Actual source code: ex22f.F

      1: ! Time-dependent advection-reaction PDE in 1d. Demonstrates IMEX methods
      2: !
      3: !   u_t + a1*u_x = -k1*u + k2*v + s1
      4: !   v_t + a2*v_x = k1*u - k2*v + s2
      5: !   0 < x < 1;
      6: !   a1 = 1, k1 = 10^6, s1 = 0,
      7: !   a2 = 0, k2 = 2*k1, s2 = 1
      8: !
      9: !   Initial conditions:
     10: !   u(x,0) = 1 + s2*x
     11: !   v(x,0) = k0/k1*u(x,0) + s1/k1
     12: !
     13: !   Upstream boundary conditions:
     14: !   u(0,t) = 1-sin(12*t)^4
     15: !

     17:       program main
     18: #include <petsc/finclude/petscts.h>
     19: #include <petsc/finclude/petscdmda.h>
     20:       use petscts
     21:       implicit none

     23: !
     24: !  Create an application context to contain data needed by the
     25: !  application-provided call-back routines, FormJacobian() and
     26: !  FormFunction(). We use a double precision array with six
     27: !  entries, two for each problem parameter a, k, s.
     28: !
     29:       PetscReal user(6)
     30:       integer user_a,user_k,user_s
     31:       parameter (user_a = 0,user_k = 2,user_s = 4)

     33:       external FormRHSFunction,FormIFunction,FormIJacobian
     34:       external FormInitialSolution

     36:       TS             ts
     37:       SNES           snes
     38:       SNESLineSearch linesearch
     39:       Vec            X
     40:       Mat            J
     41:       PetscInt       mx
     42:       PetscErrorCode ierr
     43:       DM             da
     44:       PetscReal      ftime,dt
     45:       PetscReal      one,pone
     46:       PetscInt       im11,i2
     47:       PetscBool      flg

     49:       im11 = 11
     50:       i2   = 2
     51:       one = 1.0
     52:       pone = one / 10

     54:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
     55:       if (ierr .ne. 0) then
     56:          print*,'Unable to initialize PETSc'
     57:          stop
     58:       endif

     60: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     61: !  Create distributed array (DMDA) to manage parallel grid and vectors
     62: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     63:       call DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,im11,i2,i2,   &
     64:      &     PETSC_NULL_INTEGER,da,ierr)
     65:       call DMSetFromOptions(da,ierr)
     66:       call DMSetUp(da,ierr)

     68: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     69: !    Extract global vectors from DMDA;
     70: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     71:       call DMCreateGlobalVector(da,X,ierr)

     73: ! Initialize user application context
     74: ! Use zero-based indexing for command line parameters to match ex22.c
     75:       user(user_a+1) = 1.0
     76:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,        &
     77:      &                         '-a0',user(user_a+1),flg,ierr)
     78:       user(user_a+2) = 0.0
     79:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,        &
     80:      &                        '-a1',user(user_a+2),flg,ierr)
     81:       user(user_k+1) = 1000000.0
     82:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,        &
     83:      &                         '-k0',user(user_k+1),flg,ierr)
     84:       user(user_k+2) = 2*user(user_k+1)
     85:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,        &
     86:      &                         '-k1', user(user_k+2),flg,ierr)
     87:       user(user_s+1) = 0.0
     88:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,        &
     89:      &                         '-s0',user(user_s+1),flg,ierr)
     90:       user(user_s+2) = 1.0
     91:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,        &
     92:      &                         '-s1',user(user_s+2),flg,ierr)

     94: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     95: !    Create timestepping solver context
     96: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     97:       call TSCreate(PETSC_COMM_WORLD,ts,ierr)
     98:       call TSSetDM(ts,da,ierr)
     99:       call TSSetType(ts,TSARKIMEX,ierr)
    100:       call TSSetRHSFunction(ts,PETSC_NULL_VEC,FormRHSFunction,                  &
    101:      &     user,ierr)
    102:       call TSSetIFunction(ts,PETSC_NULL_VEC,FormIFunction,user,ierr)
    103:       call DMSetMatType(da,MATAIJ,ierr)
    104:       call DMCreateMatrix(da,J,ierr)
    105:       call TSSetIJacobian(ts,J,J,FormIJacobian,user,ierr)

