Time-harmonic acoustic wave propagation is governed by the Helmholtz equation. The Helmholtz equation is an elliptic partial differential equation that governs some important physical phenomena. These include the potential in time harmonic acoustic and electromagnetic fields, acoustic wave scattering, noise reduction in silencers, water wave propagation, membrane vibration and radar scattering. The two-dimensional Helmholtz equation is described by, (k{sup}2+Δ)Φ(x,y)= -f(x,y) (1) where k is the wave number defined as k=ω/c, ω is angular velocity, c is speed of sound in the medium and f(x,y) is a prescribed source function. Over the past few years, intensive research has been done to develop efficient numerical methods for solving the Helmholtz equation using different approaches such as the finite difference method [1], the boundary element method [2], the finite element method [3] and the spectral element method [4]. In this paper, we implemented and compared two different fourth-order accurate methods based on compact finite difference method (CFDM) and finite element method (FEM). Comparison is done in terms of accuracy, performance in high wave numbers and computational cost.
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