Solving PDEs on loosely-coupled parallel processors

Partial differential equations (PDEs) account for a large part of scientific computing. As a special domain, they have a number of features which makes their solution on parallel computers particularly attractive. One is the highly-ordered structure of most solution algorithms; there is a regular pattern of memory access. Another is the wide range of solution algorithms from which to choose. Loosely-coupled parallel processors, using a message passing interprocessor communication mechanism, appear to match the data communication requirements of algorithms for PDEs. However, there are many unanswered questions: What is the best communication topology? How fast should the communication be relative to the floating-point speed? How much memory should each node have? The answers to these questions depend on the algorithms chosen. In this paper, we will look at three different classes of algorithms for PDEs and discuss their implications. From these results, we can make recommendations about the design of the next generation of these parallel computers.