Boundary integral equation methods for the solution of scattering and transmission 2D elastodynamic problems

Domínguez Baguena, Víctor; Turc, Catalin

Publication:
Boundary integral equation methods for the solution of scattering and transmission 2D elastodynamic problems

dc.contributor.author	Domínguez Baguena, Víctor
dc.contributor.author	Turc, Catalin
dc.contributor.department	Estatistika, Informatika eta Matematika	eu
dc.contributor.department	Institute for Advanced Materials and Mathematics - INAMAT2	en
dc.contributor.department	Estadística, Informática y Matemáticas	es_ES
dc.date.accessioned	2023-01-25T07:50:41Z
dc.date.available	2023-01-25T07:50:41Z
dc.date.issued	2022
dc.date.updated	2023-01-25T07:39:54Z
dc.description.abstract	We introduce and analyse various regularized combined field integral equations (CFIER) formulations of time-harmonic Navier equations in media with piece-wise constant material properties. These formulations can be derived systematically starting from suitable coercive approximations of Dirichlet-to-Neumann operators (DtN), and we present a periodic pseudodifferential calculus framework within which the well posedness of CIER formulations can be established. We also use the DtN approximations to derive and analyse OS methods for the solution of elastodynamics transmission problems. The pseudodifferential calculus we develop in this paper relies on careful singularity splittings of the kernels of Navier boundary integral operators, which is also the basis of high-order Nystrom quadratures for their discretizations. Based on these high-order discretizations we investigate the rate of convergence of iterative solvers applied to CFIER and OS formulations of scattering and transmission problems. We present a variety of numerical results that illustrate that the CFIER methodology leads to important computational savings over the classical CFIE one, whenever iterative solvers are used for the solution of the ensuing discretized boundary integral equations. Finally, we show that the OS methods are competitive in the high-frequency high-contrast regime.	en
dc.description.sponsorship	Catalin Turc gratefully acknowledges support from National Science Foundation (NSF) through contract DMS-1614270 and DMS-1908602.	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	Domínguez, V., & Turc, C. (2022). Boundary integral equation methods for the solution of scattering and transmission 2D elastodynamic problems. IMA Journal of Applied Mathematics, hxac018. https://doi.org/10.1093/imamat/hxac018	en
dc.identifier.doi	10.1093/imamat/hxac018
dc.identifier.issn	0272-4960
dc.identifier.uri	https://academica-e.unavarra.es/handle/2454/44596
dc.language.iso	eng	en
dc.publisher	Oxford University Press	en
dc.relation.ispartof	IMA Journal of Applied Mathematics 2022, 87 (4),647-706	en
dc.relation.publisherversion	https://doi.org/10.1093/imamat/hxac018
dc.rights	© The Author(s) 2022. This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.	en
dc.rights.accessRights	info:eu-repo/semantics/openAccess
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/
dc.subject	Time-harmonic Navier scattering and transmission problems	en
dc.subject	Boundary integral equations	en
dc.subject	Preconditioners	en
dc.subject	Domain decomposition methods	en
dc.subject	AMS subject classifications	en
dc.title	Boundary integral equation methods for the solution of scattering and transmission 2D elastodynamic problems	en
dc.type	info:eu-repo/semantics/article
dc.type.version	Versión publicada / Argitaratu den bertsioa	es
dc.type.version	info:eu-repo/semantics/publishedVersion	en
dspace.entity.type	Publication
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