Date: 2013-07-02T14:50:37+00:00

Actual source code: ex5f90t.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: #include <finclude/petscdmdef.h>
     40:       use petscdmdef
     41:       type userctx
     42:         type(DM) da
     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(snesIn,X,F,user,ierr)
     73: #include <finclude/petscsnesdef.h>
     74:       use petscsnes

     76: !  Input/output variables:
     77:       type(SNES)     snesIn
     78:       type(Vec)      X,F
     79:       PetscErrorCode ierr
     80:       type (userctx) user

     82: !  Declarations for use with local arrays:
     83:       PetscScalar,pointer :: lx_v(:),lf_v(:)
     84:       type(Vec)              localX

     86: !  Scatter ghost points to local vector, using the 2-step process
     87: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
     88: !  By placing code between these two statements, computations can
     89: !  be done while messages are in transition.
     90:       call DMGetLocalVector(user%da,localX,ierr)
     91:       call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,                &
     92:      &     localX,ierr)
     93:       call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)

     95: !  Get a pointer to vector data.
     96: !    - For default PETSc vectors, VecGetArray90() returns a pointer to
     97: !      the data array. Otherwise, the routine is implementation dependent.
     98: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
     99: !      the array.
    100: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
    101: !      and is useable from Fortran-90 Only.

    103:       call VecGetArrayF90(localX,lx_v,ierr)
    104:       call VecGetArrayF90(F,lf_v,ierr)

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

    109: !  Restore vectors
    110:       call VecRestoreArrayF90(localX,lx_v,ierr)
    111:       call VecRestoreArrayF90(F,lf_v,ierr)

    113: !  Insert values into global vector

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

    118: !      call VecView(X,PETSC_VIEWER_STDOUT_WORLD,ierr)
    119: !      call VecView(F,PETSC_VIEWER_STDOUT_WORLD,ierr)
    120:       return
    121:       end subroutine formfunction
    122:       end module f90module

    124:       module f90moduleinterfaces
    125:         use f90module

    127:       Interface SNESSetApplicationContext
    128:         Subroutine SNESSetApplicationContext(snesIn,ctx,ierr)
    129: #include <finclude/petscsnesdef.h>
    130:         use petscsnes
    131:         use f90module
    132:           type(SNES)    snesIn
    133:           type(userctx) ctx
    134:           PetscErrorCode ierr
    135:         End Subroutine
    136:       End Interface SNESSetApplicationContext

    138:       Interface SNESGetApplicationContext
    139:         Subroutine SNESGetApplicationContext(snesIn,ctx,ierr)
    140: #include <finclude/petscsnesdef.h>
    141:         use petscsnes
    142:         use f90module
    143:           type(SNES)     snesIn
    144:           type(userctx), pointer :: ctx
    145:           PetscErrorCode ierr
    146:         End Subroutine
    147:       End Interface SNESGetApplicationContext
    148:       end module f90moduleinterfaces

    150:       program main
    151: #include <finclude/petscdmdef.h>
    152: #include <finclude/petscsnesdef.h>
    153:       use petscdm
    154:       use petscsnes
    155:       use f90module
    156:       use f90moduleinterfaces
    157: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    158: !                   Variable declarations
    159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    160: !
    161: !  Variables:
    162: !     mysnes      - nonlinear solver
    163: !     x, r        - solution, residual vectors
    164: !     J           - Jacobian matrix
    165: !     its         - iterations for convergence
    166: !     Nx, Ny      - number of preocessors in x- and y- directions
    167: !     matrix_free - flag - 1 indicates matrix-free version
    168: !
    169:       type(SNES)       mysnes
    170:       type(Vec)        x,r
    171:       type(Mat)        J
    172:       PetscErrorCode   ierr
    173:       PetscInt         its
    174:       PetscBool        flg,matrix_free
    175:       PetscInt         ione,nfour
    176:       double precision lambda_max,lambda_min
    177:       type(userctx)    user
    178:       type(userctx), pointer:: puser

    180: !  Note: Any user-defined Fortran routines (such as FormJacobian)
    181: !  MUST be declared as external.
    182:       external FormInitialGuess,FormJacobian

    184: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    185: !  Initialize program
    186: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    187:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
    188:       call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)

