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 ex13f90aux 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 call PetscInitialize(PETSC_NULL_CHARACTER,ierr) 42 if (ierr .ne. 0) then 43 print*,'Unable to initialize PETSc' 44 stop 45 endif 46 comm = PETSC_COMM_WORLD 47 call MPI_Comm_rank(comm,rank,ierr);CHKERRA(ierr) 48 call MPI_Comm_size(comm,size,ierr);CHKERRA(ierr) 49 if (rank == 0) then 50 write(*,*) 'Hi! We are solving van der Pol using ',size,' processes.' 51 write(*,*) ' ' 52 write(*,*) ' t x1 x2' 53 endif 54 55 ! Set up the global grid 56 igmax = 50 57 jgmax = 50 58 kgmax = 50 59 xgmin = 0.0 60 ygmin = 0.0 61 zgmin = 0.0 62 xgmax = 1.0 63 ygmax = 1.0 64 zgmax = 1.0 65 stw = 1 ! stencil width 66 dof = 2 ! number of variables in this DA 67 ndim = 3 ! 3D code 68 69 ! Get the BCs and create the DMDA 70 call get_boundary_cond(b_x,b_y,b_z);CHKERRA(ierr) 71 call DMDACreate3d(comm,b_x,b_y,b_z,DMDA_STENCIL_STAR,igmax,jgmax,kgmax,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,dof,stw, & 72 PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,SolScal,ierr);CHKERRA(ierr) 73 call DMSetFromOptions(SolScal,ierr);CHKERRA(ierr) 74 call DMSetUp(SolScal,ierr);CHKERRA(ierr) 75 76 ! Set global coordinates, get a global and a local work vector 77 call DMDASetUniformCoordinates(SolScal,xgmin,xgmax,ygmin,ygmax,zgmin,zgmax,ierr);CHKERRA(ierr) 78 call DMCreateLocalVector(SolScal,Lvec,ierr);CHKERRA(ierr) 79 80 ! Get ib1,imax,ibn etc. of the local grid. 81 ! Our convention is: 82 ! the first local ghost cell is ib1 83 ! the first local cell is 1 84 ! the last local cell is imax 85 ! the last local ghost cell is ibn. 86 ! 87 ! i,j,k must be in this call, but are not used 88 call DMDAGetCorners(SolScal,i,j,k,imax,jmax,kmax,ierr);CHKERRA(ierr) 89 ib1=1-stw 90 jb1=1-stw 91 kb1=1-stw 92 ibn=imax+stw 93 jbn=jmax+stw 94 kbn=kmax+stw 95 allocate(f(dof,ib1:ibn,jb1:jbn,kb1:kbn)) 96 allocate(grid(ndim,ib1:ibn,jb1:jbn,kb1:kbn)) 97 98 ! Get xmin,xmax etc. for the local grid 99 ! The "coords" local vector here is borrowed, so we shall not destroy it. 100 call DMGetCoordinatesLocal(SolScal,coords,ierr);CHKERRA(ierr) 101 ! We need a new DM for coordinate stuff since PETSc supports unstructured grid 102 call DMGetCoordinateDM(SolScal,CoordDM,ierr);CHKERRA(ierr) 103 ! petsc_to_local and local_to_petsc are convenience functions, see 104 ! ex13f90aux.F90. 105 call petsc_to_local(CoordDM,coords,array,grid,ndim,stw);CHKERRA(ierr) 106 xmin=grid(1,1,1,1) 107 ymin=grid(2,1,1,1) 108 zmin=grid(3,1,1,1) 109 xmax=grid(1,imax,jmax,kmax) 110 ymax=grid(2,imax,jmax,kmax) 111 zmax=grid(3,imax,jmax,kmax) 112 call local_to_petsc(CoordDM,coords,array,grid,ndim,stw);CHKERRA(ierr) 113 114 ! Note that we never use xmin,xmax in this example, but the preceding way of 115 ! getting the local xmin,xmax etc. from PETSc for a structured uniform grid 116 ! is not documented in any other examples I could find. 117 118 ! Set up the time-stepping 119 t = 0.0 120 tend = 100.0 121 dt = 1e-3 122 maxstep=ceiling((tend-t)/dt) 123 ! Write output every second (of simulation-time) 124 nscreen = int(1.0/dt)+1 125 126 ! Set initial condition 127 call DMDAVecGetArrayF90(SolScal,Lvec,array,ierr);CHKERRA(ierr) 128 array(0,:,:,:) = 0.5 129 array(1,:,:,:) = 0.5 130 call DMDAVecRestoreArrayF90(SolScal,Lvec,array,ierr);CHKERRA(ierr) 131 132 ! Initial set-up finished. 133 ! Time loop 134 maxstep = 5 135 do itime=1,maxstep 136 137 ! Communicate such that everyone has the correct values in ghost cells 138 call DMLocalToLocalBegin(SolScal,Lvec,INSERT_VALUES,Lvec,ierr);CHKERRA(ierr) 139 call DMLocalToLocalEnd(SolScal,Lvec,INSERT_VALUES,Lvec,ierr);CHKERRA(ierr) 140 141 ! Get the old solution from the PETSc data structures 142 call petsc_to_local(SolScal,Lvec,array,f,dof,stw);CHKERRA(ierr) 143 144 ! Do the time step 145 call forw_euler(t,dt,ib1,ibn,jb1,jbn,kb1,kbn,imax,jmax,kmax,dof,f,dfdt_vdp) 146 t=t+dt 147 148 ! Write result to screen (if main process and it's time to) 149 if (rank == 0 .and. mod(itime,nscreen) == 0) then 150 write(*,101) t,f(1,1,1,1),f(2,1,1,1) 151 endif 152 153 ! Put our new solution in the PETSc data structures 154 call local_to_petsc(SolScal,Lvec,array,f,dof,stw) 155 end do 156 157 ! Deallocate and finalize 158 call DMRestoreLocalVector(SolScal,Lvec,ierr);CHKERRA(ierr) 159 call DMDestroy(SolScal,ierr);CHKERRA(ierr) 160 deallocate(f) 161 deallocate(grid) 162 call PetscFinalize(ierr) 163 164 ! Format for writing output to screen 165101 format(F5.1,2F11.6) 166 167end program main 168 169!/*TEST 170! 171! build: 172! requires: !complex 173! depends: ex13f90aux.F90 174! 175! test: 176! nsize: 4 177! 178!TEST*/ 179