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Exact boundary condition for time-dependent wave equation based on boundary integral

Author:

Zhen-Huan TengAuthors Info & Claims

Journal of Computational Physics, Volume 190, Issue 2

Pages 398 - 418

https://doi.org/10.1016/S0021-9991(03)00281-X

Published: 20 September 2003 Publication History

Abstract

An exact non-reflecting boundary conditions based on a boundary integral equation or a modified Kirchhoff-type formula is derived for exterior three-dimensional wave equations. The Kirchhoff-type non-reflecting boundary condition is originally proposed by L. Ting and M.J. Miksis [J. Acoust. Soc. Am. 80 (1986) 1825] and numerically tested by D. Givoli and D. Cohen [J. Comput. Phys. 117 (1995) 102] for a spherically symmetric problem. The computational advantage of Ting Miksis boundary condition is that its temporal non-locality is limited to a fixed amount of past information. However, a long-time instability is exhibited in testing numerical solutions by using a standard nondissipative finite-difference scheme. The main purpose of this work is to present a new exact boundary condition and to eliminate the long-time instability. The proposed exact boundary condition can be considered as a limit case of Ting-Miksis boundary condition when the two artificial boundaries used in their method approach each other. Our boundary condition is actually a boundary integral equation on a single artificial boundary for wave equations, which is to be solved in conjunction with the interior wave equation. The new boundary condition needs only one artificial boundary, which can be of any shape, i.e., sphere, cubic surface, etc. It keeps all merits of the original Kirchhoff boundary condition such as restricting the temporal non-locality, free of numerical evaluation of any special functions and so on. Numerical approximation to the artificial boundary condition on cubic surface is derived and three-dimensional numerical tests are carried out on the cubic computational domain.

References

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Cited By

Li XKoene Evan Manen DRobertsson JCurtis A(2022)Elastic immersive wavefield modellingJournal of Computational Physics10.1016/j.jcp.2021.110826451:COnline publication date: 15-Feb-2022
https://dl.acm.org/doi/10.1016/j.jcp.2021.110826
Han HZhang Z(2008)Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domainJournal of Computational Physics10.1016/j.jcp.2008.07.006227:20(8992-9004)Online publication date: 1-Oct-2008
https://dl.acm.org/doi/10.1016/j.jcp.2008.07.006
Grote MKirsch C(2007)Nonreflecting boundary condition for time-dependent multiple scatteringJournal of Computational Physics10.1016/j.jcp.2006.06.007221:1(41-62)Online publication date: 1-Jan-2007
https://dl.acm.org/doi/10.1016/j.jcp.2006.06.007

Index Terms

Exact boundary condition for time-dependent wave equation based on boundary integral
1. Mathematics of computing
  1. Mathematical analysis
    1. Integral equations
    2. Numerical analysis
2. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 190, Issue 2

20 September 2003

331 pages

ISSN:0021-9991

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Academic Press Professional, Inc.

United States

Publication History

Published: 20 September 2003

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Cited By

Li XKoene Evan Manen DRobertsson JCurtis A(2022)Elastic immersive wavefield modellingJournal of Computational Physics10.1016/j.jcp.2021.110826451:COnline publication date: 15-Feb-2022
https://dl.acm.org/doi/10.1016/j.jcp.2021.110826
Han HZhang Z(2008)Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domainJournal of Computational Physics10.1016/j.jcp.2008.07.006227:20(8992-9004)Online publication date: 1-Oct-2008
https://dl.acm.org/doi/10.1016/j.jcp.2008.07.006
Grote MKirsch C(2007)Nonreflecting boundary condition for time-dependent multiple scatteringJournal of Computational Physics10.1016/j.jcp.2006.06.007221:1(41-62)Online publication date: 1-Jan-2007
https://dl.acm.org/doi/10.1016/j.jcp.2006.06.007

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