Open Access

ARTICLE

An Investigation of Wave Propagation with High Wave Numbers via the Regularized LBIEM

H.B. Chen¹, D.J. Fu¹, P.Q. Zhang¹

1 CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui230026, P.R. China. Email: hbchen@ustc.edu.cn

Computer Modeling in Engineering & Sciences 2007, 20(2), 85-98. https://doi.org/10.3970/cmes.2007.020.085

Abstract

Researches today show that, both approximation and dispersion errors are encountered by classical Galerkin FEM solutions for Helmholtz equation governing the harmonic wave propagation, which leads to numerical inaccuracies especially for high wave number cases. In this paper, Local Boundary Integral Equation Method (LBIEM) is firstly implemented to solve the boundary value problem of Helmholtz equation. Then the regularized LBIE is proposed to overcome the singularities of the boundary integrals in the LBIEM. Owing to the advantages of the Moving Least Square Approximation (MLSA), the frequency-dependent basis functions modified by the harmonic wave propagation solutions are easily adopted instead of the normal monomial basis functions. A plane harmonic wave propagating case is examined in the numerical tests. Computational results show that excellent numerical accuracies can be obtained when the regularized formulation and the modified basis functions are adopted, even though the wave numbers of Helmholtz equation are high.

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Keywords

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