Group explicit complete method vs. standard explicit method on mimd parallel systems

Abstract

The explicit methods although very suitable for parallel processing always deny us reasonable accuracy and some stability; on the other hand, the implicit schemes offer stability, but the exploitation of these methods for parallel processing may be difficult and possibly inefficient. This paper investigates the applicability of a new class of group explicit methods to parallel processing, the experimental vehicle being a non-linear parabolic p.d.e. of second order. The method is briefly presented and then work is concentrated on the selection of a suitable algorithm which can effectively use the processing power of a MIMD parallel architecture and at the same time is stable and can produce highly accurate results.