Date: 2021-03-03T22:27:03+00:00

Actual source code: ex13f90.F90
petsc-3.14.5 2021-03-03
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      1: program main
      2: !
      3: ! This example intends to show how DMDA is used to solve a PDE on a decomposed
      4: ! domain. The equation we are solving is not a PDE, but a toy example: van der
      5: ! Pol's 2-variable ODE duplicated onto a 3D grid:
      6: ! dx/dt = y
      7: ! dy/dt = mu(1-x**2)y - x
      8: !
      9: ! So we are solving the same equation on all grid points, with no spatial
     10: ! dependencies. Still we tell PETSc to communicate (stencil width >0) so we
     11: ! have communication between different parts of the domain.
     12: !
     13: ! The example is structured so that one can replace the RHS function and
     14: ! the forw_euler routine with a suitable RHS and a suitable time-integration
     15: ! scheme and make little or no modifications to the DMDA parts. In particular,
     16: ! the "inner" parts of the RHS and time-integration do not "know about" the
     17: ! decomposed domain.
     18: !
     19: !     See:     http://dx.doi.org/10.6084/m9.figshare.1368581
     20: !
     21: !     Contributed by Aasmund Ervik (asmunder at pvv.org)
     22: !

     25:   use ex13f90aux

     27: #include <petsc/finclude/petscdmda.h>
     28:   use petscdmda

     30:   PetscErrorCode   ierr
     31:   PetscMPIInt      rank,size
     32:   MPI_Comm         comm
     33:   Vec              Lvec,coords
     34:   DM               SolScal,CoordDM
     35:   DMBoundaryType b_x,b_y,b_z
     36:   PetscReal, pointer :: array(:,:,:,:)
     37:   PetscReal :: t,tend,dt,xmin,xmax,ymin,ymax,zmin,zmax,xgmin,xgmax,ygmin,ygmax,zgmin,zgmax
     38:   PetscReal, allocatable :: f(:,:,:,:), grid(:,:,:,:)
     39:   PetscInt :: i,j,k,igmax,jgmax,kgmax,ib1,ibn,jb1,jbn,kb1,kbn,imax,jmax,kmax,itime,maxstep,nscreen,dof,stw,ndim

     41:   ! Fire up PETSc:
     42:   call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
     43:   if (ierr .ne. 0) then
     44:     print*,'Unable to initialize PETSc'
     45:     stop
     46:   endif
     47:   comm = PETSC_COMM_WORLD
     48:   call MPI_Comm_rank(comm,rank,ierr);CHKERRA(ierr)
     49:   call MPI_Comm_size(comm,size,ierr);CHKERRA(ierr)
     50:   if (rank == 0) then
     51:     write(*,*) 'Hi! We are solving van der Pol using ',size,' processes.'
     52:     write(*,*) ' '
     53:     write(*,*) '  t     x1         x2'
     54:   endif

     56:   ! Set up the global grid
     57:   igmax = 50
     58:   jgmax = 50
     59:   kgmax = 50
     60:   xgmin = 0.0
     61:   ygmin = 0.0
     62:   zgmin = 0.0
     63:   xgmax = 1.0
     64:   ygmax = 1.0
     65:   zgmax = 1.0
     66:   stw = 1 ! stencil width
     67:   dof = 2 ! number of variables in this DA
     68:   ndim = 3 ! 3D code

     70:   ! Get the BCs and create the DMDA
     71:   call get_boundary_cond(b_x,b_y,b_z);CHKERRA(ierr)
     72:   call DMDACreate3d(comm,b_x,b_y,b_z,DMDA_STENCIL_STAR,igmax,jgmax,kgmax,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,dof,stw,  &
     73:                     PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,SolScal,ierr);CHKERRA(ierr)
     74:   call DMSetFromOptions(SolScal,ierr);CHKERRA(ierr)
     75:   call DMSetUp(SolScal,ierr);CHKERRA(ierr)

     77:   ! Set global coordinates, get a global and a local work vector
     78:   call DMDASetUniformCoordinates(SolScal,xgmin,xgmax,ygmin,ygmax,zgmin,zgmax,ierr);CHKERRA(ierr)
     79:   call DMCreateLocalVector(SolScal,Lvec,ierr);CHKERRA(ierr)

