6.6 一个应用例子

例 6.6 图6.1的例子显示怎样在应用程序中使用网格定义和查询函数。一个偏微分方程，例如帕松等式，在规则域中解决。首先，进程将自己组织在二维结构中。每一进程然后在四个方向上（上，下，左，右）查询邻居的标识数。通过迭代方法解决数字问题，详细信息隐含在子程序relax中。

在每一松弛步中，每一进程在进程所拥有点上对解析格子函数计算新值。然后在交互进程的边缘上的值不得不同邻居进程相互交换。例如，交换子程序可以包含调用MPI_SEND（…, neigh_rank（1）,…），以发送被更新的值到左手邻居（I-1, j）。

integer ndims, num_neigh

logical reorder

parameter (ndims=2, num_neigh=4, reorder=.true.)

integer comm, comm_cart, dims (ndims）, neigh_def (ndims）, ierr

integer neigh_rank (num_neigh）, own_position (ndims）, i , j

logical periods (ndims）

real*8 u (0:101, 0:101), f (0:101, 0:101)

data dims / ndims * 0 /

comm = MPI_COMM_WORLD

C Set process grid size and periodicity

call MPI_DIMS_CREATE (comm, ndims, dims, ierr)

periods (1) = .TRUE.

periods (2) = .TRUE.

C 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_position, ierr)

C Look up the ranks for the neighbors, Own process coordinates are (i, j)。

C Neighbors are (I-1, j), (I, j+1), (I, j-1), (I, j+1)

I = own_position(1)

I = own_position(2)

neigh_def(1) = I-1

neigh_def(2) = j

call MPI_CART_RANK(comm_cart, neigh_def, neigh_rank(1), ierr)

neigh_def(1) = i+1

neigh_def(2) = j

call MPI_CART_RANK(comm_cart, neigh_def, neigh_rank(2), ierr)

neigh_def(1) = i

neigh_def(2) = j-1

call MPI_CART_RANK(comm_cart, neigh_def, neigh_rank(3), ierr)

neigh_def(1) = i

neigh_def(2) = j+1

call MPI_CART_RANK(comm_cart, neigh_def, neigh_rank(4), ierr)

C Initialize the grid functions and start the iteration

call init (u, f)

do 10 it = 1, 100

call relax (u, f)

C Exchange data with neighbor processes

call exchange (u, comm_cart, neigh_rank, num_neigh)

10 continue

call output (u)

end

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