Actual source code: ex13f90.F90

  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: !

 24:   use ex13f90auxmodule

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

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

 40:   ! Fire up PETSc:
 41:   PetscCallA(PetscInitialize(ierr))

 43:   comm = PETSC_COMM_WORLD
 44:   PetscCallMPIA(MPI_Comm_rank(comm, rank, ierr))
 45:   PetscCallMPIA(MPI_Comm_size(comm, size, ierr))
 46:   if (rank == 0) then
 47:     write (*, *) 'Hi! We are solving van der Pol using ', size, ' processes.'
 48:     write (*, *) ' '
 49:     write (*, *) '  t     x1         x2'
 50:   end if

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

 66:   ! Get the BCs and create the DMDA
 67:   call get_boundary_cond(b_x, b_y, b_z)
 68:   PetscCallA(DMDACreate3d(comm, b_x, b_y, b_z, DMDA_STENCIL_STAR, igmax, jgmax, kgmax, PETSC_DECIDE, PETSC_DECIDE, PETSC_DECIDE, dof, stw, PETSC_NULL_INTEGER_ARRAY, PETSC_NULL_INTEGER_ARRAY, PETSC_NULL_INTEGER_ARRAY, SolScal, ierr))
 69:   PetscCallA(DMSetFromOptions(SolScal, ierr))
 70:   PetscCallA(DMSetUp(SolScal, ierr))

 72:   ! Set global coordinates, get a global and a local work vector
 73:   PetscCallA(DMDASetUniformCoordinates(SolScal, xgmin, xgmax, ygmin, ygmax, zgmin, zgmax, ierr))
 74:   PetscCallA(DMCreateLocalVector(SolScal, Lvec, ierr))

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

 94:   ! Get xmin,xmax etc. for the local grid
 95:   ! The "coords" local vector here is borrowed, so we shall not destroy it.
 96:   PetscCallA(DMGetCoordinatesLocal(SolScal, coords, ierr))
 97:   ! We need a new DM for coordinate stuff since PETSc supports unstructured grid
 98:   PetscCallA(DMGetCoordinateDM(SolScal, CoordDM, ierr))
 99:   ! petsc_to_local and local_to_petsc are convenience functions, see
100:   ! ex13f90auxmodule.F90.
101:   call petsc_to_local(CoordDM, coords, array, grid, ndim, stw)
102:   xmin = grid(1, 1, 1, 1)
103:   ymin = grid(2, 1, 1, 1)
104:   zmin = grid(3, 1, 1, 1)
105:   xmax = grid(1, imax, jmax, kmax)
106:   ymax = grid(2, imax, jmax, kmax)
107:   zmax = grid(3, imax, jmax, kmax)
108:   call local_to_petsc(CoordDM, coords, array, grid, ndim, stw)

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

114:   ! Set up the time-stepping
115:   t = 0.0
116:   tend = 100.0
117:   dt = 1e-3
118:   maxstep = ceiling((tend - t)/dt)
119:   ! Write output every second (of simulation-time)
120:   nscreen = int(1.0/dt) + 1

122:   ! Set initial condition
123:   PetscCallA(DMDAVecGetArray(SolScal, Lvec, array, ierr))
124:   array(0, :, :, :) = 0.5
125:   array(1, :, :, :) = 0.5
126:   PetscCallA(DMDAVecRestoreArray(SolScal, Lvec, array, ierr))

128:   ! Initial set-up finished.
129:   ! Time loop
130:   maxstep = 5
131:   do itime = 1, maxstep

133:     ! Communicate such that everyone has the correct values in ghost cells
134:     PetscCallA(DMLocalToLocalBegin(SolScal, Lvec, INSERT_VALUES, Lvec, ierr))
135:     PetscCallA(DMLocalToLocalEnd(SolScal, Lvec, INSERT_VALUES, Lvec, ierr))

137:     ! Get the old solution from the PETSc data structures
138:     call petsc_to_local(SolScal, Lvec, array, f, dof, stw)

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

144:     ! Write result to screen (if main process and it's time to)
145:     if (rank == 0 .and. mod(itime, nscreen) == 0) then
146:       write (*, 101) t, f(1, 1, 1, 1), f(2, 1, 1, 1)
147:     end if

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

153:   ! Deallocate and finalize
154:   PetscCallA(DMRestoreLocalVector(SolScal, Lvec, ierr))
155:   PetscCallA(DMDestroy(SolScal, ierr))
156:   deallocate (f)
157:   deallocate (grid)
158:   PetscCallA(PetscFinalize(ierr))

160:   ! Format for writing output to screen
161: 101 format(F5.1, 2F11.6)

163: end program main

165: !/*TEST
166: !
167: !   build:
168: !     requires: !complex
169: !     depends:  ex13f90aux.F90
170: !
171: !   test:
172: !     nsize: 4
173: !
174: !TEST*/