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 elds: investigation of acaustic phenomena in aeronautics, electromagnetic application, migration in 3-D geophysical application, among many other areas. As shown in [2], Helmholtz equation is used in weather prediction at the Met O ce in UK. Ine ciency, that is the bottleneck in Numerical Weather Prediction, arise partly from solving of the Helmholtz equation. This study investigates the computationally e cient iterative 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 e cient method.