Array Access and Performance Regarding Numerical Algorithms

Abstract

Arrays are an important data structure in the solution of many numerical problems. In this study, the classical Poisson equation in two dimensions is used to gain insight in the consequences of the actual implementation and various possible compiler options for the performance: what is the optimal (fastest) solution? The equation is solved using a straightforward algorithm for a wide range of grid sizes to examine the effect of the memory management. The implementations include explicit loops and array operations, as well as parallellisation via OpenMP. Some general conclusions are drawn with respect to achieving good or optimal performance.