Date: 2022-03-31T04:48:34+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: !
     10: !!/*T
     11: !  Concepts: SNES^parallel Bratu example
     12: !  Concepts: DMDA^using distributed arrays;
     13: !  Processors: n
     14: !T*/

     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: !  --------------------------------------------------------------------------

     34:       program main
     35: #include <petsc/finclude/petscsnes.h>
     36:       use petscdmda
     37:       use petscsnes
     38:       implicit none
     39: !
     40: !  We place common blocks, variable declarations, and other include files
     41: !  needed for this code in the single file ex5f.h.  We then need to include
     42: !  only this file throughout the various routines in this program.  See
     43: !  additional comments in the file ex5f.h.
     44: !
     45: #include "ex5f.h"

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

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

     69:       external FormInitialGuess
     70:       external FormFunctionLocal,FormJacobianLocal
     71:       external MySNESConverged

     73: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     74: !  Initialize program
     75: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     77:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
     78:       if (ierr .ne. 0) then
     79:         print*,'Unable to initialize PETSc'
     80:         stop
     81:       endif
     82:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
     83:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,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: ! this statement is split into multiple-lines to keep lines under 132 char limit - required by 'make check'
     94:       if (lambda .ge. lambda_max .or. lambda .le. lambda_min) then
     95:         PETSC_ERR_ARG_OUTOFRANGE; SETERRA(PETSC_COMM_WORLD,ierr,'Lambda')
     96:       endif

     98: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     99: !  Create nonlinear solver context
    100: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    102:       call SNESCreate(PETSC_COMM_WORLD,snes,ierr)

    104: !  Set convergence test routine if desired

    106:       call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my_snes_convergence',flg,ierr)
    107:       if (flg) then
    108:         call SNESSetConvergenceTest(snes,MySNESConverged,0,PETSC_NULL_FUNCTION,ierr)
    109:       endif

    111: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    112: !  Create vector data structures; set function evaluation routine
    113: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    117: ! This really needs only the star-type stencil, but we use the box
    118: ! stencil temporarily.
    119:       call DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,      &
    120:      &     DMDA_STENCIL_STAR,i4,i4,PETSC_DECIDE,PETSC_DECIDE,i1,i1,                &
    121:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
    122:       call DMSetFromOptions(da,ierr)
    123:       call DMSetUp(da,ierr)

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

    128:       call DMCreateGlobalVector(da,x,ierr)
    129:       call VecDuplicate(x,r,ierr)

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

    133:       call DMDAGetInfo(da,PETSC_NULL_INTEGER,mx,my,PETSC_NULL_INTEGER,            &
    134:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
    135:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
    136:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
    137:      &               PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                     &
    138:      &               PETSC_NULL_INTEGER,ierr)
    139:       call DMDAGetCorners(da,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr)
    140:       call DMDAGetGhostCorners(da,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr)

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

    145:       xs  = xs+1
    146:       ys  = ys+1
    147:       gxs = gxs+1
    148:       gys = gys+1

    150:       ye  = ys+ym-1
    151:       xe  = xs+xm-1
    152:       gye = gys+gym-1
    153:       gxe = gxs+gxm-1

    155: !  Set function evaluation routine and vector

    157:       call DMDASNESSetFunctionLocal(da,INSERT_VALUES,FormFunctionLocal,da,ierr)
    158:       call DMDASNESSetJacobianLocal(da,FormJacobianLocal,da,ierr)
    159:       call SNESSetDM(snes,da,ierr)

    161: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    162: !  Customize nonlinear solver; set runtime options
    163: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    167:           call SNESSetFromOptions(snes,ierr)
    168: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    169: !  Evaluate initial guess; then solve nonlinear system.
    170: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

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

    177:       call FormInitialGuess(x,ierr)
    178:       call SNESSolve(snes,PETSC_NULL_VEC,x,ierr)
    179:       call SNESGetIterationNumber(snes,its,ierr)
    180:       if (rank .eq. 0) then
    181:          write(6,100) its
    182:       endif
    183:   100 format('Number of SNES iterations = ',i5)

    185: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    186: !  Free work space.  All PETSc objects should be destroyed when they
    187: !  are no longer needed.
    188: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    190:       call VecDestroy(x,ierr)
    191:       call VecDestroy(r,ierr)
    192:       call SNESDestroy(snes,ierr)
    193:       call DMDestroy(da,ierr)
    194:       call PetscFinalize(ierr)
    195:       end

