Date: 2022-08-02T03:14:56+00:00

Actual source code: ex5f.F90

      1: !
      2: !  Description: This example 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 <param>, where <param> indicates the nonlinearity of the problem
      7: !       problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)
      8: !
      9: !

     11: !
     12: !  --------------------------------------------------------------------------
     13: !
     14: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
     15: !  the partial differential equation
     16: !
     17: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
     18: !
     19: !  with boundary conditions
     20: !
     21: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
     22: !
     23: !  A finite difference approximation with the usual 5-point stencil
     24: !  is used to discretize the boundary value problem to obtain a nonlinear
     25: !  system of equations.
     26: !
     27: !  --------------------------------------------------------------------------

     29:       program main
     30: #include <petsc/finclude/petscsnes.h>
     31:       use petscdmda
     32:       use petscsnes
     33:       implicit none
     34: !
     35: !  We place common blocks, variable declarations, and other include files
     36: !  needed for this code in the single file ex5f.h.  We then need to include
     37: !  only this file throughout the various routines in this program.  See
     38: !  additional comments in the file ex5f.h.
     39: !
     40: #include "ex5f.h"

     42: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     43: !                   Variable declarations
     44: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     45: !
     46: !  Variables:
     47: !     snes        - nonlinear solver
     48: !     x, r        - solution, residual vectors
     49: !     its         - iterations for convergence
     50: !
     51: !  See additional variable declarations in the file ex5f.h
     52: !
     53:       SNES           snes
     54:       Vec            x,r
     55:       PetscInt       its,i1,i4
     56:       PetscErrorCode ierr
     57:       PetscReal      lambda_max,lambda_min
     58:       PetscBool      flg
     59:       DM             da

     61: !  Note: Any user-defined Fortran routines (such as FormJacobianLocal)
     62: !  MUST be declared as external.

     64:       external FormInitialGuess
     65:       external FormFunctionLocal,FormJacobianLocal
     66:       external MySNESConverged

     68: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     69: !  Initialize program
     70: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     72:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
     73:       if (ierr .ne. 0) then
     74:         print*,'Unable to initialize PETSc'
     75:         stop
     76:       endif
     77:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
     78:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)

     80: !  Initialize problem parameters

     82:       i1 = 1
     83:       i4 = 4
     84:       lambda_max = 6.81
     85:       lambda_min = 0.0
     86:       lambda     = 6.0
     87:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,PETSC_NULL_BOOL,ierr)
     88: ! this statement is split into multiple-lines to keep lines under 132 char limit - required by 'make check'
     89:       if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
     90:         PETSC_ERR_ARG_OUTOFRANGE; SETERRA(PETSC_COMM_WORLD,ierr,'Lambda')
     91:       endif

     93: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     94: !  Create nonlinear solver context
     95: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     97:       call SNESCreate(PETSC_COMM_WORLD,snes,ierr)

     99: !  Set convergence test routine if desired

    101:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_snes_convergence',flg,ierr)
    102:       if (flg) then
    103:         call SNESSetConvergenceTest(snes,MySNESConverged,0,PETSC_NULL_FUNCTION,ierr)
    104:       endif

    106: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    107: !  Create vector data structures; set function evaluation routine
    108: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    112: ! This really needs only the star-type stencil, but we use the box
    113: ! stencil temporarily.
    114:       call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,      &
    115:      &     DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE,i1,i1,                &
    116:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
    117:       call DMSetFromOptions(da,ierr)
    118:       call DMSetUp(da,ierr)

    120: !  Extract global and local vectors from DMDA; then duplicate for remaining
    121: !  vectors that are the same types

    123:       call DMCreateGlobalVector(da,x,ierr)
    124:       call VecDuplicate(x,r,ierr)

    126: !  Get local grid boundaries (for 2-dimensional DMDA)

    128:       call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER,            &
    129:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
    130:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
    131:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
    132:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
    133:      &               PETSC_NULL_INTEGER,ierr)
    134:       call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr)
    135:       call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr)

    137: !  Here we shift the starting indices up by one so that we can easily
    138: !  use the Fortran convention of 1-based indices (rather 0-based indices).

