A stable high-order absorbing boundary based on continued fraction for scalar wave propagation in 2D and 3D unbounded layers

Huifang Li (College of Architecture and Civil Engineering, Beijing University of Technology, Beijing, China)
Mi Zhao (College of Architecture and Civil Engineering, Beijing University of Technology, Beijing, China)
Lihua Wu (College of Architecture and Civil Engineering, Beijing University of Technology, Beijing, China)
Piguang Wang (College of Architecture and Civil Engineering, Beijing University of Technology, Beijing, China)
Xiuli Du (College of Architecture and Civil Engineering, Beijing University of Technology, Beijing, China)

Engineering Computations

ISSN: 0264-4401

Publication date: 12 August 2019

Abstract

Purpose

The purpose of this paper is to propose a stable high-order absorbing boundary condition (ABC) based on new continued fraction for scalar wave propagation in 2D and 3D unbounded layers.

Design/methodology/approach

The ABC is obtained based on continued fraction (CF) expansion of the frequency-domain dynamic stiffness coefficient (DtN kernel) on the artificial boundary of a truncated infinite domain. The CF which has been used to the thin layer method in [69] will be applied to the DtN method to develop a time-domain high-order ABC for the transient scalar wave propagation in 2D. Furthermore, a new stable composite-CF is proposed in this study for 3D unbounded layers by nesting the above CF for 2D layer and another CF.

Findings

The ABS has been transformed from frequency to time domain by using the auxiliary variable technique. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the ABC-FEM coupled system is discussed and cured.

Originality/value

This manuscript establishes a stable high-order time-domain ABC for the scalar wave equation in 2D and 3D unbounded layers, which is based on the new continued fraction. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the coupled system is discussed and cured.

Keywords

Acknowledgements

This work is supported by the National Basic Research Program of China (2015CB057902) and the National Natural Science Foundation of China (51421005, 51678015 and 51738001). The financial supports provided by these projects are gratefully acknowledged.

Citation

Li, H., Zhao, M., Wu, L., Wang, P. and Du, X. (2019), "A stable high-order absorbing boundary based on continued fraction for scalar wave propagation in 2D and 3D unbounded layers", Engineering Computations, Vol. 36 No. 7, pp. 2445-2479. https://doi.org/10.1108/EC-12-2018-0578

Publisher

:

Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited

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