Date: 2025-03-29T05:58:41+00:00

Actual source code: ex5f.F90

      1: !
      2: !  This example shows how to avoid Fortran line lengths larger than 132 characters.
      3: !  It avoids used of certain macros such as PetscCallA() and PetscCheckA() that
      4: !  generate very long lines
      5: !
      6: !  We recommend starting from src/snes/tutorials/ex5f90.F90 instead of this example
      7: !  because that does not have the restricted formatting that makes this version
      8: !  more difficult to read
      9: !
     10: !  Description: This example solves a nonlinear system in parallel with SNES.
     11: !  We solve the  Bratu (SFI - solid fuel ignition) problem in a 2D rectangular
     12: !  domain, using distributed arrays (DMDAs) to partition the parallel grid.
     13: !  The command line options include:
     14: !    -par <param>, where <param> indicates the nonlinearity of the problem
     15: !       problem SFI:  <parameter> = Bratu parameter (0 <= par <= 6.81)
     16: !
     17: !  --------------------------------------------------------------------------
     18: !
     19: !  Solid Fuel Ignition (SFI) problem.  This problem is modeled by
     20: !  the partial differential equation
     21: !
     22: !          -Laplacian u - lambda*exp(u) = 0,  0 < x,y < 1,
     23: !
     24: !  with boundary conditions
     25: !
     26: !           u = 0  for  x = 0, x = 1, y = 0, y = 1.
     27: !
     28: !  A finite difference approximation with the usual 5-point stencil
     29: !  is used to discretize the boundary value problem to obtain a nonlinear
     30: !  system of equations.
     31: !
     32: !  --------------------------------------------------------------------------
     33:       module ex5fmodule
     34:       use petscsnes
     35:       use petscdmda
     36: #include <petsc/finclude/petscsnes.h>
     37: #include <petsc/finclude/petscdmda.h>
     38:       PetscInt xs,xe,xm,gxs,gxe,gxm
     39:       PetscInt ys,ye,ym,gys,gye,gym
     40:       PetscInt mx,my
     41:       PetscMPIInt rank,size
     42:       PetscReal lambda
     43:       end module ex5fmodule

     45:       program main
     46:       use ex5fmodule
     47:       implicit none

     49: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     50: !                   Variable declarations
     51: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52: !
     53: !  Variables:
     54: !     snes        - nonlinear solver
     55: !     x, r        - solution, residual vectors
     56: !     its         - iterations for convergence
     57: !
     58: !  See additional variable declarations in the file ex5f.h
     59: !
     60:       SNES           snes
     61:       Vec            x,r
     62:       PetscInt       its,i1,i4
     63:       PetscErrorCode ierr
     64:       PetscReal      lambda_max,lambda_min
     65:       PetscBool      flg
     66:       DM             da

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

     71:       external FormInitialGuess
     72:       external FormFunctionLocal,FormJacobianLocal
     73:       external MySNESConverged

     75: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     76: !  Initialize program
     77: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     79:       call PetscInitialize(ierr)
     80:       CHKERRA(ierr)
     81:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
     82:       CHKERRMPIA(ierr)
     83:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
     84:       CHKERRMPIA(ierr)
     85: !  Initialize problem parameters

     87:       i1 = 1
     88:       i4 = 4
     89:       lambda_max = 6.81
     90:       lambda_min = 0.0
     91:       lambda     = 6.0
     92:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',lambda,PETSC_NULL_BOOL,ierr)
     93:       CHKERRA(ierr)

     95: ! this statement is split into multiple-lines to keep lines under 132 char limit - required by 'make check'
     96:       if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
     97:          ierr = PETSC_ERR_ARG_OUTOFRANGE;
     98:          SETERRA(PETSC_COMM_WORLD,ierr,'Lambda')
     99:       endif

    101: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    102: !  Create nonlinear solver context
    103: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    105:       call SNESCreate(PETSC_COMM_WORLD,snes,ierr)
    106:       CHKERRA(ierr)

    108: !  Set convergence test routine if desired

    110:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_snes_convergence',flg,ierr)
    111:       CHKERRA(ierr)
    112:       if (flg) then
    113:         call SNESSetConvergenceTest(snes,MySNESConverged,0,PETSC_NULL_FUNCTION,ierr)
    114:         CHKERRA(ierr)
    115:       endif

    117: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    118: !  Create vector data structures; set function evaluation routine
    119: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    123: !     This really needs only the star-type stencil, but we use the box stencil

    125:       call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE, &
    126:                         i1,i1, PETSC_NULL_INTEGER_ARRAY,PETSC_NULL_INTEGER_ARRAY,da,ierr)
    127:       CHKERRA(ierr)
    128:       call DMSetFromOptions(da,ierr)
    129:       CHKERRA(ierr)
    130:       call DMSetUp(da,ierr)
    131:       CHKERRA(ierr)