    107:       call TSGetSNES(ts,snes,ierr)
    108:       call SNESGetLineSearch(snes,linesearch,ierr)
    109:       call SNESLineSearchSetType(linesearch,SNESLINESEARCHBASIC,ierr)

    111:       ftime = 1.0
    112:       call TSSetMaxTime(ts,ftime,ierr)
    113:       call TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER,ierr)

    115: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    116: !  Set initial conditions
    117: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    118:       call FormInitialSolution(ts,X,user,ierr)
    119:       call TSSetSolution(ts,X,ierr)
    120:       call VecGetSize(X,mx,ierr)
    121: !  Advective CFL, I don't know why it needs so much safety factor.
    122:       dt = pone * max(user(user_a+1),user(user_a+2)) / mx;
    123:       call TSSetTimeStep(ts,dt,ierr)

    125: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    126: !   Set runtime options
    127: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    128:       call TSSetFromOptions(ts,ierr)

    130: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    131: !  Solve nonlinear system
    132: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    133:       call TSSolve(ts,X,ierr)

    135: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    136: !  Free work space.
    137: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    138:       call MatDestroy(J,ierr)
    139:       call VecDestroy(X,ierr)
    140:       call TSDestroy(ts,ierr)
    141:       call DMDestroy(da,ierr)
    142:       call PetscFinalize(ierr)
    143:       end program

    145: ! Small helper to extract the layout, result uses 1-based indexing.
    146:       subroutine GetLayout(da,mx,xs,xe,gxs,gxe,ierr)
    147:       use petscdmda
    148:       implicit none

    150:       DM da
    151:       PetscInt mx,xs,xe,gxs,gxe
    152:       PetscErrorCode ierr
    153:       PetscInt xm,gxm
    154:             call DMDAGetInfo(da,PETSC_NULL_INTEGER,                     &
    155:      &     mx,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                    &
    156:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,    &
    157:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                       &
    158:      &     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,    &
    159:      &     PETSC_NULL_INTEGER,ierr)
    160:       call DMDAGetCorners(da,xs,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,  &
    161:      &     xm,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)
    162:       call DMDAGetGhostCorners(da,                                      &
    163:      &     gxs,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,                   &
    164:      &     gxm,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr)
    165:       xs = xs + 1
    166:       gxs = gxs + 1
    167:       xe = xs + xm - 1
    168:       gxe = gxs + gxm - 1
    169:       end subroutine

    171:       subroutine FormIFunctionLocal(mx,xs,xe,gxs,gxe,x,xdot,f,          &
    172:      &     a,k,s,ierr)
    173:       implicit none
    174:       PetscInt mx,xs,xe,gxs,gxe
    175:       PetscScalar x(2,xs:xe)
    176:       PetscScalar xdot(2,xs:xe)
    177:       PetscScalar f(2,xs:xe)
    178:       PetscReal a(2),k(2),s(2)
    179:       PetscErrorCode ierr
    180:       PetscInt i
    181:       do 10 i = xs,xe
    182:          f(1,i) = xdot(1,i) + k(1)*x(1,i) - k(2)*x(2,i) - s(1)
    183:          f(2,i) = xdot(2,i) - k(1)*x(1,i) + k(2)*x(2,i) - s(2)
    184:  10   continue
    185:       end subroutine

    187:       subroutine FormIFunction(ts,t,X,Xdot,F,user,ierr)
    188:       use petscts
    189:       implicit none

    191:       TS ts
    192:       PetscReal t
    193:       Vec X,Xdot,F
    194:       PetscReal user(6)
    195:       PetscErrorCode ierr
    196:       integer user_a,user_k,user_s
    197:       parameter (user_a = 1,user_k = 3,user_s = 5)

    199:       DM             da
    200:       PetscInt       mx,xs,xe,gxs,gxe
    201:       PetscOffset    ixx,ixxdot,iff
    202:       PetscScalar    xx(0:1),xxdot(0:1),ff(0:1)

    204:       call TSGetDM(ts,da,ierr)
    205:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

    207: ! Get access to vector data
    208:       call VecGetArrayRead(X,xx,ixx,ierr)
    209:       call VecGetArrayRead(Xdot,xxdot,ixxdot,ierr)
    210:       call VecGetArray(F,ff,iff,ierr)

