Actual source code: ex5f90t.F90

      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: !  TODO: Need to update to latest API
     14: !T*/
     15: !
     16: !  --------------------------------------------------------------------------
     17: !
     18: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
     19: !  the partial differential equation
     20: !
     21: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
     22: !
     23: !  with boundary conditions
     24: !
     25: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
     26: !
     27: !  A finite difference approximation with the usual 5-point stencil
     28: !  is used to discretize the boundary value problem to obtain a nonlinear
     29: !  system of equations.
     30: !
     31: !  The uniprocessor version of this code is snes/tutorials/ex4f.F
     32: !
     33: !  --------------------------------------------------------------------------
     34: !  The following define must be used before including any PETSc include files
     35: !  into a module or interface. This is because they can't handle declarations
     36: !  in them
     37: !

     39:       module f90modulet
     40: #include <petsc/finclude/petscdm.h>
     41:       use petscdmdef
     42:       type userctx
     43:         type(tDM) da
     44:         PetscInt xs,xe,xm,gxs,gxe,gxm
     45:         PetscInt ys,ye,ym,gys,gye,gym
     46:         PetscInt mx,my
     47:         PetscMPIInt rank
     48:         PetscReal lambda
     49:       end type userctx

     51:       contains
     52: ! ---------------------------------------------------------------------
     53: !
     54: !  FormFunction - Evaluates nonlinear function, F(x).
     55: !
     56: !  Input Parameters:
     57: !  snes - the SNES context
     58: !  X - input vector
     59: !  dummy - optional user-defined context, as set by SNESSetFunction()
     60: !          (not used here)
     61: !
     62: !  Output Parameter:
     63: !  F - function vector
     64: !
     65: !  Notes:
     66: !  This routine serves as a wrapper for the lower-level routine
     67: !  "FormFunctionLocal", where the actual computations are
     68: !  done using the standard Fortran style of treating the local
     69: !  vector data as a multidimensional array over the local mesh.
     70: !  This routine merely handles ghost point scatters and accesses
     71: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
     72: !
     73:       subroutine FormFunction(snesIn,X,F,user,ierr)
     74: #include <petsc/finclude/petscsnes.h>
     75:       use petscsnes

     77: !  Input/output variables:
     78:       type(tSNES)     snesIn
     79:       type(tVec)      X,F
     80:       PetscErrorCode ierr
     81:       type (userctx) user

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

     87: !  Scatter ghost points to local vector, using the 2-step process
     88: !     DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
     89: !  By placing code between these two statements, computations can
     90: !  be done while messages are in transition.
     91:       call DMGetLocalVector(user%da,localX,ierr);CHKERRQ(ierr)
     92:       call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,ierr);CHKERRQ(ierr)
     93:       call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr);CHKERRQ(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);CHKERRQ(ierr)
    104:       call VecGetArrayF90(F,lf_v,ierr);CHKERRQ(ierr)

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

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

    113: !  Insert values into global vector

    115:       call DMRestoreLocalVector(user%da,localX,ierr);CHKERRQ(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 f90modulet

    124:       module f90moduleinterfacest
    125:         use f90modulet

    127:       Interface SNESSetApplicationContext
    128:         Subroutine SNESSetApplicationContext(snesIn,ctx,ierr)
    129: #include <petsc/finclude/petscsnes.h>
    130:         use petscsnes
    131:         use f90modulet
    132:           type(tSNES)    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 <petsc/finclude/petscsnes.h>
    141:         use petscsnes
    142:         use f90modulet
    143:           type(tSNES)     snesIn
    144:           type(userctx), pointer :: ctx
    145:           PetscErrorCode ierr
    146:         End Subroutine
    147:       End Interface SNESGetApplicationContext
    148:       end module f90moduleinterfacest

