Multiple sequential staging of tasks: a new approach to parallel computations

Abstract

Developing an ecient algorithm for solving a large linear system in a parallel computing environment is the major problem associated with the application of parallel processing to the numerical solution of large-scale engineering problems. This paper presents a new algorithm called Multiple Sequential Staging of Tasks (MSST) to speed up the solution of a large linear system. The technique of Sequential Staging of Tasks (SST) is a highly ecient approach to the parallel solution of a large linear system, but it is not suitable for middle-and large-scale parallel computers due to the idle periods of processors. The MSST technique partitions processors into groups and makes each group start its operation from a dierent row of a large linear system to remove the idle period. Therefore, MSST can be performed eectively on middle-and largescale parallel computers and achieves a higher speed-up. Numerical results were obtained from computer experiments performed with a numerical solution method of the Poisson equation on a Dawning-1000 supercomputer (a distributed-memory MIMD architecture). The parallel speed-up is satisfactory.