    212:       call FormIFunctionLocal(mx,xs,xe,gxs,gxe,                         &
    213:      &     xx(ixx),xxdot(ixxdot),ff(iff),                               &
    214:      &     user(user_a),user(user_k),user(user_s),ierr)

    216:       call VecRestoreArrayRead(X,xx,ixx,ierr)
    217:       call VecRestoreArrayRead(Xdot,xxdot,ixxdot,ierr)
    218:       call VecRestoreArray(F,ff,iff,ierr)
    219:       end subroutine

    221:       subroutine FormRHSFunctionLocal(mx,xs,xe,gxs,gxe,t,x,f,           &
    222:      &     a,k,s,ierr)
    223:       implicit none
    224:       PetscInt mx,xs,xe,gxs,gxe
    225:       PetscReal t
    226:       PetscScalar x(2,gxs:gxe),f(2,xs:xe)
    227:       PetscReal a(2),k(2),s(2)
    228:       PetscErrorCode ierr
    229:       PetscInt i,j
    230:       PetscReal hx,u0t(2)
    231:       PetscReal one,two,three,four,six,twelve
    232:       PetscReal half,third,twothird,sixth
    233:       PetscReal twelfth

    235:       one = 1.0
    236:       two = 2.0
    237:       three = 3.0
    238:       four = 4.0
    239:       six = 6.0
    240:       twelve = 12.0
    241:       hx = one / mx
    242: !     The Fortran standard only allows positive base for power functions; Nag compiler fails on this
    243:       u0t(1) = one - abs(sin(twelve*t))**four
    244:       u0t(2) = 0.0
    245:       half = one/two
    246:       third = one / three
    247:       twothird = two / three
    248:       sixth = one / six
    249:       twelfth = one / twelve
    250:       do 20 i = xs,xe
    251:          do 10 j = 1,2
    252:             if (i .eq. 1) then
    253:                f(j,i) = a(j)/hx*(third*u0t(j) + half*x(j,i) - x(j,i+1)  &
    254:      &              + sixth*x(j,i+2))
    255:             else if (i .eq. 2) then
    256:                f(j,i) = a(j)/hx*(-twelfth*u0t(j) + twothird*x(j,i-1)    &
    257:      &              - twothird*x(j,i+1) + twelfth*x(j,i+2))
    258:             else if (i .eq. mx-1) then
    259:                f(j,i) = a(j)/hx*(-sixth*x(j,i-2) + x(j,i-1)             &
    260:      &         - half*x(j,i) -third*x(j,i+1))
    261:             else if (i .eq. mx) then
    262:                f(j,i) = a(j)/hx*(-x(j,i) + x(j,i-1))
    263:             else
    264:                f(j,i) = a(j)/hx*(-twelfth*x(j,i-2)                      &
    265:      &              + twothird*x(j,i-1)                                 &
    266:      &              - twothird*x(j,i+1) + twelfth*x(j,i+2))
    267:             end if
    268:  10      continue
    269:  20   continue
    270:       end subroutine

    272:       subroutine FormRHSFunction(ts,t,X,F,user,ierr)
    273:       use petscts
    274:       implicit none

    276:       TS ts
    277:       PetscReal t
    278:       Vec X,F
    279:       PetscReal user(6)
    280:       PetscErrorCode ierr
    281:       integer user_a,user_k,user_s
    282:       parameter (user_a = 1,user_k = 3,user_s = 5)
    283:       DM             da
    284:       Vec            Xloc
    285:       PetscInt       mx,xs,xe,gxs,gxe
    286:       PetscOffset    ixx,iff
    287:       PetscScalar    xx(0:1),ff(0:1)

    289:       call TSGetDM(ts,da,ierr)
    290:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

    292: !     Scatter ghost points to local vector,using the 2-step process
    293: !        DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
    294: !     By placing code between these two statements, computations can be
    295: !     done while messages are in transition.
    296:       call DMGetLocalVector(da,Xloc,ierr)
    297:       call DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc,ierr)
    298:       call DMGlobalToLocalEnd(da,X,INSERT_VALUES,Xloc,ierr)

    300: ! Get access to vector data
    301:       call VecGetArrayRead(Xloc,xx,ixx,ierr)
    302:       call VecGetArray(F,ff,iff,ierr)