    150:       program main
    151: #include <petsc/finclude/petscdm.h>
    152: #include <petsc/finclude/petscsnes.h>
    153:       use petscdmda
    154:       use petscdm
    155:       use petscsnes
    156:       use f90modulet
    157:       use f90moduleinterfacest
    158:       implicit none
    159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    160: !                   Variable declarations
    161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    162: !
    163: !  Variables:
    164: !     mysnes      - nonlinear solver
    165: !     x, r        - solution, residual vectors
    166: !     J           - Jacobian matrix
    167: !     its         - iterations for convergence
    168: !     Nx, Ny      - number of preocessors in x- and y- directions
    169: !     matrix_free - flag - 1 indicates matrix-free version
    170: !
    171:       type(tSNES)       mysnes
    172:       type(tVec)        x,r
    173:       type(tMat)        J
    174:       PetscErrorCode   ierr
    175:       PetscInt         its
    176:       PetscBool        flg,matrix_free,set
    177:       PetscInt         ione,nfour
    178:       PetscReal lambda_max,lambda_min
    179:       type(userctx)    user
    180:       type(userctx), pointer:: puser
    181:       type(tPetscOptions) :: options

    183: !  Note: Any user-defined Fortran routines (such as FormJacobian)
    184: !  MUST be declared as external.
    185:       external FormInitialGuess,FormJacobian

    187: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    188: !  Initialize program
    189: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    190:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
    191:       if (ierr .ne. 0) then
    192:         print*,'Unable to initialize PETSc'
    193:         stop
    194:       endif
    195:       call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr)

    197: !  Initialize problem parameters
    198:       options%v = 0
    199:       lambda_max  = 6.81
    200:       lambda_min  = 0.0
    201:       user%lambda = 6.0
    202:       ione = 1
    203:       nfour = 4
    204:       call PetscOptionsGetReal(options,PETSC_NULL_CHARACTER,'-par',user%lambda,flg,ierr);CHKERRA(ierr)
    205:       if (user%lambda .ge. lambda_max .or. user%lambda .le. lambda_min) then; SETERRA(PETSC_COMM_SELF,PETSC_ERR_USER,'Lambda provided with -par is out of range '); endif

    207: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    208: !  Create nonlinear solver context
    209: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    210:       call SNESCreate(PETSC_COMM_WORLD,mysnes,ierr);CHKERRA(ierr)

    212: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    213: !  Create vector data structures; set function evaluation routine
    214: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

    227: !
    228: !   Visualize the distribution of the array across the processors
    229: !
    230: !     call DMView(user%da,PETSC_VIEWER_DRAW_WORLD,ierr)

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

    237: !  Get local grid boundaries (for 2-dimensional DMDA)
    238:       call DMDAGetCorners(user%da,user%xs,user%ys,PETSC_NULL_INTEGER,user%xm,user%ym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
    239:       call DMDAGetGhostCorners(user%da,user%gxs,user%gys,PETSC_NULL_INTEGER,user%gxm,user%gym,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)

    241: !  Here we shift the starting indices up by one so that we can easily
    242: !  use the Fortran convention of 1-based indices (rather 0-based indices).
    243:       user%xs  = user%xs+1
    244:       user%ys  = user%ys+1
    245:       user%gxs = user%gxs+1
    246:       user%gys = user%gys+1

    248:       user%ye  = user%ys+user%ym-1
    249:       user%xe  = user%xs+user%xm-1
    250:       user%gye = user%gys+user%gym-1
    251:       user%gxe = user%gxs+user%gxm-1

    253:       call SNESSetApplicationContext(mysnes,user,ierr);CHKERRA(ierr)

    255: !  Set function evaluation routine and vector
    256:       call SNESSetFunction(mysnes,r,FormFunction,user,ierr);CHKERRA(ierr)

    258: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    259: !  Create matrix data structure; set Jacobian evaluation routine
    260: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    282:       call PetscOptionsHasName(options,PETSC_NULL_CHARACTER,'-snes_mf',matrix_free,ierr);CHKERRA(ierr)
    283:       if (.not. matrix_free) then
    284:         call DMSetMatType(user%da,MATAIJ,ierr);CHKERRA(ierr)
    285:         call DMCreateMatrix(user%da,J,ierr);CHKERRA(ierr)
    286:         call SNESSetJacobian(mysnes,J,J,FormJacobian,user,ierr);CHKERRA(ierr)
    287:       endif