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

    136:       call DMCreateGlobalVector(da,x,ierr)
    137:       CHKERRA(ierr)
    138:       call VecDuplicate(x,r,ierr)
    139:       CHKERRA(ierr)

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

    143:       call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER, &
    144:                        PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_DMBOUNDARYTYPE,PETSC_NULL_DMBOUNDARYTYPE, &
    145:                        PETSC_NULL_DMBOUNDARYTYPE,PETSC_NULL_DMDASTENCILTYPE,ierr)
    146:       CHKERRA(ierr)
    147:       call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr)
    148:       CHKERRA(ierr)
    149:       call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr)
    150:       CHKERRA(ierr)

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

    155:       xs  = xs+1
    156:       ys  = ys+1
    157:       gxs = gxs+1
    158:       gys = gys+1

    160:       ye  = ys+ym-1
    161:       xe  = xs+xm-1
    162:       gye = gys+gym-1
    163:       gxe = gxs+gxm-1

    165: !  Set function evaluation routine and vector

    167:       call DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal,da,ierr)
    168:       CHKERRA(ierr)
    169:       call DMDASNESSetJacobianLocal(da,FormJacobianLocal,da,ierr)
    170:       CHKERRA(ierr)
    171:       call SNESSetDM(snes,da,ierr)
    172:       CHKERRA(ierr)

    174: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    175: !  Customize nonlinear solver; set runtime options
    176: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    180:       call SNESSetFromOptions(snes,ierr)
    181:       CHKERRA(ierr)
    182: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    183: !  Evaluate initial guess; then solve nonlinear system.
    184: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    191:       call FormInitialGuess(x,ierr)
    192:       CHKERRA(ierr)
    193:       call SNESSolve(snes,PETSC_NULL_VEC,x,ierr)
    194:       CHKERRA(ierr)
    195:       call SNESGetIterationNumber(snes,its,ierr)
    196:       CHKERRA(ierr)
    197:       if (rank .eq. 0) then
    198:          write(6,100) its
    199:       endif
    200:   100 format('Number of SNES iterations = ',i5)

    202: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    203: !  Free work space.  All PETSc objects should be destroyed when they
    204: !  are no longer needed.
    205: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    207:       call VecDestroy(x,ierr)
    208:       CHKERRA(ierr)
    209:       call VecDestroy(r,ierr)
    210:       CHKERRA(ierr)
    211:       call SNESDestroy(snes,ierr)
    212:       CHKERRA(ierr)
    213:       call DMDestroy(da,ierr)
    214:       CHKERRA(ierr)
    215:       call PetscFinalize(ierr)
    216:       CHKERRA(ierr)
    217:       end

    219: ! ---------------------------------------------------------------------
    220: !
    221: !  FormInitialGuess - Forms initial approximation.
    222: !
    223: !  Input Parameters:
    224: !  X - vector
    225: !
    226: !  Output Parameter:
    227: !  X - vector
    228: !
    229: !  Notes:
    230: !  This routine serves as a wrapper for the lower-level routine
    231: !  "ApplicationInitialGuess", where the actual computations are
    232: !  done using the standard Fortran style of treating the local
    233: !  vector data as a multidimensional array over the local mesh.
    234: !  This routine merely handles ghost point scatters and accesses
    235: !  the local vector data via VecGetArray() and VecRestoreArray().
    236: !
    237:       subroutine FormInitialGuess(X,ierr)
    238:       use ex5fmodule
    239:       implicit none

    241: !  Input/output variables:
    242:       Vec      X
    243:       PetscErrorCode  ierr
    244: !  Declarations for use with local arrays:
    245:       PetscScalar, pointer :: lx_v(:)

    247:       ierr = 0

    249: !  Get a pointer to vector data.
    250: !    - For default PETSc vectors, VecGetArray() returns a pointer to
    251: !      the data array.  Otherwise, the routine is implementation dependent.
    252: !    - You MUST call VecRestoreArray() when you no longer need access to
    253: !      the array.
    254: !    - Note that the Fortran interface to VecGetArray() differs from the
    255: !      C version.  See the users manual for details.