    304:       call FormRHSFunctionLocal(mx,xs,xe,gxs,gxe,                       &
    305:      &     t,xx(ixx),ff(iff),                                           &
    306:      &     user(user_a),user(user_k),user(user_s),ierr)

    308:       call VecRestoreArrayRead(Xloc,xx,ixx,ierr)
    309:       call VecRestoreArray(F,ff,iff,ierr)
    310:       call DMRestoreLocalVector(da,Xloc,ierr)
    311:       end subroutine

    313: ! ---------------------------------------------------------------------
    314: !
    315: !  IJacobian - Compute IJacobian = dF/dU + shift*dF/dUdot
    316: !
    317:       subroutine FormIJacobian(ts,t,X,Xdot,shift,J,Jpre,user,ierr)
    318:       use petscts
    319:       implicit none

    321:       TS ts
    322:       PetscReal t,shift
    323:       Vec X,Xdot
    324:       Mat J,Jpre
    325:       PetscReal user(6)
    326:       PetscErrorCode ierr
    327:       integer user_a,user_k,user_s
    328:       parameter (user_a = 0,user_k = 2,user_s = 4)

    330:       DM             da
    331:       PetscInt       mx,xs,xe,gxs,gxe
    332:       PetscInt       i,i1,row,col
    333:       PetscReal      k1,k2;
    334:       PetscScalar    val(4)

    336:       call TSGetDM(ts,da,ierr)
    337:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

    339:       i1 = 1
    340:       k1 = user(user_k+1)
    341:       k2 = user(user_k+2)
    342:       do 10 i = xs,xe
    343:          row = i-gxs
    344:          col = i-gxs
    345:          val(1) = shift + k1
    346:          val(2) = -k2
    347:          val(3) = -k1
    348:          val(4) = shift + k2
    349:          call MatSetValuesBlockedLocal(Jpre,i1,row,i1,col,val,          &
    350:      &        INSERT_VALUES,ierr)
    351:  10   continue
    352:       call MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY,ierr)
    353:       call MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY,ierr)
    354:       if (J /= Jpre) then
    355:          call MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY,ierr)
    356:          call MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY,ierr)
    357:       end if
    358:       end subroutine

    360:       subroutine FormInitialSolutionLocal(mx,xs,xe,gxs,gxe,x,a,k,s,ierr)
    361:       implicit none
    362:       PetscInt mx,xs,xe,gxs,gxe
    363:       PetscScalar x(2,xs:xe)
    364:       PetscReal a(2),k(2),s(2)
    365:       PetscErrorCode ierr

    367:       PetscInt i
    368:       PetscReal one,hx,r,ik
    369:       one = 1.0
    370:       hx = one / mx
    371:       do 10 i=xs,xe
    372:          r = i*hx
    373:          if (k(2) .ne. 0.0) then
    374:             ik = one/k(2)
    375:          else
    376:             ik = one
    377:          end if
    378:          x(1,i) = one + s(2)*r
    379:          x(2,i) = k(1)*ik*x(1,i) + s(2)*ik
    380:  10   continue
    381:       end subroutine

    383:       subroutine FormInitialSolution(ts,X,user,ierr)
    384:       use petscts
    385:       implicit none

    387:       TS ts
    388:       Vec X
    389:       PetscReal user(6)
    390:       PetscErrorCode ierr
    391:       integer user_a,user_k,user_s
    392:       parameter (user_a = 1,user_k = 3,user_s = 5)

    394:       DM             da
    395:       PetscInt       mx,xs,xe,gxs,gxe
    396:       PetscOffset    ixx
    397:       PetscScalar    xx(0:1)

    399:       call TSGetDM(ts,da,ierr)
    400:       call GetLayout(da,mx,xs,xe,gxs,gxe,ierr)

    402: ! Get access to vector data
    403:       call VecGetArray(X,xx,ixx,ierr)

    405:       call FormInitialSolutionLocal(mx,xs,xe,gxs,gxe,                       &
    406:      &     xx(ixx),user(user_a),user(user_k),user(user_s),ierr)

    408:       call VecRestoreArray(X,xx,ixx,ierr)
    409:       end subroutine

    411: !/*TEST
    412: !
    413: !    test:
    414: !      args: -da_grid_x 200 -ts_arkimex_type 4
    415: !      requires: !single
    416: !
    417: !TEST*/