    289: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    290: !  Customize nonlinear solver; set runtime options
    291: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    292: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)
    293:       call SNESSetFromOptions(mysnes,ierr);CHKERRA(ierr)

    295: !     Test Fortran90 wrapper for SNESSet/Get ApplicationContext()
    296:       call PetscOptionsGetBool(options,PETSC_NULL_CHARACTER,'-test_appctx',flg,set,ierr);CHKERRA(ierr)
    297:       if (flg) then
    298:         call SNESGetApplicationContext(mysnes,puser,ierr);CHKERRA(ierr)
    299:       endif

    301: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    302: !  Evaluate initial guess; then solve nonlinear system.
    303: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    304: !  Note: The user should initialize the vector, x, with the initial guess
    305: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
    306: !  to employ an initial guess of zero, the user should explicitly set
    307: !  this vector to zero by calling VecSet().

    309:       call FormInitialGuess(mysnes,x,ierr);CHKERRA(ierr)
    310:       call SNESSolve(mysnes,PETSC_NULL_VEC,x,ierr);CHKERRA(ierr)
    311:       call SNESGetIterationNumber(mysnes,its,ierr);CHKERRA(ierr)
    312:       if (user%rank .eq. 0) then
    313:          write(6,100) its
    314:       endif
    315:   100 format('Number of SNES iterations = ',i5)

    317: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    318: !  Free work space.  All PETSc objects should be destroyed when they
    319: !  are no longer needed.
    320: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    321:       if (.not. matrix_free) call MatDestroy(J,ierr);CHKERRA(ierr)
    322:       call VecDestroy(x,ierr);CHKERRA(ierr)
    323:       call VecDestroy(r,ierr);CHKERRA(ierr)
    324:       call SNESDestroy(mysnes,ierr);CHKERRA(ierr)
    325:       call DMDestroy(user%da,ierr);CHKERRA(ierr)

    327:       call PetscFinalize(ierr)
    328:       end

    330: ! ---------------------------------------------------------------------
    331: !
    332: !  FormInitialGuess - Forms initial approximation.
    333: !
    334: !  Input Parameters:
    335: !  X - vector
    336: !
    337: !  Output Parameter:
    338: !  X - vector
    339: !
    340: !  Notes:
    341: !  This routine serves as a wrapper for the lower-level routine
    342: !  "InitialGuessLocal", where the actual computations are
    343: !  done using the standard Fortran style of treating the local
    344: !  vector data as a multidimensional array over the local mesh.
    345: !  This routine merely handles ghost point scatters and accesses
    346: !  the local vector data via VecGetArrayF90() and VecRestoreArrayF90().
    347: !
    348:       subroutine FormInitialGuess(mysnes,X,ierr)
    349: #include <petsc/finclude/petscsnes.h>
    350:       use petscsnes
    351:       use f90modulet
    352:       use f90moduleinterfacest
    353: !  Input/output variables:
    354:       type(tSNES)     mysnes
    355:       type(userctx), pointer:: puser
    356:       type(tVec)      X
    357:       PetscErrorCode ierr

    359: !  Declarations for use with local arrays:
    360:       PetscScalar,pointer :: lx_v(:)

    362:       0
    363:       call SNESGetApplicationContext(mysnes,puser,ierr)
    364: !  Get a pointer to vector data.
    365: !    - For default PETSc vectors, VecGetArray90() returns a pointer to
    366: !      the data array. Otherwise, the routine is implementation dependent.
    367: !    - You MUST call VecRestoreArrayF90() when you no longer need access to
    368: !      the array.
    369: !    - Note that the interface to VecGetArrayF90() differs from VecGetArray(),
    370: !      and is useable from Fortran-90 Only.

