An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation

A natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free-space. Frequency-domain wave propagation models in the medium, such as the variable coefficient Helmholtz equation, include a faraway decay radiation condition (RC). It is desirab...

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Autores: Domínguez Baguena, Víctor, Ganesh, M., Sayas, Francisco Javier
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2020
País:España
Recursos:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/36929
Acesso em linha:https://hdl.handle.net/2454/36929
Access Level:acceso abierto
Palavra-chave:Heterogeneous
Unbounded
Wave propagation
Finite/boundary element methods
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spelling An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulationDomínguez Baguena, VíctorGanesh, M.Sayas, Francisco JavierHeterogeneousUnboundedWave propagationFinite/boundary element methodsA natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free-space. Frequency-domain wave propagation models in the medium, such as the variable coefficient Helmholtz equation, include a faraway decay radiation condition (RC). It is desirable to develop algorithms that incorporate the full physics of the heterogeneous and unbounded medium wave propagation model, and avoid an approximation of the RC. In this work we first present and analyze an overlapping decomposition framework that is equivalent to the full-space heterogeneous-homogenous continuous model, governed by the Helmholtz equation with a spatially dependent refractive index and the RC. Our novel overlapping framework allows the user to choose two free boundaries, and gain the advantage of applying established high-order finite and boundary element methods (FEM and BEM) to simulate an equivalent coupled model. The coupled model comprises auxiliary interior bounded heterogeneous and exterior unbounded homogeneous Helmholtz problems. A smooth boundary can be chosen for simulating the exterior problem using a spectrally accurate BEM, and a simple boundary can be used to develop a high-order FEM for the interior problem. Thanks to the spectral accuracy of the exterior computational model, the resulting coupled system in the overlapping region is relatively very small. Using the decomposed equivalent framework, we develop a novel overlapping FEM-BEM algorithm for simulating the acoustic or electromagnetic wave propagation in two dimensions. Our FEM-BEM algorithm for the full-space model incorporates the RC exactly. Numerical experiments demonstrate the efficiency of the FEM-BEM approach for simulating smooth and non-smooth wave fields, with the latter induced by a complex heterogeneous medium and a discontinuous refractive index.Víctor Domínguez thanks the support of the project MTM2017-83490-P. Francisco-Javier Sayas was partially supported by the NSF grant DMS-1818867.ElsevierEstatistika, Informatika eta MatematikaInstitute for Advanced Materials and Mathematics - INAMAT2Estadística, Informática y Matemáticas2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2454/36929reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83490-P© 2018 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/369292026-06-17T12:41:47Z
dc.title.none.fl_str_mv An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation
title An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation
spellingShingle An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation
Domínguez Baguena, Víctor
Heterogeneous
Unbounded
Wave propagation
Finite/boundary element methods
title_short An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation
title_full An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation
title_fullStr An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation
title_full_unstemmed An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation
title_sort An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: formulation, analysis, algorithm, and simulation
dc.creator.none.fl_str_mv Domínguez Baguena, Víctor
Ganesh, M.
Sayas, Francisco Javier
author Domínguez Baguena, Víctor
author_facet Domínguez Baguena, Víctor
Ganesh, M.
Sayas, Francisco Javier
author_role author
author2 Ganesh, M.
Sayas, Francisco Javier
author2_role author
author
dc.contributor.none.fl_str_mv Estatistika, Informatika eta Matematika
Institute for Advanced Materials and Mathematics - INAMAT2
Estadística, Informática y Matemáticas
dc.subject.none.fl_str_mv Heterogeneous
Unbounded
Wave propagation
Finite/boundary element methods
topic Heterogeneous
Unbounded
Wave propagation
Finite/boundary element methods
description A natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free-space. Frequency-domain wave propagation models in the medium, such as the variable coefficient Helmholtz equation, include a faraway decay radiation condition (RC). It is desirable to develop algorithms that incorporate the full physics of the heterogeneous and unbounded medium wave propagation model, and avoid an approximation of the RC. In this work we first present and analyze an overlapping decomposition framework that is equivalent to the full-space heterogeneous-homogenous continuous model, governed by the Helmholtz equation with a spatially dependent refractive index and the RC. Our novel overlapping framework allows the user to choose two free boundaries, and gain the advantage of applying established high-order finite and boundary element methods (FEM and BEM) to simulate an equivalent coupled model. The coupled model comprises auxiliary interior bounded heterogeneous and exterior unbounded homogeneous Helmholtz problems. A smooth boundary can be chosen for simulating the exterior problem using a spectrally accurate BEM, and a simple boundary can be used to develop a high-order FEM for the interior problem. Thanks to the spectral accuracy of the exterior computational model, the resulting coupled system in the overlapping region is relatively very small. Using the decomposed equivalent framework, we develop a novel overlapping FEM-BEM algorithm for simulating the acoustic or electromagnetic wave propagation in two dimensions. Our FEM-BEM algorithm for the full-space model incorporates the RC exactly. Numerical experiments demonstrate the efficiency of the FEM-BEM approach for simulating smooth and non-smooth wave fields, with the latter induced by a complex heterogeneous medium and a discontinuous refractive index.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/36929
url https://hdl.handle.net/2454/36929
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83490-P
dc.rights.none.fl_str_mv © 2018 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © 2018 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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