Cluster Computation in Maple

Based on software developed at RISC in Linz (Austria) we illustrate several uses of the Beowulf Cluster being run out of a Maple session.

1.  The High Performance Computing Group at SFU has recently acquired a 192-processor Beowulf cluster, Bugaboo, running 96 2-way 1.2 Gigahertz AMD Athlon processors, is a world class cluster capable of performing 144.6 billion operations per second---good enough to rank 465 on the top 500 list, One of the tools we are using to harness this computational power is the Distributed Maple package, written  by Wolfgang Schreiner of the University of Linz, Austria. Distributed Maple provides a simple yet powerful interface for scheduling and executing Maple commands in parallel across a network, making it possible to conduct high-level mathematical research in a powerful computational environment.

2.  In our first demo, we survey Distributed Maple's interface and try out some examples on the Bugaboo cluster. These simple examples---parallel summation, factorization, and matrix multiplication---demonstrate in real-time the advantages of (symbolic) parallel computation. The Maple worksheet for the first demo is available here.

3.  Our second demo shows ongoing research that illustrates graphically the use of the Beowulf cluster for numerical optimization. The standard-bearers in numerical optimization have been quasi-Newton methods, which use gradient and function evaluations to direct the search for a minimum; however, the gradient is often quite expensive to calculate. With the increased power of parallel environments, there has been renewed interest in Generalized Pattern Search methods for optimization, which use only function evaluations to direct the optimization process. The primary advantages of these methods are that they can be easily parallelized by splitting the function evaluations among processes, and are less sensitive to `noise' that often leads to inaccurate gradient evaluations.

This demo illustrates the ability to run parallel function evaluations over the Beowulf cluster. Each example is an animation of the function plot, with the function evaluations plotted as points; the colors of the plot points identify which processor is used in the function evaluation. The Maple worksheet for the second demo is available here and here.

Given the strong Computer Algebra Group at CECM, it was natural to start with Maple. Plans are to enhance these tools and to provide similar functionality for MatLab in the next few months, here and within WestGrid. This includes integrating MapleNet.

Parallel Maple Team:
Herre Wiersma - - CECM and CoLab RA
Mason Macklem - - CECM and CoLab RA