    372:       call VecGetArrayF90(X,lx_v,ierr)

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

    377: !  Restore vector
    378:       call VecRestoreArrayF90(X,lx_v,ierr)

    380: !  Insert values into global vector

    382:       return
    383:       end

    385: ! ---------------------------------------------------------------------
    386: !
    387: !  InitialGuessLocal - Computes initial approximation, called by
    388: !  the higher level routine FormInitialGuess().
    389: !
    390: !  Input Parameter:
    391: !  x - local vector data
    392: !
    393: !  Output Parameters:
    394: !  x - local vector data
    395: !  ierr - error code
    396: !
    397: !  Notes:
    398: !  This routine uses standard Fortran-style computations over a 2-dim array.
    399: !
    400:       subroutine InitialGuessLocal(user,x,ierr)
    401: #include <petsc/finclude/petscsys.h>
    402:       use petscsys
    403:       use f90modulet
    404: !  Input/output variables:
    405:       type (userctx)         user
    406:       PetscScalar  x(user%xs:user%xe,user%ys:user%ye)
    407:       PetscErrorCode ierr

    409: !  Local variables:
    410:       PetscInt  i,j
    411:       PetscScalar   temp1,temp,hx,hy
    412:       PetscScalar   one

    414: !  Set parameters

    416:       0
    417:       one    = 1.0
    418:       hx     = one/(PetscIntToReal(user%mx-1))
    419:       hy     = one/(PetscIntToReal(user%my-1))
    420:       temp1  = user%lambda/(user%lambda + one)

    422:       do 20 j=user%ys,user%ye
    423:          temp = PetscIntToReal(min(j-1,user%my-j))*hy
    424:          do 10 i=user%xs,user%xe
    425:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
    426:               x(i,j) = 0.0
    427:             else
    428:               x(i,j) = temp1 * sqrt(min(PetscIntToReal(min(i-1,user%mx-i)*hx),PetscIntToReal(temp)))
    429:             endif
    430:  10      continue
    431:  20   continue

    433:       return
    434:       end

    436: ! ---------------------------------------------------------------------
    437: !
    438: !  FormFunctionLocal - Computes nonlinear function, called by
    439: !  the higher level routine FormFunction().
    440: !
    441: !  Input Parameter:
    442: !  x - local vector data
    443: !
    444: !  Output Parameters:
    445: !  f - local vector data, f(x)
    446: !  ierr - error code
    447: !
    448: !  Notes:
    449: !  This routine uses standard Fortran-style computations over a 2-dim array.
    450: !
    451:       subroutine FormFunctionLocal(x,f,user,ierr)
    452: #include <petsc/finclude/petscsys.h>
    453:       use petscsys
    454:       use f90modulet
    455: !  Input/output variables:
    456:       type (userctx) user
    457:       PetscScalar  x(user%gxs:user%gxe,user%gys:user%gye)
    458:       PetscScalar  f(user%xs:user%xe,user%ys:user%ye)
    459:       PetscErrorCode ierr

    461: !  Local variables:
    462:       PetscScalar two,one,hx,hy,hxdhy,hydhx,sc
    463:       PetscScalar u,uxx,uyy
    464:       PetscInt  i,j

    466:       one    = 1.0
    467:       two    = 2.0
    468:       hx     = one/PetscIntToReal(user%mx-1)
    469:       hy     = one/PetscIntToReal(user%my-1)
    470:       sc     = hx*hy*user%lambda
    471:       hxdhy  = hx/hy
    472:       hydhx  = hy/hx

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

    476:       do 20 j=user%ys,user%ye
    477:          do 10 i=user%xs,user%xe
    478:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
    479:                f(i,j) = x(i,j)
    480:             else
    481:                u = x(i,j)
    482:                uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
    483:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
    484:                f(i,j) = uxx + uyy - sc*exp(u)
    485:             endif
    486:  10      continue
    487:  20   continue
    488:       0
    489:       return
    490:       end

