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

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.

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