    140:       xs  = xs+1
    141:       ys  = ys+1
    142:       gxs = gxs+1
    143:       gys = gys+1

    145:       ye  = ys+ym-1
    146:       xe  = xs+xm-1
    147:       gye = gys+gym-1
    148:       gxe = gxs+gxm-1

    150: !  Set function evaluation routine and vector

    152:       call DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal,da,ierr)
    153:       call DMDASNESSetJacobianLocal(da,FormJacobianLocal,da,ierr)
    154:       call SNESSetDM(snes,da,ierr)

    156: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    157: !  Customize nonlinear solver; set runtime options
    158: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    160: !  Set runtime options (e.g., -snes_monitor -snes_rtol <rtol> -ksp_type <type>)

    162:           call SNESSetFromOptions(snes,ierr)
    163: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    164: !  Evaluate initial guess; then solve nonlinear system.
    165: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    167: !  Note: The user should initialize the vector, x, with the initial guess
    168: !  for the nonlinear solver prior to calling SNESSolve().  In particular,
    169: !  to employ an initial guess of zero, the user should explicitly set
    170: !  this vector to zero by calling VecSet().

    172:       call FormInitialGuess(x,ierr)
    173:       call SNESSolve(snes,PETSC_NULL_VEC,x,ierr)
    174:       call SNESGetIterationNumber(snes,its,ierr)
    175:       if (rank .eq. 0) then
    176:          write(6,100) its
    177:       endif
    178:   100 format('Number of SNES iterations = ',i5)

    180: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    181: !  Free work space.  All PETSc objects should be destroyed when they
    182: !  are no longer needed.
    183: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    185:       call VecDestroy(x,ierr)
    186:       call VecDestroy(r,ierr)
    187:       call SNESDestroy(snes,ierr)
    188:       call DMDestroy(da,ierr)
    189:       call PetscFinalize(ierr)
    190:       end

    192: ! ---------------------------------------------------------------------
    193: !
    194: !  FormInitialGuess - Forms initial approximation.
    195: !
    196: !  Input Parameters:
    197: !  X - vector
    198: !
    199: !  Output Parameter:
    200: !  X - vector
    201: !
    202: !  Notes:
    203: !  This routine serves as a wrapper for the lower-level routine
    204: !  "ApplicationInitialGuess", where the actual computations are
    205: !  done using the standard Fortran style of treating the local
    206: !  vector data as a multidimensional array over the local mesh.
    207: !  This routine merely handles ghost point scatters and accesses
    208: !  the local vector data via VecGetArray() and VecRestoreArray().
    209: !
    210:       subroutine FormInitialGuess(X,ierr)
    211:       use petscsnes
    212:       implicit none

    214: #include "ex5f.h"

    216: !  Input/output variables:
    217:       Vec      X
    218:       PetscErrorCode  ierr

    220: !  Declarations for use with local arrays:
    221:       PetscScalar lx_v(0:1)
    222:       PetscOffset lx_i

    224:       0

    226: !  Get a pointer to vector data.
    227: !    - For default PETSc vectors, VecGetArray() returns a pointer to
    228: !      the data array.  Otherwise, the routine is implementation dependent.
    229: !    - You MUST call VecRestoreArray() when you no longer need access to
    230: !      the array.
    231: !    - Note that the Fortran interface to VecGetArray() differs from the
    232: !      C version.  See the users manual for details.

    234:       call VecGetArray(X,lx_v,lx_i,ierr)

    236: !  Compute initial guess over the locally owned part of the grid

    238:       call InitialGuessLocal(lx_v(lx_i),ierr)

    240: !  Restore vector

    242:       call VecRestoreArray(X,lx_v,lx_i,ierr)

    244:       return
    245:       end

    247: ! ---------------------------------------------------------------------
    248: !
    249: !  InitialGuessLocal - Computes initial approximation, called by
    250: !  the higher level routine FormInitialGuess().
    251: !
    252: !  Input Parameter:
    253: !  x - local vector data
    254: !
    255: !  Output Parameters:
    256: !  x - local vector data
    257: !  ierr - error code
    258: !
    259: !  Notes:
    260: !  This routine uses standard Fortran-style computations over a 2-dim array.
    261: !
    262:       subroutine InitialGuessLocal(x,ierr)
    263:       use petscsnes
    264:       implicit none

    266: #include "ex5f.h"

    268: !  Input/output variables:
    269:       PetscScalar    x(xs:xe,ys:ye)
    270:       PetscErrorCode ierr

    272: !  Local variables:
    273:       PetscInt  i,j
    274:       PetscReal temp1,temp,one,hx,hy