    190: !  Initialize problem parameters
    191:       lambda_max  = 6.81
    192:       lambda_min  = 0.0
    193:       user%lambda = 6.0
    194:       ione = 1
    195:       nfour = -4
    196:       call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-par',             &
    197:      &     user%lambda,flg,ierr)
    198:       if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) &
    199:      &     then
    200:          if (user%rank .eq. 0) write(6,*) 'Lambda is out of range'
    201:          SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
    202:       endif

    204: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    205: !  Create nonlinear solver context
    206: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    207:       call SNESCreate(PETSC_COMM_WORLD,mysnes,ierr)

    209: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    210: !  Create vector data structures; set function evaluation routine
    211: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    215: ! This really needs only the star-type stencil, but we use the box
    216: ! stencil temporarily.
    217:       call DMDACreate2d(PETSC_COMM_WORLD,                               &
    218:      &     DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,                      &
    219:      &     DMDA_STENCIL_BOX,nfour,nfour,PETSC_DECIDE,PETSC_DECIDE,          &
    220:      &     ione,ione,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,user%da,ierr)
    221:       call DMDAGetInfo(user%da,PETSC_NULL_INTEGER,user%mx,user%my,        &
    222:      &               PETSC_NULL_INTEGER,                                &
    223:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
    224:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
    225:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
    226:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,             &
    227:      &               PETSC_NULL_INTEGER,ierr)

    229: !
    230: !   Visualize the distribution of the array across the processors
    231: !
    232: !     call DMView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)

    234: !  Extract global and local vectors from DMDA; then duplicate for remaining
    235: !  vectors that are the same types
    236:       call DMCreateGlobalVector(user%da,x,ierr)
    237:       call VecDuplicate(x,r,ierr)

    239: !  Get local grid boundaries (for 2-dimensional DMDA)
    240:       call DMDAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER,     &
    241:      &     user%xm,user%ym,PETSC_NULL_INTEGER,ierr)
    242:       call DMDAGetGhostCorners(user%da,user%gxs,user%gys,                 &
    243:      &     PETSC_NULL_INTEGER,user%gxm,user%gym,                        &
    244:      &     PETSC_NULL_INTEGER,ierr)

    246: !  Here we shift the starting indices up by one so that we can easily
    247: !  use the Fortran convention of 1-based indices (rather 0-based indices).
    248:       user%xs  = user%xs+1
    249:       user%ys  = user%ys+1
    250:       user%gxs = user%gxs+1
    251:       user%gys = user%gys+1

    253:       user%ye  = user%ys+user%ym-1
    254:       user%xe  = user%xs+user%xm-1
    255:       user%gye = user%gys+user%gym-1
    256:       user%gxe = user%gxs+user%gxm-1

    258:       call SNESSetApplicationContext(mysnes,user,ierr)

    260: !  Set function evaluation routine and vector
    261:       call SNESSetFunction(mysnes,r,FormFunction,user,ierr)

    263: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    264: !  Create matrix data structure; set Jacobian evaluation routine
    265: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    267: !  Set Jacobian matrix data structure and default Jacobian evaluation
    268: !  routine. User can override with:
    269: !     -snes_fd : default finite differencing approximation of Jacobian
    270: !     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
    271: !                (unless user explicitly sets preconditioner)
    272: !     -snes_mf_operator : form preconditioning matrix as set by the user,
    273: !                         but use matrix-free approx for Jacobian-vector
    274: !                         products within Newton-Krylov method
    275: !
    276: !  Note:  For the parallel case, vectors and matrices MUST be partitioned
    277: !     accordingly.  When using distributed arrays (DMDAs) to create vectors,
    278: !     the DMDAs determine the problem partitioning.  We must explicitly
    279: !     specify the local matrix dimensions upon its creation for compatibility
    280: !     with the vector distribution.  Thus, the generic MatCreate() routine
    281: !     is NOT sufficient when working with distributed arrays.
    282: !
    283: !     Note: Here we only approximately preallocate storage space for the
    284: !     Jacobian.  See the users manual for a discussion of better techniques
    285: !     for preallocating matrix memory.

