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Coupling of boundary integral equation and finite element methods for transmission problems in acoustics

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Abstract

In this paper, we propose a coupling of finite element method (FEM) and boundary integral equation (BIE) method for solving acoustic transmission problems in two dimensions. The original transmission problem is firstly reduced to a nonlocal boundary value problem by introducing an artificial boundary and defining a transparent boundary condition from the relation between Dirichlet data and Neumann data on the artificial boundary. In this work, such relationship is described in terms of boundary integral operators. Then, essential mathematical analysis for the weak formulation corresponding to the nonlocal boundary value problem is discussed. Three different algorithms are utilized for the solution of boundary integral equations to be involved in the computational formulations, and numerical results are presented to demonstrate the efficiency and accuracy of the schemes.

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Acknowledgments

The authors are grateful for the useful comments provided by anonymous referees. They also would like to thank Prof. Liwei Xu at the University of Electronic Science and Technology of China in China and Dr. Tao Yin at the University of Grenoble Alpes in France for their helpful suggestions.

Funding

The work of H. Geng is partially supported by the National Natural Science Foundation of China (Nos. 11701526, 11501063, 11701527), the Foundation of Henan Educational Committee (18A110035), and the Doctor Scientific Research Fund of Zhengzhou University of Light Industry. Research of Z. Xu is partially supported by the National Natural Science Foundation of China (No. 11626223).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, 450002, China

    Hongrui Geng & Zhenhua Xu

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  1. Hongrui Geng
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  2. Zhenhua Xu
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Correspondence to Hongrui Geng.

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Geng, H., Xu, Z. Coupling of boundary integral equation and finite element methods for transmission problems in acoustics. Numer Algor 82, 479–501 (2019). https://doi.org/10.1007/s11075-018-0610-3

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