    492: ! ---------------------------------------------------------------------
    493: !
    494: !  FormJacobian - Evaluates Jacobian matrix.
    495: !
    496: !  Input Parameters:
    497: !  snes     - the SNES context
    498: !  x        - input vector
    499: !  dummy    - optional user-defined context, as set by SNESSetJacobian()
    500: !             (not used here)
    501: !
    502: !  Output Parameters:
    503: !  jac      - Jacobian matrix
    504: !  jac_prec - optionally different preconditioning matrix (not used here)
    505: !  flag     - flag indicating matrix structure
    506: !
    507: !  Notes:
    508: !  This routine serves as a wrapper for the lower-level routine
    509: !  "FormJacobianLocal", where the actual computations are
    510: !  done using the standard Fortran style of treating the local
    511: !  vector data as a multidimensional array over the local mesh.
    512: !  This routine merely accesses the local vector data via
    513: !  VecGetArrayF90() and VecRestoreArrayF90().
    514: !
    515: !  Notes:
    516: !  Due to grid point reordering with DMDAs, we must always work
    517: !  with the local grid points, and then transform them to the new
    518: !  global numbering with the "ltog" mapping
    519: !  We cannot work directly with the global numbers for the original
    520: !  uniprocessor grid!
    521: !
    522: !  Two methods are available for imposing this transformation
    523: !  when setting matrix entries:
    524: !    (A) MatSetValuesLocal(), using the local ordering (including
    525: !        ghost points!)
    526: !        - Set matrix entries using the local ordering
    527: !          by calling MatSetValuesLocal()
    528: !    (B) MatSetValues(), using the global ordering
    529: !        - Use DMGetLocalToGlobalMapping() then
    530: !          ISLocalToGlobalMappingGetIndicesF90() to extract the local-to-global map
    531: !        - Then apply this map explicitly yourself
    532: !        - Set matrix entries using the global ordering by calling
    533: !          MatSetValues()
    534: !  Option (A) seems cleaner/easier in many cases, and is the procedure
    535: !  used in this example.
    536: !
    537:       subroutine FormJacobian(mysnes,X,jac,jac_prec,user,ierr)
    538: #include <petsc/finclude/petscsnes.h>
    539:       use petscsnes
    540:       use f90modulet
    541: !  Input/output variables:
    542:       type(tSNES)     mysnes
    543:       type(tVec)      X
    544:       type(tMat)      jac,jac_prec
    545:       type(userctx)  user
    546:       PetscErrorCode ierr

    548: !  Declarations for use with local arrays:
    549:       PetscScalar,pointer :: lx_v(:)
    550:       type(tVec)      localX

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

    557:       call DMGetLocalVector(user%da,localX,ierr)
    558:       call DMGlobalToLocalBegin(user%da,X,INSERT_VALUES,localX,ierr)
    559:       call DMGlobalToLocalEnd(user%da,X,INSERT_VALUES,localX,ierr)

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

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

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

    572:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
    573: !      if (jac .ne. jac_prec) then
    574:          call MatAssemblyBegin(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
    575: !      endif
    576:       call VecRestoreArrayF90(localX,lx_v,ierr)
    577:       call DMRestoreLocalVector(user%da,localX,ierr)
    578:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
    579: !      if (jac .ne. jac_prec) then
    580:         call MatAssemblyEnd(jac_prec,MAT_FINAL_ASSEMBLY,ierr)
    581: !      endif

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

    586:       call MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr)