    287:       call PetscOptionsHasName(PETSC_NULL_CHARACTER,'-snes_mf',         &
    288:      &     matrix_free,ierr)
    289:       if (.not. matrix_free) then
    290:         call DMCreateMatrix(user%da,MATAIJ,J,ierr)
    291:         call SNESSetJacobian(mysnes,J,J,FormJacobian,user,ierr)
    292:       endif

    294: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    295: !  Customize nonlinear solver; set runtime options
    296: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    297: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
    298:       call SNESSetFromOptions(mysnes,ierr)

    300: !     Test Fortran90 wrapper for SNESSet/Get ApplicationContext()
    301:       call PetscOptionsGetBool(PETSC_NULL_CHARACTER,'-test_appctx',             &
    302:      &     flg,PETSC_NULL_CHARACTER,ierr)
    303:       if (flg) then
    304:         call SNESGetApplicationContext(mysnes,puser,ierr)
    305:       endif

    307: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    308: !  Evaluate initial guess; then solve nonlinear system.
    309: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    310: !  Note: The user should initialize the vector, x, with the initial guess
    311: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
    312: !  to employ an initial guess of zero, the user should explicitly set
    313: !  this vector to zero by calling VecSet().

    315:       call FormInitialGuess(mysnes,x,ierr)
    316:       call SNESSolve(mysnes,PETSC_NULL_OBJECT,x,ierr)
    317:       call SNESGetIterationNumber(mysnes,its,ierr);
    318:       if (user%rank .eq. 0) then
    319:          write(6,100) its
    320:       endif
    321:   100 format('Number of SNES iterations = ',i5)

    323: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    324: !  Free work space.  All PETSc objects should be destroyed when they
    325: !  are no longer needed.
    326: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    327:       if (.not. matrix_free) call MatDestroy(J,ierr)
    328:       call VecDestroy(x,ierr)
    329:       call VecDestroy(r,ierr)
    330:       call SNESDestroy(mysnes,ierr)
    331:       call DMDestroy(user%da,ierr)

    333:       call PetscFinalize(ierr)
    334:       end

    336: ! ---------------------------------------------------------------------
    337: !
    338: !  FormInitialGuess - Forms initial approximation.
    339: !
    340: !  Input Parameters:
    341: !  X - vector
    342: !
    343: !  Output Parameter:
    344: !  X - vector
    345: !
    346: !  Notes:
    347: !  This routine serves as a wrapper for the lower-level routine
    348: !  "InitialGuessLocal", where the actual computations are
    349: !  done using the standard Fortran style of treating the local
    350: !  vector data as a multidimensional array over the local mesh.
    351: !  This routine merely handles ghost point scatters and accesses
    352: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
    353: !
    354:       subroutine FormInitialGuess(mysnes,X,ierr)
    355: #include <finclude/petscsnesdef.h>
    356:       use petscsnes
    357:       use f90module
    358:       use f90moduleinterfaces
    359: !  Input/output variables:
    360:       type(SNES)     mysnes
    361:       type(userctx), pointer:: puser
    362:       type(Vec)      X
    363:       PetscErrorCode ierr

    365: !  Declarations for use with local arrays:
    366:       PetscScalar,pointer :: lx_v(:)
    367:       type(Vec)      localX

    369:       0
    370:       call SNESGetApplicationContext(mysnes,puser,ierr)
    371: !  Get a pointer to vector data.
    372: !    - For default PETSc vectors, VecGetArray90() returns a pointer to
    373: !      the data array. Otherwise, the routine is implementation dependent.
    374: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
    375: !      the array.
    376: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
    377: !      and is useable from Fortran-90 Only.

    379:       call DMGetLocalVector(puser%da,localX,ierr)
    380:       call VecGetArrayF90(localX,lx_v,ierr)

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

    385: !  Restore vector
    386:       call VecRestoreArrayF90(localX,lx_v,ierr)

    388: !  Insert values into global vector
    389:       call DMLocalToGlobalBegin(puser%da,localX,INSERT_VALUES,X,ierr)
    390:       call DMLocalToGlobalEnd(puser%da,localX,INSERT_VALUES,X,ierr)
    391:       call DMRestoreLocalVector(puser%da,localX,ierr)

