Isoefficiency Analysis of Parallel QMR-Like Iterative Methods and its Implications on Parallel Algorithm Design.

Abstract

A specific problem arising out of electrostatics is taken as an example to demonstrate the process of, firstly, transforming a physical problem into a mathematical model and, secondly, its numerical solution by generating a system of linear equations via finite difference approximations. The resulting nonsymmetric sparse linear system is solved by a class of iterative methods that is defined by taking the Quasi-Minimal Residual (QMR) method as a typical member. A performance model called isoefficiency concept is used to analyze the behavior of such methods implemented on parallel distributed memory computers with two-dimensional mesh topology. The isoefficiency concept is employed to compare two different mappings of data to processors as well as to give hints how QMR-like iterative methods should be designed with respect to parallel computing.