work
    569: !  with the local grid points, and then transform them to the new
    570: !  global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
    571: !  We cannot work directly with the global numbers for the original
    572: !  uniprocessor grid!
    573: !
    574: !  Two methods are available for imposing this transformation
    575: !  when setting matrix entries:
    576: !    (A) MatSetValuesLocal(), using the local ordering (including
    577: !        ghost points!)
    578: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
    579: !        - Associate this map with the matrix by calling
    580: !          MatSetLocalToGlobalMapping() once
    581: !        - Set matrix entries using the local ordering
    582: !          by calling MatSetValuesLocal()
    583: !    (B) MatSetValues(), using the global ordering
    584: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
    585: !        - Then apply this map explicitly yourself
    586: !        - Set matrix entries using the global ordering by calling
    587: !          MatSetValues()
    588: !  Option (A) seems cleaner/easier in many cases, and is the procedure
    589: !  used in this example.
    590: !
    591:       subroutine FormJacobian(snes,X,jac,jac_prec,flag,user,ierr)
    592:       use f90module
    593:       implicit none

    595: #include <finclude/petscsys.h>
    596: #include <finclude/petscvec.h>
    597: #include <finclude/petscdmda.h>
    598: #include <finclude/petscis.h>
    599: #include <finclude/petscmat.h>
    600: #include <finclude/petscksp.h>
    601: #include <finclude/petscpc.h>
    602: #include <finclude/petscsnes.h>

    604: #include <finclude/petscvec.h90>

    606: !  Input/output variables:
    607:       SNES         snes
    608:       Vec          X
    609:       Mat          jac,jac_prec
    610:       MatStructure flag
    611:       type(userctx)  user
    612:       PetscErrorCode ierr
    613:       DM             da

    615: !  Declarations for use with local arrays:
    616:       PetscScalar,pointer :: lx_v(:)
    617:       Vec            localX

    619: !  Scatter ghost points to local vector, using the 2-step process
    620: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd()
    621: !  Computations can be done while messages are in transition,
    622: !  by placing code between these two statements.

    624:       call SNESGetDM(snes,da,ierr)
    625:       call DMGetLocalVector(da,localX,ierr)
    626:       call DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX,              &
    627:      &     ierr)
    628:       call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr)

    630: !  Get a pointer to vector data
    631:       call VecGetArrayF90(localX,lx_v,ierr)

    633: !  Compute entries for the locally owned part of the Jacobian preconditioner.
    634:       call FormJacobianLocal(lx_v,jac_prec,user,ierr)

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

    641:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
    642:       if (jac .ne. jac_prec) then
    643:          call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
    644:       endif
    645:       call VecRestoreArrayF90(localX,lx_v,ierr)
    646:       call DMRestoreLocalVector(da,localX,ierr)
    647:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
    648:       if (jac .ne. jac_prec) then
    649:         call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
    650:       endif

    652: !  Set flag to indicate that the Jacobian matrix retains an identical
    653: !  nonzero structure throughout all nonlinear iterations (although the
    654: !  values of the entries change). Thus, we can save some work in setting
    655: !  up the preconditioner (e.g., no need to redo symbolic factorization for
    656: !  ILU/ICC preconditioners).
    657: !   - If the nonzero structure of the matrix is different during
    658: !     successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
    659: !     must be used instead.  If you are unsure whether the matrix
    660: !     structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
    661: !   - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
    662: !     believes your assertion and does not check the structure
    663: !     of the matrix.  If you erroneously claim that the structure
    664: !     is the same when it actually is not, the new preconditioner
    665: !     will not function correctly.  Thus, use this optimization
    666: !     feature with caution!

    668:       flag = SAME_NONZERO_PATTERN

    670: !  Tell the matrix we will never add a new nonzero location to the
    671: !  matrix. If we do it will generate an error.

