** Example**
The example in
Figures 18
-An Application Example
shows how the grid definition and
inquiry functions can be used in an application program. A partial
differential equation, for instance the Poisson equation, is to be
solved on a rectangular domain.
First, the processes organize themselves in a two-dimensional
structure. Each process then inquires about the ranks of its
neighbors in the four directions (up, down, right, left).
The numerical problem is solved by an iterative method, the details
of which are hidden in the subroutine `relax`.

In each relaxation step each process computes new values for the solution grid
function at the points `u(1:100,1:100)`
owned by the process. Then the values at inter-process
boundaries have to be exchanged with neighboring processes.
For example, the
newly calculated values in `u(1,1:100)`
must be sent into the halo cells `u(101,1:100)`
of the left-hand neighbor with coordinates `(own_coord(1)-1,own_coord(2))`.

INTEGER ndims, num_neigh LOGICAL reorder PARAMETER (ndims=2, num_neigh=4, reorder=.true.) INTEGER comm, comm_cart, dims(ndims), ierr INTEGER neigh_rank(num_neigh), own_coords(ndims), i, j, it LOGICAL periods(ndims) REAL u(0:101,0:101), f(0:101,0:101) DATA dims / ndims * 0 / comm = MPI_COMM_WORLD ! Set process grid size and periodicity CALL MPI_DIMS_CREATE(comm, ndims, dims, ierr) periods(1) = .TRUE. periods(2) = .TRUE. ! Create a grid structure in WORLD group and inquire about own position CALL MPI_CART_CREATE (comm, ndims, dims, periods, reorder, & comm_cart, ierr) CALL MPI_CART_GET (comm_cart, ndims, dims, periods, own_coords, ierr) i = own_coords(1) j = own_coords(2) ! Look up the ranks for the neighbors. Own process coordinates are (i,j). ! Neighbors are (i-1,j), (i+1,j), (i,j-1), (i,j+1) modulo (dims(1),dims(2)) CALL MPI_CART_SHIFT (comm_cart, 0,1, neigh_rank(1),neigh_rank(2), ierr) CALL MPI_CART_SHIFT (comm_cart, 1,1, neigh_rank(3),neigh_rank(4), ierr) ! Initialize the grid functions and start the iteration CALL init (u, f) DO it=1,100 CALL relax (u, f) ! Exchange data with neighbor processes CALL exchange (u, comm_cart, neigh_rank, num_neigh) END DO CALL output (u)

SUBROUTINE exchange (u, comm_cart, neigh_rank, num_neigh) REAL u(0:101,0:101) INTEGER comm_cart, num_neigh, neigh_rank(num_neigh) REAL sndbuf(100,num_neigh), rcvbuf(100,num_neigh) INTEGER ierr sndbuf(1:100,1) = u( 1,1:100) sndbuf(1:100,2) = u(100,1:100) sndbuf(1:100,3) = u(1:100, 1) sndbuf(1:100,4) = u(1:100,100) CALL MPI_NEIGHBOR_ALLTOALL (sndbuf, 100, MPI_REAL, rcvbuf, 100, MPI_REAL, & comm_cart, ierr) ! instead of ! DO i=1,num_neigh ! CALL MPI_IRECV(rcvbuf(1,i),100,MPI_REAL,neigh_rank(i),...,rq(2*i-1),& ! ierr) ! CALL MPI_ISEND(sndbuf(1,i),100,MPI_REAL,neigh_rank(i),...,rq(2*i ),& ! ierr) ! END DO ! CALL MPI_WAITALL (2*num_neigh, rq, statuses, ierr) u( 0,1:100) = rcvbuf(1:100,1) u(101,1:100) = rcvbuf(1:100,2) u(1:100, 0) = rcvbuf(1:100,3) u(1:100,101) = rcvbuf(1:100,4) END

Communication routine with sparse neighborhood all-to-all-w and without local data copying.

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