*
* README 9.1 92/07/01 17:54:55 
*

examples/fortran/gauss


This program illustrates how a program would pass messages  to exchange
information during each cycle of an iterative procedure.  Specifically, 
the program solves LaPlace's Equation in two dimensions with fixed 
boundary conditions using a finite difference approximation and the 
iterative Gauss-Seidel method.  

The program illustrates the domain decomposition method.  It sets up a
rectangular grid over the domain and assigns portions of the domain 
to different nodes.  In second order, each iteration cycle 
consists of starting with some guessed value and then replacing 
the value at each grid point with the average value of its nearest 
neighbors. 

The grid is represented as a two-dimensional array and assigned in
vertical strips to each node. A node with an internal strip shares 
boundaries with two other nodes, a left node and a right node. 
When it calculates a value for a point on its boundaries, it needs those
nearest neighbor values from those left and right nodes. Those 
values change with each iteration.  The solution is for each node 
to maintain a "shadow" buffer.  Before each iteration cycle, a node 
receives values from the boundaries of adjacent nodes into its shadow
buffer and sends the values of its own boundaries to the shadow buffers 
of its neighbor nodes.

The rectangular grid for this example is a 16 x 16 array.  If you
partition this among four nodes, each nodes gets four columns.  
It doesn't make sense to partition it over more that 16  nodes, and the 
program won't allow you to do it.  If you partition it over eight nodes,
each node has no interior columns.  The program best illustrates the 
technique with a four-node cube.