Stability for Imposing Absorbing Boundary Conditions in the Finite Element Simulation of Acoustic Wave Propagation
Year: 2014
Journal of Computational Mathematics, Vol. 32 (2014), Iss. 1 : pp. 1–20
Abstract
It is well-known that artificial boundary conditions are crucial for the efficient and accurate computations of wavefields on unbounded domains. In this paper, we investigate stability analysis for the wave equation coupled with the first and the second order absorbing boundary conditions. The computational scheme is also developed. The approach allows the absorbing boundary conditions to be naturally imposed, which makes it easier for us to construct high order schemes for the absorbing boundary conditions. A third-order Lagrange finite element method with mass lumping is applied to obtain the spatial discretization of the wave equation. The resulting scheme is stable and is very efficient since no matrix inversion is needed at each time step. Moreover, we have shown both abstract and explicit conditional stability results for the fully-discrete schemes. The results are helpful for designing computational parameters in computations. Numerical computations are illustrated to show the efficiency and accuracy of our method. In particular, essentially no boundary reflection is seen at the artificial boundaries.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1310-m3942
Journal of Computational Mathematics, Vol. 32 (2014), Iss. 1 : pp. 1–20
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Stability Acoustic wave equation Simulation Finite element method Absorbing boundary conditions Wave operator decomposition.
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