Parallel algorithms for solving certain elliptic boundary value problems

Abstract

The results given so far, concerning the acceleration of computation processes involved in solving elliptic partial differential equations, were achieved by designing fast algorithms for serial computers. Applying parallel processing methods is another effective and yet very natural way of accelerating the computation. Multiplying the processors in a parallel computer system makes it possible to design new schemes for the organization of computation. Here the main advantage, compared with the classical serial processing model, is that operations of the computational process can be performed simultaneously on different processor units. Another advantage is the improved reliability, because a failure in one or several processors does not necessarily result in breaking the computation. Parallel computers often enable their configuration to be adapted to suit best the character of the problem to be solved. Modern trends in microelectronics also find their application in the domain of parallel processing; the latest hardware components developed on the basis of VLSI (Very Large Scale Integration) and WSI (Wafer Scale Integration) technologies are advantageously used in parallel computers. Recent examples are the massively parallel computer systems Connection Machine and MasPar with thousands of processors based on VLSI technology.