SEMINAR

Distributed Computation of Numerical Solutions of Partial Differential Equations (PDEs) in Java

Department of Mathematics and Computer Science
Loyola University, New Orleans

ABSTRACT

Solving a partial differential equation requires a certain amount of computer resources, including memory, CPU power and system I/O. Most of today's computers are quite capable of providing sufficient amount of computing resources for solving many relatively small problems.

The amount of computing resources a computer is able to provide, however large it can be, is limited by the physics of electricity. Whereas the amount of computing resources required to solve a particular problem (PDE) is virtually unlimited. It is estimated that in order to model a 3-dimensional environment of small size with reasonable accuracy, about 800Gb of computer memory is needed. This is way beyond what most computers can provide today.

A simple alternative is to solve a large problem using multiple computers. I will discuss the distributed implementation of numerical methods for elliptic type PDEs (Laplace equation) and hyperbolic type PDEs (Euler equations), using asynchronous message passing. Issues such as shared variables and the use of semaphores will be discussed. A demo of a version of distributed implementation of a numerical method will be shown if multiple CPUs (PCs with JDK 2.0 installed) are available.

An algorithm needs to be implemented in a programming language before it can be used to solve problems on computers. I will provide an evaluation of programming languages based on criteria such as readability, writability and reliability, among other things. A set of language selection criteria will also be presented.

WHERE: TEC 251

WHEN(day): Friday, September 24th, 1999

WHEN(time): 2:00 PM

EVERYBODY IS INVITED