    393:       return
    394:       end

    396: ! ---------------------------------------------------------------------
    397: !
    398: !  InitialGuessLocal - Computes initial approximation, called by
    399: !  the higher level routine FormInitialGuess().
    400: !
    401: !  Input Parameter:
    402: !  x - local vector data
    403: !
    404: !  Output Parameters:
    405: !  x - local vector data
    406: !  ierr - error code
    407: !
    408: !  Notes:
    409: !  This routine uses standard Fortran-style computations over a 2-dim array.
    410: !
    411:       subroutine InitialGuessLocal(user,x,ierr)
    412: #include <finclude/petscsysdef.h>
    413:       use petscsys
    414:       use f90module
    415: !  Input/output variables:
    416:       type (userctx)         user
    417:       PetscScalar  x(user%gxs:user%gxe,                                 &
    418:      &              user%gys:user%gye)
    419:       PetscErrorCode ierr

    421: !  Local variables:
    422:       PetscInt  i,j
    423:       PetscScalar   temp1,temp,hx,hy
    424:       PetscScalar   one

    426: !  Set parameters

    428:       0
    429:       one    = 1.0
    430:       hx     = one/(dble(user%mx-1))
    431:       hy     = one/(dble(user%my-1))
    432:       temp1  = user%lambda/(user%lambda + one)

    434:       do 20 j=user%ys,user%ye
    435:          temp = dble(min(j-1,user%my-j))*hy
    436:          do 10 i=user%xs,user%xe
    437:             if (i .eq. 1 .or. j .eq. 1                                  &
    438:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
    439:               x(i,j) = 0.0
    440:             else
    441:               x(i,j) = temp1 *                                          &
    442:      &          sqrt(min(dble(min(i-1,user%mx-i)*hx),dble(temp)))
    443:             endif
    444:  10      continue
    445:  20   continue

    447:       return
    448:       end

    450: ! ---------------------------------------------------------------------
    451: !
    452: !  FormFunctionLocal - Computes nonlinear function, called by
    453: !  the higher level routine FormFunction().
    454: !
    455: !  Input Parameter:
    456: !  x - local vector data
    457: !
    458: !  Output Parameters:
    459: !  f - local vector data, f(x)
    460: !  ierr - error code
    461: !
    462: !  Notes:
    463: !  This routine uses standard Fortran-style computations over a 2-dim array.
    464: !
    465:       subroutine FormFunctionLocal(x,f,user,ierr)
    466: #include <finclude/petscsysdef.h>
    467:       use petscsys
    468:       use f90module
    469: !  Input/output variables:
    470:       type (userctx) user
    471:       PetscScalar  x(user%gxs:user%gxe,                                         &
    472:      &              user%gys:user%gye)
    473:       PetscScalar  f(user%xs:user%xe,                                           &
    474:      &              user%ys:user%ye)
    475:       PetscErrorCode ierr

    477: !  Local variables:
    478:       PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
    479:       PetscScalar u,uxx,uyy
    480:       PetscInt  i,j

    482:       one    = 1.0
    483:       two    = 2.0
    484:       hx     = one/dble(user%mx-1)
    485:       hy     = one/dble(user%my-1)
    486:       sc     = hx*hy*user%lambda
    487:       hxdhy  = hx/hy
    488:       hydhx  = hy/hx

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

    492:       do 20 j=user%ys,user%ye
    493:          do 10 i=user%xs,user%xe
    494:             if (i .eq. 1 .or. j .eq. 1                                  &
    495:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
    496:                f(i,j) = x(i,j)
    497:             else
    498:                u = x(i,j)
    499:                uxx = hydhx * (two*u                                     &
    500:      &                - x(i-1,j) - x(i+1,j))
    501:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
    502:                f(i,j) = uxx + uyy - sc*exp(u)
    503:             endif
    504:  10      continue
    505:  20   continue
    506:       0
    507:       return
    508:       end

