Parallel extrapolation methods for computational fluid dynamics

Iterative solution methods for large, sparse linear systems of equations usually require significantly less time and memory than direct methods, and so are important in solving the systems which often arise in computational fluid dynamics. There are a number of eztrapolation algorithms which have been closely studied in the past as methods of accelerating convergence of iterative processes [3]. Usually it has been stressed that these are very general, can achieve quadratic convergence for non-linear problems and require no knowledge of the way in which the sequence to be extrapolated is generated. But extrapolation techniques also have obvious application in parallel computing, and this has not been widely recognized in the literature. This paper explains and develops several parallel extrapolation methods and compares their performance using a test problem of Laplace type.