     81:   ! Get ib1,imax,ibn etc. of the local grid.
     82:   ! Our convention is:
     83:   ! the first local ghost cell is ib1
     84:   ! the first local       cell is 1
     85:   ! the last  local       cell is imax
     86:   ! the last  local ghost cell is ibn.
     87:   !
     88:   ! i,j,k must be in this call, but are not used
     89:   call DMDAGetCorners(SolScal,i,j,k,imax,jmax,kmax,ierr);CHKERRA(ierr)
     90:   ib1=1-stw
     91:   jb1=1-stw
     92:   kb1=1-stw
     93:   ibn=imax+stw
     94:   jbn=jmax+stw
     95:   kbn=kmax+stw
     96:   allocate(f(dof,ib1:ibn,jb1:jbn,kb1:kbn))
     97:   allocate(grid(ndim,ib1:ibn,jb1:jbn,kb1:kbn))

     99:   ! Get xmin,xmax etc. for the local grid
    100:   ! The "coords" local vector here is borrowed, so we shall not destroy it.
    101:   call DMGetCoordinatesLocal(SolScal,coords,ierr);CHKERRA(ierr)
    102:   ! We need a new DM for coordinate stuff since PETSc supports unstructured grid
    103:   call DMGetCoordinateDM(SolScal,CoordDM,ierr);CHKERRA(ierr)
    104:   ! petsc_to_local and local_to_petsc are convenience functions, see
    105:   ! ex13f90aux.F90.
    106:   call petsc_to_local(CoordDM,coords,array,grid,ndim,stw);CHKERRA(ierr)
    107:   xmin=grid(1,1,1,1)
    108:   ymin=grid(2,1,1,1)
    109:   zmin=grid(3,1,1,1)
    110:   xmax=grid(1,imax,jmax,kmax)
    111:   ymax=grid(2,imax,jmax,kmax)
    112:   zmax=grid(3,imax,jmax,kmax)
    113:   call local_to_petsc(CoordDM,coords,array,grid,ndim,stw);CHKERRA(ierr)

    115:   ! Note that we never use xmin,xmax in this example, but the preceding way of
    116:   ! getting the local xmin,xmax etc. from PETSc for a structured uniform grid
    117:   ! is not documented in any other examples I could find.

    119:   ! Set up the time-stepping
    120:   t = 0.0
    121:   tend = 100.0
    122:   dt = 1e-3
    123:   maxstep=ceiling((tend-t)/dt)
    124:   ! Write output every second (of simulation-time)
    125:   nscreen = int(1.0/dt)+1

    127:   ! Set initial condition
    128:   call DMDAVecGetArrayF90(SolScal,Lvec,array,ierr);CHKERRA(ierr)
    129:   array(0,:,:,:) = 0.5
    130:   array(1,:,:,:) = 0.5
    131:   call DMDAVecRestoreArrayF90(SolScal,Lvec,array,ierr);CHKERRA(ierr)

    133:   ! Initial set-up finished.
    134:   ! Time loop
    135:   maxstep = 5
    136:   do itime=1,maxstep

    138:     ! Communicate such that everyone has the correct values in ghost cells
    139:     call DMLocalToLocalBegin(SolScal,Lvec,INSERT_VALUES,Lvec,ierr);CHKERRA(ierr)
    140:     call DMLocalToLocalEnd(SolScal,Lvec,INSERT_VALUES,Lvec,ierr);CHKERRA(ierr)

    142:     ! Get the old solution from the PETSc data structures
    143:     call petsc_to_local(SolScal,Lvec,array,f,dof,stw);CHKERRA(ierr)

    145:     ! Do the time step
    146:     call forw_euler(t,dt,ib1,ibn,jb1,jbn,kb1,kbn,imax,jmax,kmax,dof,f,dfdt_vdp)
    147:     t=t+dt

    149:     ! Write result to screen (if main process and it's time to)
    150:     if (rank == 0 .and. mod(itime,nscreen) == 0) then
    151:       write(*,101) t,f(1,1,1,1),f(2,1,1,1)
    152:     endif

    154:     ! Put our new solution in the PETSc data structures
    155:     call local_to_petsc(SolScal,Lvec,array,f,dof,stw)
    156:   end do

    158:   ! Deallocate and finalize
    159:   call DMRestoreLocalVector(SolScal,Lvec,ierr);CHKERRA(ierr)
    160:   call DMDestroy(SolScal,ierr);CHKERRA(ierr)
    161:   deallocate(f)
    162:   deallocate(grid)
    163:   call PetscFinalize(ierr)

    165:   ! Format for writing output to screen
    166: 101 format(F5.1,2F11.6)

    168: end program main

    170: !/*TEST
    171: !
    172: !   build:
    173: !     requires: !complex
    174: !     depends:  ex13f90aux.F90
    175: !
    176: !   test:
    177: !     nsize: 4
    178: !
    179: !TEST*/