    257:        call VecGetArray(X,lx_v,ierr)
    258:       CHKERRQ(ierr)

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

    262:       call InitialGuessLocal(lx_v,ierr)
    263:       CHKERRQ(ierr)

    265: !  Restore vector

    267:       call VecRestoreArray(X,lx_v,ierr)
    268:       CHKERRQ(ierr)

    270:       end

    272: ! ---------------------------------------------------------------------
    273: !
    274: !  InitialGuessLocal - Computes initial approximation, called by
    275: !  the higher level routine FormInitialGuess().
    276: !
    277: !  Input Parameter:
    278: !  x - local vector data
    279: !
    280: !  Output Parameters:
    281: !  x - local vector data
    282: !  ierr - error code
    283: !
    284: !  Notes:
    285: !  This routine uses standard Fortran-style computations over a 2-dim array.
    286: !
    287:       subroutine InitialGuessLocal(x,ierr)
    288:       use ex5fmodule
    289:       implicit none

    291: !  Input/output variables:
    292:       PetscScalar    x(xs:xe,ys:ye)
    293:       PetscErrorCode ierr

    295: !  Local variables:
    296:       PetscInt  i,j
    297:       PetscReal temp1,temp,one,hx,hy

    299: !  Set parameters

    301:       ierr   = 0
    302:       one    = 1.0
    303:       hx     = one/((real(mx)-1))
    304:       hy     = one/((real(my)-1))
    305:       temp1  = lambda/(lambda + one)

    307:       do 20 j=ys,ye
    308:          temp = (real(min(j-1,my-j)))*hy
    309:          do 10 i=xs,xe
    310:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
    311:               x(i,j) = 0.0
    312:             else
    313:               x(i,j) = temp1 * sqrt(min(real(min(i-1,mx-i))*hx,(temp)))
    314:             endif
    315:  10      continue
    316:  20   continue

    318:       end

    320: ! ---------------------------------------------------------------------
    321: !
    322: !  FormFunctionLocal - Computes nonlinear function, called by
    323: !  the higher level routine FormFunction().
    324: !
    325: !  Input Parameter:
    326: !  x - local vector data
    327: !
    328: !  Output Parameters:
    329: !  f - local vector data, f(x)
    330: !  ierr - error code
    331: !
    332: !  Notes:
    333: !  This routine uses standard Fortran-style computations over a 2-dim array.
    334: !
    335: !
    336:       subroutine FormFunctionLocal(info,x,f,da,ierr)
    337:       use ex5fmodule
    338:       implicit none

    340:       DM da

    342: !  Input/output variables:
    343:       DMDALocalInfo info
    344:       PetscScalar x(gxs:gxe,gys:gye)
    345:       PetscScalar f(xs:xe,ys:ye)
    346:       PetscErrorCode     ierr

    348: !  Local variables:
    349:       PetscScalar two,one,hx,hy
    350:       PetscScalar hxdhy,hydhx,sc
    351:       PetscScalar u,uxx,uyy
    352:       PetscInt  i,j

    354:       xs     = info%XS+1
    355:       xe     = xs+info%XM-1
    356:       ys     = info%YS+1
    357:       ye     = ys+info%YM-1
    358:       mx     = info%MX
    359:       my     = info%MY

    361:       one    = 1.0
    362:       two    = 2.0
    363:       hx     = one/(real(mx)-1)
    364:       hy     = one/(real(my)-1)
    365:       sc     = hx*hy*lambda
    366:       hxdhy  = hx/hy
    367:       hydhx  = hy/hx

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

    371:       do 20 j=ys,ye
    372:          do 10 i=xs,xe
    373:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
    374:                f(i,j) = x(i,j)
    375:             else
    376:                u = x(i,j)
    377:                uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
    378:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
    379:                f(i,j) = uxx + uyy - sc*exp(u)
    380:             endif
    381:  10      continue
    382:  20   continue

    384:       call PetscLogFlops(11.0d0*ym*xm,ierr)
    385:       CHKERRQ(ierr)

    387:       end

    389: ! ---------------------------------------------------------------------
    390: !
    391: !  FormJacobianLocal - Computes Jacobian matrix, called by
    392: !  the higher level routine FormJacobian().
    393: !
    394: !  Input Parameters:
    395: !  x        - local vector data
    396: !
    397: !  Output Parameters:
    398: !  jac      - Jacobian matrix
    399: !  jac_prec - optionally different preconditioning matrix (not used here)
    400: !  ierr     - error code
    401: !
    402: !  Notes:
    403: !  This routine uses standard Fortran-style computations over a 2-dim array.
    404: !
    405: !  Notes:
    406: !  Due to grid point reordering with DMDAs, we must always work
    407: !  with the local grid points, and then transform them to the new
    408: !  global numbering with the "ltog" mapping
    409: !  We cannot work directly with the global numbers for the original
    410: !  uniprocessor grid!
    411: !
    412: !  Two methods are available for imposing this transformation
    413: !  when setting matrix entries:
    414: !    (A) MatSetValuesLocal(), using the local ordering (including
    415: !        ghost points!)
    416: !          by calling MatSetValuesLocal()
    417: !    (B) MatSetValues(), using the global ordering
    418: !        - Use DMDAGetGlobalIndices() to extract the local-to-global map
    419: !        - Then apply this map explicitly yourself
    420: !        - Set matrix entries using the global ordering by calling
    421: !          MatSetValues()
    422: !  Option (A) seems cleaner/easier in many cases, and is the procedure
    423: !  used in this example.
    424: !
    425:       subroutine FormJacobianLocal(info,x,A,jac,da,ierr)
    426:       use ex5fmodule
    427:       implicit none

