Open Access

ARTICLE

A RIM-based Time-domain Boundary Element Method for Three-Dimensional Non-homogeneousWave Propagations

by Liu Liqi¹, Wang Haitao¹

1 Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China.
2 Corresponding author. Tel.: +86 10 6279 7882; fax: +86 10 6279 7136; E-mail: wanght@tsinghua.edu.cn

Computer Modeling in Engineering & Sciences 2015, 109-110(4), 303-324. https://doi.org/10.3970/cmes.2015.109.303

Abstract

This paper presents a three-dimensional (3-D) boundary element method (BEM) scheme based on the Radial Integration Method (RIM) for wave propagation analysis of continuously non-homogeneous problems. The Kelvin fundamental solutions are adopted to derive the boundary-domain integral equation (BDIE). The RIM proposed by Gao (Engineering Analysis with Boundary Elements 2002; 26(10):905-916) is implemented to treat the domain integrals in the BDIE so that only boundary discretization is required. After boundary discretization, a set of second-order ordinary differential equations with respect to time variable are derived, which are solved using the Wilson-q method. Main advantages of the proposed method are that 1) it can treat wave propagations in non-homogeneous domains with only boundary mesh required, and that 2) coefficient matrices arising from the BEM are evaluated and stored only once so that solving large-scale problems with huge time steps is possible. In the numerical examples, the present method is tested in terms of accuracy, capacity to treat non-homogeneous problems and large-scale potentials.

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Keywords

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