    510: ! ---------------------------------------------------------------------
    511: !
    512: !  FormJacobian - Evaluates Jacobian matrix.
    513: !
    514: !  Input Parameters:
    515: !  snes     - the SNES context
    516: !  x        - input vector
    517: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
    518: !             (not used here)
    519: !
    520: !  Output Parameters:
    521: !  jac      - Jacobian matrix
    522: !  jac_prec - optionally different preconditioning matrix (not used here)
    523: !  flag     - flag indicating matrix structure
    524: !
    525: !  Notes:
    526: !  This routine serves as a wrapper for the lower-level routine
    527: !  "FormJacobianLocal", where the actual computations are
    528: !  done using the standard Fortran style of treating the local
    529: !  vector data as a multidimensional array over the local mesh.
    530: !  This routine merely accesses the local vector data via
    531: !  VecGetArrayF90() and VecRestoreArrayF90().
    532: !
    533: !  Notes:
    534: !  Due to grid point reordering with DMDAs, we must always work
    535: !  with the local grid points, and then transform them to the new
    536: !  global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
    537: !  We cannot work directly with the global numbers for the original
    538: !  uniprocessor grid!
    539: !
    540: !  Two methods are available for imposing this transformation
    541: !  when setting matrix entries:
    542: !    (A) MatSetValuesLocal(), using the local ordering (including
    543: !        ghost points!)
    544: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
    545: !        - Associate this map with the matrix by calling
    546: !          MatSetLocalToGlobalMapping() once
    547: !        - Set matrix entries using the local ordering
    548: !          by calling MatSetValuesLocal()
    549: !    (B) MatSetValues(), using the global ordering
    550: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
    551: !        - Then apply this map explicitly yourself
    552: !        - Set matrix entries using the global ordering by calling
    553: !          MatSetValues()
    554: !  Option (A) seems cleaner/easier in many cases, and is the procedure
    555: !  used in this example.
    556: !
    557:       subroutine FormJacobian(mysnes,X,jac,jac_prec,flag,user,ierr)
    558: #include <finclude/petscsnesdef.h>
    559:       use petscsnes
    560:       use f90module
    561: !  Input/output variables:
    562:       type(SNES)     mysnes
    563:       type(Vec)      X
    564:       type(Mat)      jac,jac_prec
    565:       MatStructure   flag
    566:       type(userctx)  user
    567:       PetscErrorCode ierr

    569: !  Declarations for use with local arrays:
    570:       PetscScalar,pointer :: lx_v(:)
    571:       type(Vec)      localX

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

    578:       call DMGetLocalVector(user%da,localX,ierr)
    579:       call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,            &
    580:      &     ierr)
    581:       call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)

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

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

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

    594:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
    595: !      if (jac .ne. jac_prec) then
    596:          call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
    597: !      endif
    598:       call VecRestoreArrayF90(localX,lx_v,ierr)
    599:       call DMRestoreLocalVector(user%da,localX,ierr)
    600:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
    601: !      if (jac .ne. jac_prec) then
    602:         call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
    603: !      endif

    605: !  Set flag to indicate that the Jacobian matrix retains an identical
    606: !  nonzero structure throughout all nonlinear iterations (although the
    607: !  values of the entries change). Thus, we can save some work in setting
    608: !  up the preconditioner (e.g., no need to redo symbolic factorization for
    609: !  ILU/ICC preconditioners).
    610: !   - If the nonzero structure of the matrix is different during
    611: !     successive linear solves, then the flag DIFFERENT_NONZERO_PATTERN
    612: !     must be used instead.  If you are unsure whether the matrix
    613: !     structure has changed or not, use the flag DIFFERENT_NONZERO_PATTERN.
    614: !   - Caution:  If you specify SAME_NONZERO_PATTERN, PETSc
    615: !     believes your assertion and does not check the structure
    616: !     of the matrix.  If you erroneously claim that the structure
    617: !     is the same when it actually is not, the new preconditioner
    618: !     will not function correctly.  Thus, use this optimization
    619: !     feature with caution!