    276: !  Set parameters

    278:       0
    279:       one    = 1.0
    280:       hx     = one/((mx-1))
    281:       hy     = one/((my-1))
    282:       temp1  = lambda/(lambda + one)

    284:       do 20 j=ys,ye
    285:          temp = (min(j-1,my-j))*hy
    286:          do 10 i=xs,xe
    287:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
    288:               x(i,j) = 0.0
    289:             else
    290:               x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,(temp)))
    291:             endif
    292:  10      continue
    293:  20   continue

    295:       return
    296:       end

    298: ! ---------------------------------------------------------------------
    299: !
    300: !  FormFunctionLocal - Computes nonlinear function, called by
    301: !  the higher level routine FormFunction().
    302: !
    303: !  Input Parameter:
    304: !  x - local vector data
    305: !
    306: !  Output Parameters:
    307: !  f - local vector data, f(x)
    308: !  ierr - error code
    309: !
    310: !  Notes:
    311: !  This routine uses standard Fortran-style computations over a 2-dim array.
    312: !
    313: !
    314:       subroutine FormFunctionLocal(info,x,f,da,ierr)
    315: #include <petsc/finclude/petscdmda.h>
    316:       use petscsnes
    317:       implicit none

    319: #include "ex5f.h"
    320:       DM da

    322: !  Input/output variables:
    323:       DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
    324:       PetscScalar x(gxs:gxe,gys:gye)
    325:       PetscScalar f(xs:xe,ys:ye)
    326:       PetscErrorCode     ierr

    328: !  Local variables:
    329:       PetscScalar two,one,hx,hy
    330:       PetscScalar hxdhy,hydhx,sc
    331:       PetscScalar u,uxx,uyy
    332:       PetscInt  i,j

    334:       xs     = info(DMDA_LOCAL_INFO_XS)+1
    335:       xe     = xs+info(DMDA_LOCAL_INFO_XM)-1
    336:       ys     = info(DMDA_LOCAL_INFO_YS)+1
    337:       ye     = ys+info(DMDA_LOCAL_INFO_YM)-1
    338:       mx     = info(DMDA_LOCAL_INFO_MX)
    339:       my     = info(DMDA_LOCAL_INFO_MY)

    341:       one    = 1.0
    342:       two    = 2.0
    343:       hx     = one/(mx-1)
    344:       hy     = one/(my-1)
    345:       sc     = hx*hy*lambda
    346:       hxdhy  = hx/hy
    347:       hydhx  = hy/hx

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

    351:       do 20 j=ys,ye
    352:          do 10 i=xs,xe
    353:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
    354:                f(i,j) = x(i,j)
    355:             else
    356:                u = x(i,j)
    357:                uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
    358:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
    359:                f(i,j) = uxx + uyy - sc*exp(u)
    360:             endif
    361:  10      continue
    362:  20   continue

    364:       call PetscLogFlops(11.0d0*ym*xm,ierr)

    366:       return
    367:       end

    369: ! ---------------------------------------------------------------------
    370: !
    371: !  FormJacobianLocal - Computes Jacobian matrix, called by
    372: !  the higher level routine FormJacobian().
    373: !
    374: !  Input Parameters:
    375: !  x        - local vector data
    376: !
    377: !  Output Parameters:
    378: !  jac      - Jacobian matrix
    379: !  jac_prec - optionally different preconditioning matrix (not used here)
    380: !  ierr     - error code
    381: !
    382: !  Notes:
    383: !  This routine uses standard Fortran-style computations over a 2-dim array.
    384: !
    385: !  Notes:
    386: !  Due to grid point reordering with DMDAs, we must always work
    387: !  with the local grid points, and then transform them to the new
    388: !  global numbering with the "ltog" mapping
    389: !  We cannot work directly with the global numbers for the original
    390: !  uniprocessor grid!
    391: !
    392: !  Two methods are available for imposing this transformation
    393: !  when setting matrix entries:
    394: !    (A) MatSetValuesLocal(), using the local ordering (including
    395: !        ghost points!)
    396: !          by calling MatSetValuesLocal()
    397: !    (B) MatSetValues(), using the global ordering
    398: !        - Use DMDAGetGlobalIndices() to extract the local-to-global map
    399: !        - Then apply this map explicitly yourself
    400: !        - Set matrix entries using the global ordering by calling
    401: !          MatSetValues()
    402: !  Option (A) seems cleaner/easier in many cases, and is the procedure
    403: !  used in this example.
    404: !
    405:       subroutine FormJacobianLocal(info,x,A,jac,da,ierr)
    406:       use petscsnes
    407:       implicit none

