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DC Field | Value | Language |
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dc.contributor.author | Gibbs, A | - |
dc.contributor.author | Langdon, S | - |
dc.date.accessioned | 2024-04-12T08:44:35Z | - |
dc.date.available | 2024-04-12T08:44:35Z | - |
dc.date.issued | 2024-03-05 | - |
dc.identifier.citation | Gibbs, A. and Langdon, S. (2024) 'An efficient frequency-independent numerical method for computing the far-field pattern induced by polygonal obstacles', SIAM Journal on Scientific Computing, 0 (accepted, in press), pp. 1 - 26. | en_US |
dc.identifier.issn | 1064-8275 | - |
dc.identifier.uri | https://bura.brunel.ac.uk/handle/2438/28755 | - |
dc.description | MSC codes. 35J05, 78A45, 30E20, 65F20 | en_US |
dc.description | The preprint archived on this institutional repository is available on arXiv at https://doi.org/10.48550/arXiv.2310.17603. It is licensed under a CC-BY licence (https://creativecommons.org/licenses/by/4.0/) to meet UKRI terms and conditions. It has not been certified by peer review. Cite as arXiv:2310.17603v2 [math.NA] for this version). | - |
dc.description.abstract | For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent) set of canonical incident angles. Although these remarkable formulae are exact in theory, here we demonstrate that: (i) they are highly sensitive to numerical errors in practice, and (ii) direct calculation of the coefficients in these formulae may be impossible for particular sets of canonical incident angles, even in exact arithmetic. Only by overcoming these practical issues can embedding formulae provide a highly efficient approach to computing the far-field pattern induced by a large number of incident angles. Here we address challenges (i) and (ii), supporting our theory with numerical experiments. Challenge (i) is solved using techniques from computational complex analysis: we reformulate the embedding formula as a complex contour integral and prove that this is much less sensitive to numerical errors. In practice, this contour integral can be efficiently evaluated by residue calculus. Challenge (ii) is addressed using techniques from numerical linear algebra: we oversample, considering more canonical incident angles than are necessary, thus expanding the set of valid coefficient vectors. The coefficient vector can then be selected using either a least squares approach or column subset selection. | en_US |
dc.description.sponsorship | AG is grateful for support from EPSRC grants EP/S01375X/1 and EP/V053868/1. | en_US |
dc.language.iso | en_US | en_US |
dc.publisher | Society for Industrial and Applied Mathematics (SIAM) | en_US |
dc.rights | Copyright © 2024 The Author(s) The preprint archived on this institutional repository is available on arXiv at https://doi.org/10.48550/arXiv.2310.17603. It is licensed under a CC-BY licence (https://creativecommons.org/licenses/by/4.0/) to meet UKRI terms and conditions. It has not been certified by peer review. Cite as arXiv:2310.17603v2 [math.NA] for this version). | - |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | - |
dc.subject | embedding formula | en_US |
dc.subject | far-field pattern | en_US |
dc.subject | scattering | en_US |
dc.subject | Cauchy integral | en_US |
dc.subject | oversampling | en_US |
dc.title | An efficient frequency-independent numerical method for computing the far-field pattern induced by polygonal obstacles | en_US |
dc.type | Article | en_US |
dc.identifier.doi | https://doi.org/10.48550/arXiv.2310.17603 | - |
dc.relation.isPartOf | SIAM Journal on Scientific Computing | - |
pubs.publication-status | Accepted | - |
dc.rights.license | https://creativecommons.org/licenses/by/4.0/legalcode.en | - |
Appears in Collections: | Dept of Mathematics Embargoed Research Papers |
Files in This Item:
File | Description | Size | Format | |
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Preprint.pdf | Embargoed until publication | 3.84 MB | Adobe PDF | View/Open |
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