Embedding a ``Tree-Code" on a MIMD parallel computer 
              using a domain decomposition paradigm. 


                              Abstract

  "Tree-codes" and ``Multigrid" methods are both hierarchical, recursive 
algorithms for solving vector field equations, faster than traditional methods.
If the methods are non-adaptive, then both Tree-codes and Multigrid methods
require identical parallel communication strategies since they share the same 
internal structure.

  This paper contains a description of Tree-codes followed by an overview of one
Tree-code in particular, namely the Greengard-Rokhlin Fast Multipole Method 
in 2 dimensions.  The parallel version of this method is then discussed at 
length with the presentation of two communication strategies; An "All-to-all" 
broadcast and a routine which enables neighbouring transputers to swap 
information in a predetermined sequence. 

  The computer used is the Meiko Computing Surface, a MIMD parallel computer 
employing T800 transputers running the CSTools communication harness using a
SPMD (Single Program, Multiple Data), domain decomposition paradigm. 

  The 3D versions of the communication algorithms have also been implemented
and are  simple extensions of the 2D routines.


Keywords: Fast Multipole Method, Multigrid, message passing.`

  Gavin J. Pringle
  Napier University
  Edinburgh
  EH14 1DJ
  SCOTLAND
  Tel : +44 31 455 4631
  Email : gavin@uk.ac.edinburgh.castle