    409: #include "ex5f.h"
    410:       DM da

    412: !  Input/output variables:
    413:       PetscScalar x(gxs:gxe,gys:gye)
    414:       Mat         A,jac
    415:       PetscErrorCode  ierr
    416:       DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)

    418: !  Local variables:
    419:       PetscInt  row,col(5),i,j,i1,i5
    420:       PetscScalar two,one,hx,hy,v(5)
    421:       PetscScalar hxdhy,hydhx,sc

    423: !  Set parameters

    425:       i1     = 1
    426:       i5     = 5
    427:       one    = 1.0
    428:       two    = 2.0
    429:       hx     = one/(mx-1)
    430:       hy     = one/(my-1)
    431:       sc     = hx*hy
    432:       hxdhy  = hx/hy
    433:       hydhx  = hy/hx

    435: !  Compute entries for the locally owned part of the Jacobian.
    436: !   - Currently, all PETSc parallel matrix formats are partitioned by
    437: !     contiguous chunks of rows across the processors.
    438: !   - Each processor needs to insert only elements that it owns
    439: !     locally (but any non-local elements will be sent to the
    440: !     appropriate processor during matrix assembly).
    441: !   - Here, we set all entries for a particular row at once.
    442: !   - We can set matrix entries either using either
    443: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
    444: !   - Note that MatSetValues() uses 0-based row and column numbers
    445: !     in Fortran as well as in C.

    447:       do 20 j=ys,ye
    448:          row = (j - gys)*gxm + xs - gxs - 1
    449:          do 10 i=xs,xe
    450:             row = row + 1
    451: !           boundary points
    452:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
    453: !       Some f90 compilers need 4th arg to be of same type in both calls
    454:                col(1) = row
    455:                v(1)   = one
    456:                call MatSetValuesLocal(jac,i1,row,i1,col,v,INSERT_VALUES,ierr)
    457: !           interior grid points
    458:             else
    459:                v(1) = -hxdhy
    460:                v(2) = -hydhx
    461:                v(3) = two*(hydhx + hxdhy) - sc*lambda*exp(x(i,j))
    462:                v(4) = -hydhx
    463:                v(5) = -hxdhy
    464:                col(1) = row - gxm
    465:                col(2) = row - 1
    466:                col(3) = row
    467:                col(4) = row + 1
    468:                col(5) = row + gxm
    469:                call MatSetValuesLocal(jac,i1,row,i5,col,v, INSERT_VALUES,ierr)
    470:             endif
    471:  10      continue
    472:  20   continue
    473:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
    474:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
    475:       if (A .ne. jac) then
    476:          call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
    477:          call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
    478:       endif
    479:       return
    480:       end

    482: !
    483: !     Simple convergence test based on the infinity norm of the residual being small
    484: !
    485:       subroutine MySNESConverged(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr)
    486:       use petscsnes
    487:       implicit none

    489:       SNES snes
    490:       PetscInt it,dummy
    491:       PetscReal xnorm,snorm,fnorm,nrm
    492:       SNESConvergedReason reason
    493:       Vec f
    494:       PetscErrorCode ierr

    496:       call SNESGetFunction(snes,f,PETSC_NULL_FUNCTION,dummy,ierr)
    497:       call VecNorm(f,NORM_INFINITY,nrm,ierr)
    498:       if (nrm .le. 1.e-5) reason = SNES_CONVERGED_FNORM_ABS

    500:       end

    502: !/*TEST
    503: !
    504: !   build:
    505: !      requires: !complex !single
    506: !
    507: !   test:
    508: !      nsize: 4
    509: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short \
    510: !            -ksp_gmres_cgs_refinement_type refine_always
    511: !
    512: !   test:
    513: !      suffix: 2
    514: !      nsize: 4
    515: !      args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
    516: !
    517: !   test:
    518: !      suffix: 3
    519: !      nsize: 3
    520: !      args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
    521: !
    522: !   test:
    523: !      suffix: 6
    524: !      nsize: 1
    525: !      args: -snes_monitor_short -my_snes_convergence
    526: !
    527: !TEST*/