    673:       call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,      &
    674:      &                  ierr)

    676:       return
    677:       end

    679: ! ---------------------------------------------------------------------
    680: !
    681: !  FormJacobianLocal - Computes Jacobian preconditioner matrix,
    682: !  called by the higher level routine FormJacobian().
    683: !
    684: !  Input Parameters:
    685: !  x        - local vector data
    686: !
    687: !  Output Parameters:
    688: !  jac_prec - Jacobian preconditioner matrix
    689: !  ierr     - error code
    690: !
    691: !  Notes:
    692: !  This routine uses standard Fortran-style computations over a 2-dim array.
    693: !
    694: !  Notes:
    695: !  Due to grid point reordering with DMDAs, we must always work
    696: !  with the local grid points, and then transform them to the new
    697: !  global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
    698: !  We cannot work directly with the global numbers for the original
    699: !  uniprocessor grid!
    700: !
    701: !  Two methods are available for imposing this transformation
    702: !  when setting matrix entries:
    703: !    (A) MatSetValuesLocal(), using the local ordering (including
    704: !        ghost points!)
    705: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
    706: !        - Associate this map with the matrix by calling
    707: !          MatSetLocalToGlobalMapping() once
    708: !        - Set matrix entries using the local ordering
    709: !          by calling MatSetValuesLocal()
    710: !    (B) MatSetValues(), using the global ordering
    711: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
    712: !        - Then apply this map explicitly yourself
    713: !        - Set matrix entries using the global ordering by calling
    714: !          MatSetValues()
    715: !  Option (A) seems cleaner/easier in many cases, and is the procedure
    716: !  used in this example.
    717: !
    718:       subroutine FormJacobianLocal(x,jac_prec,user,ierr)
    719:       use f90module
    720:       implicit none

    722: #include <finclude/petscsys.h>
    723: #include <finclude/petscvec.h>
    724: #include <finclude/petscdmda.h>
    725: #include <finclude/petscis.h>
    726: #include <finclude/petscmat.h>
    727: #include <finclude/petscksp.h>
    728: #include <finclude/petscpc.h>
    729: #include <finclude/petscsnes.h>

    731: !  Input/output variables:
    732:       type (userctx) user
    733:       PetscScalar    x(user%gxs:user%gxe,                                      &
    734:      &               user%gys:user%gye)
    735:       Mat            jac_prec
    736:       PetscErrorCode ierr

    738: !  Local variables:
    739:       PetscInt    row,col(5),i,j
    740:       PetscInt    ione,ifive
    741:       PetscScalar two,one,hx,hy,hxdhy
    742:       PetscScalar hydhx,sc,v(5)

    744: !  Set parameters
    745:       ione   = 1
    746:       ifive  = 5
    747:       one    = 1.0
    748:       two    = 2.0
    749:       hx     = one/dble(user%mx-1)
    750:       hy     = one/dble(user%my-1)
    751:       sc     = hx*hy
    752:       hxdhy  = hx/hy
    753:       hydhx  = hy/hx

    755: !  Compute entries for the locally owned part of the Jacobian.
    756: !   - Currently, all PETSc parallel matrix formats are partitioned by
    757: !     contiguous chunks of rows across the processors.
    758: !   - Each processor needs to insert only elements that it owns
    759: !     locally (but any non-local elements will be sent to the
    760: !     appropriate processor during matrix assembly).
    761: !   - Here, we set all entries for a particular row at once.
    762: !   - We can set matrix entries either using either
    763: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
    764: !   - Note that MatSetValues() uses 0-based row and column numbers
    765: !     in Fortran as well as in C.

    767:       do 20 j=user%ys,user%ye
    768:          row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
    769:          do 10 i=user%xs,user%xe
    770:             row = row + 1
    771: !           boundary points
    772:             if (i .eq. 1 .or. j .eq. 1                                  &
    773:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
    774:                col(1) = row
    775:                v(1)   = one
    776:                call MatSetValuesLocal(jac_prec,ione,row,ione,col,v,          &
    777:      &                           INSERT_VALUES,ierr)
    778: !           interior grid points
    779:             else
    780:                v(1) = -hxdhy
    781:                v(2) = -hydhx
    782:                v(3) = two*(hydhx + hxdhy)                               &
    783:      &                  - sc*user%lambda*exp(x(i,j))
    784:                v(4) = -hydhx
    785:                v(5) = -hxdhy
    786:                col(1) = row - user%gxm
    787:                col(2) = row - 1
    788:                col(3) = row
    789:                col(4) = row + 1
    790:                col(5) = row + user%gxm
    791:                call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v,         &
    792:      &                                INSERT_VALUES,ierr)
    793:             endif
    794:  10      continue
    795:  20   continue

    797:       return
    798:       end