    197: ! ---------------------------------------------------------------------
    198: !
    199: !  FormInitialGuess - Forms initial approximation.
    200: !
    201: !  Input Parameters:
    202: !  X - vector
    203: !
    204: !  Output Parameter:
    205: !  X - vector
    206: !
    207: !  Notes:
    208: !  This routine serves as a wrapper for the lower-level routine
    209: !  "ApplicationInitialGuess", where the actual computations are
    210: !  done using the standard Fortran style of treating the local
    211: !  vector data as a multidimensional array over the local mesh.
    212: !  This routine merely handles ghost point scatters and accesses
    213: !  the local vector data via VecGetArray() and VecRestoreArray().
    214: !
    215:       subroutine FormInitialGuess(X,ierr)
    216:       use petscsnes
    217:       implicit none

    219: #include "ex5f.h"

    221: !  Input/output variables:
    222:       Vec      X
    223:       PetscErrorCode  ierr

    225: !  Declarations for use with local arrays:
    226:       PetscScalar lx_v(0:1)
    227:       PetscOffset lx_i

    229:       0

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

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

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

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

    245: !  Restore vector

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

    249:       return
    250:       end

    252: ! ---------------------------------------------------------------------
    253: !
    254: !  InitialGuessLocal - Computes initial approximation, called by
    255: !  the higher level routine FormInitialGuess().
    256: !
    257: !  Input Parameter:
    258: !  x - local vector data
    259: !
    260: !  Output Parameters:
    261: !  x - local vector data
    262: !  ierr - error code
    263: !
    264: !  Notes:
    265: !  This routine uses standard Fortran-style computations over a 2-dim array.
    266: !
    267:       subroutine InitialGuessLocal(x,ierr)
    268:       use petscsnes
    269:       implicit none

    271: #include "ex5f.h"

    273: !  Input/output variables:
    274:       PetscScalar    x(xs:xe,ys:ye)
    275:       PetscErrorCode ierr

    277: !  Local variables:
    278:       PetscInt  i,j
    279:       PetscReal temp1,temp,one,hx,hy

    281: !  Set parameters

    283:       0
    284:       one    = 1.0
    285:       hx     = one/((mx-1))
    286:       hy     = one/((my-1))
    287:       temp1  = lambda/(lambda + one)

    289:       do 20 j=ys,ye
    290:          temp = (min(j-1,my-j))*hy
    291:          do 10 i=xs,xe
    292:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
    293:               x(i,j) = 0.0
    294:             else
    295:               x(i,j) = temp1 * sqrt(min(min(i-1,mx-i)*hx,(temp)))
    296:             endif
    297:  10      continue
    298:  20   continue

    300:       return
    301:       end

    303: ! ---------------------------------------------------------------------
    304: !
    305: !  FormFunctionLocal - Computes nonlinear function, called by
    306: !  the higher level routine FormFunction().
    307: !
    308: !  Input Parameter:
    309: !  x - local vector data
    310: !
    311: !  Output Parameters:
    312: !  f - local vector data, f(x)
    313: !  ierr - error code
    314: !
    315: !  Notes:
    316: !  This routine uses standard Fortran-style computations over a 2-dim array.
    317: !
    318: !
    319:       subroutine FormFunctionLocal(info,x,f,da,ierr)
    320: #include <petsc/finclude/petscdmda.h>
    321:       use petscsnes
    322:       implicit none

    324: #include "ex5f.h"
    325:       DM da

    327: !  Input/output variables:
    328:       DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)
    329:       PetscScalar x(gxs:gxe,gys:gye)
    330:       PetscScalar f(xs:xe,ys:ye)
    331:       PetscErrorCode     ierr

    333: !  Local variables:
    334:       PetscScalar two,one,hx,hy
    335:       PetscScalar hxdhy,hydhx,sc
    336:       PetscScalar u,uxx,uyy
    337:       PetscInt  i,j

    339:       xs     = info(DMDA_LOCAL_INFO_XS)+1
    340:       xe     = xs+info(DMDA_LOCAL_INFO_XM)-1
    341:       ys     = info(DMDA_LOCAL_INFO_YS)+1
    342:       ye     = ys+info(DMDA_LOCAL_INFO_YM)-1
    343:       mx     = info(DMDA_LOCAL_INFO_MX)
    344:       my     = info(DMDA_LOCAL_INFO_MY)

    346:       one    = 1.0
    347:       two    = 2.0
    348:       hx     = one/(mx-1)
    349:       hy     = one/(my-1)
    350:       sc     = hx*hy*lambda
    351:       hxdhy  = hx/hy
    352:       hydhx  = hy/hx

