Vectorization of algorithms for solving systems of elliptic difference equations
B.L. Buzbee · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1983
Today's fastest computers achieve their highest level of performance when processing vectors. Consequently, considerable effort has been spent in the past decade developing algorithms that can be expressed as operations on vectors. In this paper we define two types of vector architecture. We discuss the variation of performance that can occur on a vector processor as a function of algorithm and implementation, the consequences of this variation, and the performance of some basic operators on the two classes of vector architecture. We also discuss the performance of higher level operators, including some that should be used with caution. Using both basic and high level operators, we discuss vector implementation of techniques for solving systems of elliptic difference equations. Included are fast Poisson solvers and point, line, and conjugate gradient techniques.