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Mathematics > Numerical Analysis

arXiv:2203.00996 (math)
[Submitted on 2 Mar 2022]

Title:A modified convolution quadrature combined with the method of fundamental solutions and Galerkin BEM for acoustic scattering

Authors:Ebraheem Aldahham, Lehel Banjai
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Abstract:We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution. As the spatial discretization of the resulting time-domain boundary integral equation we use either the method of fundamental solutions (MFS) or the Galerkin boundary element method (BEM). In time we apply either a standard convolution quadrature (CQ) based on an A-stable linear multistep method or a modified CQ scheme. It is well-known that the standard low-order CQ schemes for hyperbolic problems suffer from strong dissipation and dispersion properties. The modified scheme is designed to avoid these properties. We give a careful description of the modified scheme and its implementation with differences due to different spatial discretizations highlighted. Numerous numerical experiments illustrate the effectiveness of the modified scheme and dramatic improvement with errors up to two orders of magnitude smaller in comparison with the standard scheme
Subjects: Numerical Analysis (math.NA)
MSC classes: 45E10, 65M80, 65L60, 65T50
Cite as: arXiv:2203.00996 [math.NA]
  (or arXiv:2203.00996v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2203.00996

Submission history

From: Lehel Banjai [view email]
[v1] Wed, 2 Mar 2022 10:06:38 UTC (1,203 KB)
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