    429:       DM da

    431: !  Input/output variables:
    432:       PetscScalar x(gxs:gxe,gys:gye)
    433:       Mat         A,jac
    434:       PetscErrorCode  ierr
    435:       DMDALocalInfo info

    437: !  Local variables:
    438:       PetscInt  row,col(5),i,j,i1,i5
    439:       PetscScalar two,one,hx,hy,v(5)
    440:       PetscScalar hxdhy,hydhx,sc

    442: !  Set parameters

    444:       i1     = 1
    445:       i5     = 5
    446:       one    = 1.0
    447:       two    = 2.0
    448:       hx     = one/(real(mx)-1)
    449:       hy     = one/(real(my)-1)
    450:       sc     = hx*hy
    451:       hxdhy  = hx/hy
    452:       hydhx  = hy/hx
    453: ! -Wmaybe-uninitialized
    454:       v      = 0.0
    455:       col    = 0

    457: !  Compute entries for the locally owned part of the Jacobian.
    458: !   - Currently, all PETSc parallel matrix formats are partitioned by
    459: !     contiguous chunks of rows across the processors.
    460: !   - Each processor needs to insert only elements that it owns
    461: !     locally (but any non-local elements will be sent to the
    462: !     appropriate processor during matrix assembly).
    463: !   - Here, we set all entries for a particular row at once.
    464: !   - We can set matrix entries either using either
    465: !     MatSetValuesLocal() or MatSetValues(), as discussed above.
    466: !   - Note that MatSetValues() uses 0-based row and column numbers
    467: !     in Fortran as well as in C.

    469:       do 20 j=ys,ye
    470:          row = (j - gys)*gxm + xs - gxs - 1
    471:          do 10 i=xs,xe
    472:             row = row + 1
    473: !           boundary points
    474:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
    475: !       Some f90 compilers need 4th arg to be of same type in both calls
    476:                col(1) = row
    477:                v(1)   = one
    478:                call MatSetValuesLocal(jac,i1,[row],i1,[col],[v],INSERT_VALUES,ierr)
    479:                CHKERRQ(ierr)
    480: !           interior grid points
    481:             else
    482:                v(1) = -hxdhy
    483:                v(2) = -hydhx
    484:                v(3) = two*(hydhx + hxdhy) - sc*lambda*exp(x(i,j))
    485:                v(4) = -hydhx
    486:                v(5) = -hxdhy
    487:                col(1) = row - gxm
    488:                col(2) = row - 1
    489:                col(3) = row
    490:                col(4) = row + 1
    491:                col(5) = row + gxm
    492:                call MatSetValuesLocal(jac,i1,[row],i5,[col],[v], INSERT_VALUES,ierr)
    493:                CHKERRQ(ierr)
    494:             endif
    495:  10      continue
    496:  20   continue
    497:       call MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr)
    498:       CHKERRQ(ierr)
    499:       call MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr)
    500:       CHKERRQ(ierr)
    501:       if (A .ne. jac) then
    502:          call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY,ierr)
    503:          CHKERRQ(ierr)
    504:          call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY,ierr)
    505:          CHKERRQ(ierr)
    506:       endif
    507:       end

    509: !
    510: !     Simple convergence test based on the infinity norm of the residual being small
    511: !
    512:       subroutine MySNESConverged(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr)
    513:       use ex5fmodule
    514:       implicit none

    516:       SNES snes
    517:       PetscInt it,dummy
    518:       PetscReal xnorm,snorm,fnorm,nrm
    519:       SNESConvergedReason reason
    520:       Vec f
    521:       PetscErrorCode ierr

    523:       call SNESGetFunction(snes,f,PETSC_NULL_FUNCTION,dummy,ierr)
    524:       CHKERRQ(ierr)
    525:       call VecNorm(f,NORM_INFINITY,nrm,ierr)
    526:       CHKERRQ(ierr)
    527:       if (nrm .le. 1.e-5) reason = SNES_CONVERGED_FNORM_ABS

    529:       end

    531: !/*TEST
    532: !
    533: !   build:
    534: !      requires: !complex !single
    535: !
    536: !   test:
    537: !      nsize: 4
    538: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short \
    539: !            -ksp_gmres_cgs_refinement_type refine_always
    540: !
    541: !   test:
    542: !      suffix: 2
    543: !      nsize: 4
    544: !      args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
    545: !
    546: !   test:
    547: !      suffix: 3
    548: !      nsize: 3
    549: !      args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
    550: !
    551: !   test:
    552: !      suffix: 6
    553: !      nsize: 1
    554: !      args: -snes_monitor_short -my_snes_convergence
    555: !
    556: !TEST*/