1program 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! 23 24 use ex13f90auxmodule 25 26#include <petsc/finclude/petscdmda.h> 27 use petscdmda 28 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 39 40 ! Fire up PETSc: 41 PetscCallA(PetscInitialize(ierr)) 42 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 51 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 65 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)) 71 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)) 75 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)) 93 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) 109 110 ! 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. 113 114 ! 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) + 1 121 122 ! 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)) 127 128 ! Initial set-up finished. 129 ! Time loop 130 maxstep = 5 131 do itime = 1, maxstep 132 133 ! 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)) 136 137 ! Get the old solution from the PETSc data structures 138 call petsc_to_local(SolScal, Lvec, array, f, dof, stw) 139 140 ! 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 143 144 ! 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 148 149 ! Put our new solution in the PETSc data structures 150 call local_to_petsc(SolScal, Lvec, array, f, dof, stw) 151 end do 152 153 ! Deallocate and finalize 154 PetscCallA(DMRestoreLocalVector(SolScal, Lvec, ierr)) 155 PetscCallA(DMDestroy(SolScal, ierr)) 156 deallocate (f) 157 deallocate (grid) 158 PetscCallA(PetscFinalize(ierr)) 159 160 ! Format for writing output to screen 161101 format(F5.1, 2F11.6) 162 163end program main 164 165!/*TEST 166! 167! build: 168! requires: !complex 169! depends: ex13f90aux.F90 170! 171! test: 172! nsize: 4 173! 174!TEST*/ 175