    588:       return
    589:       end

    591: ! ---------------------------------------------------------------------
    592: !
    593: !  FormJacobianLocal - Computes Jacobian preconditioner matrix,
    594: !  called by the higher level routine FormJacobian().
    595: !
    596: !  Input Parameters:
    597: !  x        - local vector data
    598: !
    599: !  Output Parameters:
    600: !  jac_prec - Jacobian preconditioner matrix
    601: !  ierr     - error code
    602: !
    603: !  Notes:
    604: !  This routine uses standard Fortran-style computations over a 2-dim array.
    605: !
    606: !  Notes:
    607: !  Due to grid point reordering with DMDAs, we must always work
    608: !  with the local grid points, and then transform them to the new
    609: !  global numbering with the "ltog" mapping
    610: !  We cannot work directly with the global numbers for the original
    611: !  uniprocessor grid!
    612: !
    613: !  Two methods are available for imposing this transformation
    614: !  when setting matrix entries:
    615: !    (A) MatSetValuesLocal(), using the local ordering (including
    616: !        ghost points!)
    617: !        - Set matrix entries using the local ordering
    618: !          by calling MatSetValuesLocal()
    619: !    (B) MatSetValues(), using the global ordering
    620: !        - Set matrix entries using the global ordering by calling
    621: !          MatSetValues()
    622: !  Option (A) seems cleaner/easier in many cases, and is the procedure
    623: !  used in this example.
    624: !
    625:       subroutine FormJacobianLocal(x,jac_prec,user,ierr)
    626: #include <petsc/finclude/petscmat.h>
    627:       use petscmat
    628:       use f90modulet
    629: !  Input/output variables:
    630:       type (userctx) user
    631:       PetscScalar    x(user%gxs:user%gxe,user%gys:user%gye)
    632:       type(tMat)      jac_prec
    633:       PetscErrorCode ierr

    635: !  Local variables:
    636:       PetscInt    row,col(5),i,j
    637:       PetscInt    ione,ifive
    638:       PetscScalar two,one,hx,hy,hxdhy
    639:       PetscScalar hydhx,sc,v(5)

    641: !  Set parameters
    642:       ione   = 1
    643:       ifive  = 5
    644:       one    = 1.0
    645:       two    = 2.0
    646:       hx     = one/PetscIntToReal(user%mx-1)
    647:       hy     = one/PetscIntToReal(user%my-1)
    648:       sc     = hx*hy
    649:       hxdhy  = hx/hy
    650:       hydhx  = hy/hx

    652: !  Compute entries for the locally owned part of the Jacobian.
    653: !   - Currently, all PETSc parallel matrix formats are partitioned by
    654: !     contiguous chunks of rows across the processors.
    655: !   - Each processor needs to insert only elements that it owns
    656: !     locally (but any non-local elements will be sent to the
    657: !     appropriate processor during matrix assembly).
    658: !   - Here, we set all entries for a particular row at once.
    659: !   - We can set matrix entries either using either
    660: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
    661: !   - Note that MatSetValues() uses 0-based row and column numbers
    662: !     in Fortran as well as in C.

    664:       do 20 j=user%ys,user%ye
    665:          row = (j - user%gys)*user%gxm + user%xs - user%gxs - 1
    666:          do 10 i=user%xs,user%xe
    667:             row = row + 1
    668: !           boundary points
    669:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. user%mx .or. j .eq. user%my) then
    670:                col(1) = row
    671:                v(1)   = one
    672:                call MatSetValuesLocal(jac_prec,ione,row,ione,col,v,INSERT_VALUES,ierr)
    673: !           interior grid points
    674:             else
    675:                v(1) = -hxdhy
    676:                v(2) = -hydhx
    677:                v(3) = two*(hydhx + hxdhy) - sc*user%lambda*exp(x(i,j))
    678:                v(4) = -hydhx
    679:                v(5) = -hxdhy
    680:                col(1) = row - user%gxm
    681:                col(2) = row - 1
    682:                col(3) = row
    683:                col(4) = row + 1
    684:                col(5) = row + user%gxm
    685:                call MatSetValuesLocal(jac_prec,ione,row,ifive,col,v,INSERT_VALUES,ierr)
    686:             endif
    687:  10      continue
    688:  20   continue
    689:       return
    690:       end

    692: !/*TEST
    693: !
    694: !   test:
    695: !      nsize: 4
    696: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
    697: !
    698: !TEST*/