Miaomiao Yang, Wentao Ma, Yongbin Ge^*

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 25-54, 2021, DOI:10.32604/cmes.2021.012575

Abstract In this paper, Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation. First of all, the interpolation basis function is applied to treat the spatial variables and their partial derivatives, and the collocation method for solving the second order differential equations is established. Secondly, the differential equations on a given test node. Finally, based on three kinds of test nodes, numerical experiments show that the present scheme can not only calculate the high wave numbers problems, but also calculate the variable wave numbers problems. In addition, the algorithm has… More >

H.B. Chen¹, D.J. Fu¹, P.Q. Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 85-98, 2007, DOI: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… More >