On the Computationally Efficient Numerical Solution to the Helmholtz Equation

Abstract

Named after Hermann L. F. von Helmholtz (1821-1894), Helmholtz equation has obtained application in many fields: investigation of acaustic phenomena in aeronautics, electromagnetic application, migration in 3-D geophysical ap plication, among many other areas. As shown in [2], Helmholtz equation is used in weather prediction at the Met Office in UK. Inefficiency, that is the bottleneck in Numerical Weather Prediction, arise partly from solving of the Helmholtz equation. This study investigates the computationally efficient it erative method for solving the Helmholtz equation. We begin by analysing the condition for stability of Jacobi Iterative method using Von Neumann method. Finally, we conclude that Bi-Conjugate Gradient Stabilised Method is the most computationally efficient method.