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High order methods for acoustic scattering: Coupling farfield expansions ABC with deferred-correction methods

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10.1016/j.wavemoti.2020.102529
 
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hdl:2117/345928

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Villamizar, Vianey
Grundvig, Dane
Rojas, Otilio
Acosta, Sebastian
Document typeArticle
Defense date2020
PublisherElsevier
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs) with finite difference methods for the Helmholtz equation. These ABCs are based on exact representations of the outgoing waves by means of farfield expansions. The finite difference methods, which are constructed from a deferred-correction (DC) technique, approximate the Helmholtz equation and the ABCs, with the appropriate number of terms, to any desired order. As a result, high order numerical methods with an overall order of convergence equal to the order of the DC schemes are obtained. A detailed construction of these DC finite difference schemes is presented. Additionally, a rigorous proof of the consistency of the DC schemes with the Helmholtz equation and the ABCs in polar coordinates is also given. The results of several numerical experiments corroborate the high order convergence of the novel method.
CitationVillamizar, V. [et al.]. High order methods for acoustic scattering: Coupling farfield expansions ABC with deferred-correction methods. "Wave Motion", 2020, vol. 95, 102529. 
URIhttp://hdl.handle.net/2117/345928
DOI10.1016/j.wavemoti.2020.102529
ISSN0165-2125
Publisher versionhttps://www.sciencedirect.com/science/article/abs/pii/S0165212519304202#!
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