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

    356:       do 20 j=ys,ye
    357:          do 10 i=xs,xe
    358:             if (i .eq. 1 .or. j .eq. 1 .or. i .eq. mx .or. j .eq. my) then
    359:                f(i,j) = x(i,j)
    360:             else
    361:                u = x(i,j)
    362:                uxx = hydhx * (two*u - x(i-1,j) - x(i+1,j))
    363:                uyy = hxdhy * (two*u - x(i,j-1) - x(i,j+1))
    364:                f(i,j) = uxx + uyy - sc*exp(u)
    365:             endif
    366:  10      continue
    367:  20   continue

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

    371:       return
    372:       end

    374: ! ---------------------------------------------------------------------
    375: !
    376: !  FormJacobianLocal - Computes Jacobian matrix, called by
    377: !  the higher level routine FormJacobian().
    378: !
    379: !  Input Parameters:
    380: !  x        - local vector data
    381: !
    382: !  Output Parameters:
    383: !  jac      - Jacobian matrix
    384: !  jac_prec - optionally different preconditioning matrix (not used here)
    385: !  ierr     - error code
    386: !
    387: !  Notes:
    388: !  This routine uses standard Fortran-style computations over a 2-dim array.
    389: !
    390: !  Notes:
    391: !  Due to grid point reordering with DMDAs, we must always work
    392: !  with the local grid points, and then transform them to the new
    393: !  global numbering with the "ltog" mapping
    394: !  We cannot work directly with the global numbers for the original
    395: !  uniprocessor grid!
    396: !
    397: !  Two methods are available for imposing this transformation
    398: !  when setting matrix entries:
    399: !    (A) MatSetValuesLocal(), using the local ordering (including
    400: !        ghost points!)
    401: !          by calling MatSetValuesLocal()
    402: !    (B) MatSetValues(), using the global ordering
    403: !        - Use DMDAGetGlobalIndices() to extract the local-to-global map
    404: !        - Then apply this map explicitly yourself
    405: !        - Set matrix entries using the global ordering by calling
    406: !          MatSetValues()
    407: !  Option (A) seems cleaner/easier in many cases, and is the procedure
    408: !  used in this example.
    409: !
    410:       subroutine FormJacobianLocal(info,x,A,jac,da,ierr)
    411:       use petscsnes
    412:       implicit none

    414: #include "ex5f.h"
    415:       DM da

    417: !  Input/output variables:
    418:       PetscScalar x(gxs:gxe,gys:gye)
    419:       Mat         A,jac
    420:       PetscErrorCode  ierr
    421:       DMDALocalInfo info(DMDA_LOCAL_INFO_SIZE)

    423: !  Local variables:
    424:       PetscInt  row,col(5),i,j,i1,i5
    425:       PetscScalar two,one,hx,hy,v(5)
    426:       PetscScalar hxdhy,hydhx,sc

    428: !  Set parameters

    430:       i1     = 1
    431:       i5     = 5
    432:       one    = 1.0
    433:       two    = 2.0
    434:       hx     = one/(mx-1)
    435:       hy     = one/(my-1)
    436:       sc     = hx*hy
    437:       hxdhy  = hx/hy
    438:       hydhx  = hy/hx

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

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

    487: !
    488: !     Simple convergence test based on the infinity norm of the residual being small
    489: !
    490:       subroutine MySNESConverged(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr)
    491:       use petscsnes
    492:       implicit none

    494:       SNES snes
    495:       PetscInt it,dummy
    496:       PetscReal xnorm,snorm,fnorm,nrm
    497:       SNESConvergedReason reason
    498:       Vec f
    499:       PetscErrorCode ierr

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

    505:       end

    507: !/*TEST
    508: !
    509: !   build:
    510: !      requires: !complex !single
    511: !
    512: !   test:
    513: !      nsize: 4
    514: !      args: -snes_mf -pc_type none -da_processors_x 4 -da_processors_y 1 -snes_monitor_short \
    515: !            -ksp_gmres_cgs_refinement_type refine_always
    516: !
    517: !   test:
    518: !      suffix: 2
    519: !      nsize: 4
    520: !      args: -da_processors_x 2 -da_processors_y 2 -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
    521: !
    522: !   test:
    523: !      suffix: 3
    524: !      nsize: 3
    525: !      args: -snes_fd -snes_monitor_short -ksp_gmres_cgs_refinement_type refine_always
    526: !
    527: !   test:
    528: !      suffix: 6
    529: !      nsize: 1
    530: !      args: -snes_monitor_short -my_snes_convergence
    531: !
    532: !TEST*/