The Romberg-Like Parallel Numerical Integration on a Cluster System

Abstract

In this paper, an approximation of a double integral over a triangular region using a Romberg-like buffered extrapolation technique is considered. A master-worker algorithm organization was developed and implemented using the Message Passing Interface (MPI) paradigm which aims at computing the function f(x,y) at the nodes of the triangle by the worker processes in parallel. The algorithm is implemented on a Sun Cluster consisting of 8xX2200 Sun Fire dual core processors using Sun's OpenMPI message passing environment. Here, the Sun Studio Performance Analyzer is utilized to display the runtime behavior of the processes and CPU's involved in the computations. A simple model is developed to predict the speed-up factor.