    621:       flag = SAME_NONZERO_PATTERN

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

    626:       call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,      &
    627:      &                  ierr)

    629:       return
    630:       end

    632: ! ---------------------------------------------------------------------
    633: !
    634: !  FormJacobianLocal - Computes Jacobian preconditioner matrix,
    635: !  called by the higher level routine FormJacobian().
    636: !
    637: !  Input Parameters:
    638: !  x        - local vector data
    639: !
    640: !  Output Parameters:
    641: !  jac_prec - Jacobian preconditioner matrix
    642: !  ierr     - error code
    643: !
    644: !  Notes:
    645: !  This routine uses standard Fortran-style computations over a 2-dim array.
    646: !
    647: !  Notes:
    648: !  Due to grid point reordering with DMDAs, we must always work
    649: !  with the local grid points, and then transform them to the new
    650: !  global numbering with the "ltog" mapping (via DMDAGetGlobalIndicesF90()).
    651: !  We cannot work directly with the global numbers for the original
    652: !  uniprocessor grid!
    653: !
    654: !  Two methods are available for imposing this transformation
    655: !  when setting matrix entries:
    656: !    (A) MatSetValuesLocal(), using the local ordering (including
    657: !        ghost points!)
    658: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
    659: !        - Associate this map with the matrix by calling
    660: !          MatSetLocalToGlobalMapping() once
    661: !        - Set matrix entries using the local ordering
    662: !          by calling MatSetValuesLocal()
    663: !    (B) MatSetValues(), using the global ordering
    664: !        - Use DMDAGetGlobalIndicesF90() to extract the local-to-global map
    665: !        - Then apply this map explicitly yourself
    666: !        - Set matrix entries using the global ordering by calling
    667: !          MatSetValues()
    668: !  Option (A) seems cleaner/easier in many cases, and is the procedure
    669: !  used in this example.
    670: !
    671:       subroutine FormJacobianLocal(x,jac_prec,user,ierr)
    672: #include <finclude/petscmatdef.h>
    673:       use petscmat
    674:       use f90module
    675: !  Input/output variables:
    676:       type (userctx) user
    677:       PetscScalar    x(user%gxs:user%gxe,                                      &
    678:      &               user%gys:user%gye)
    679:       type(Mat)      jac_prec
    680:       PetscErrorCode ierr

    682: !  Local variables:
    683:       PetscInt    row,col(5),i,j
    684:       PetscInt    ione,ifive
    685:       PetscScalar two,one,hx,hy,hxdhy
    686:       PetscScalar hydhx,sc,v(5)

    688: !  Set parameters
    689:       ione   = 1
    690:       ifive  = 5
    691:       one    = 1.0
    692:       two    = 2.0
    693:       hx     = one/dble(user%mx-1)
    694:       hy     = one/dble(user%my-1)
    695:       sc     = hx*hy
    696:       hxdhy  = hx/hy
    697:       hydhx  = hy/hx

    699: !  Compute entries for the locally owned part of the Jacobian.
    700: !   - Currently, all PETSc parallel matrix formats are partitioned by
    701: !     contiguous chunks of rows across the processors.
    702: !   - Each processor needs to insert only elements that it owns
    703: !     locally (but any non-local elements will be sent to the
    704: !     appropriate processor during matrix assembly).
    705: !   - Here, we set all entries for a particular row at once.
    706: !   - We can set matrix entries either using either
    707: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
    708: !   - Note that MatSetValues() uses 0-based row and column numbers
    709: !     in Fortran as well as in C.

    711:       do 20 j=user%ys,user%ye
    712:          row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
    713:          do 10 i=user%xs,user%xe
    714:             row = row + 1
    715: !           boundary points
    716:             if (i .eq. 1 .or. j .eq. 1                                  &
    717:      &             .or. i .eq. user%mx .or. j .eq. user%my) then
    718:                col(1) = row
    719:                v(1)   = one
    720:                call MatSetValuesLocal(jac_prec,ione,row,ione,col,v,          &
    721:      &                           INSERT_VALUES,ierr)
    722: !           interior grid points
    723:             else
    724:                v(1) = -hxdhy
    725:                v(2) = -hydhx
    726:                v(3) = two*(hydhx + hxdhy)                               &
    727:      &                  - sc*user%lambda*exp(x(i,j))
    728:                v(4) = -hydhx
    729:                v(5) = -hxdhy
    730:                col(1) = row - user%gxm
    731:                col(2) = row - 1
    732:                col(3) = row
    733:                col(4) = row + 1
    734:                col(5) = row + user%gxm
    735:                call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v,         &
    736:      &                                INSERT_VALUES,ierr)
    737:             endif
    738:  10      continue
    739:  20   continue
    740:       return
    741:       end