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Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures

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Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures

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dc.contributor.author Demesy, Guillaume es_ES
dc.contributor.author Nicolet, André es_ES
dc.contributor.author Gralak, Boris es_ES
dc.contributor.author Geuzaine, Christophe es_ES
dc.contributor.author Campos, Carmen es_ES
dc.contributor.author Roman, Jose E. es_ES
dc.date.accessioned 2021-03-03T04:32:13Z
dc.date.available 2021-03-03T04:32:13Z
dc.date.issued 2020-12 es_ES
dc.identifier.issn 0010-4655 es_ES
dc.identifier.uri http://hdl.handle.net/10251/162869
dc.description.abstract [EN] We present a framework to solve non-linear eigenvalue problems suitable for a Finite Element discretization. The implementation is based on the open-source finite element software GetDP and the open-source library SLEPc. As template examples, we propose and compare in detail different ways to address the numerical computation of the electromagnetic modes of frequency-dispersive objects. This is a non-linear eigenvalue problem involving a non-Hermitian operator. A classical finite element formulation is derived for five different solutions and solved using algorithms adapted to the large size of the resulting discrete problem. The proposed solutions are applied to the computation of the dispersion relation of a diffraction grating made of a Drude material. The important numerical consequences linked to the presence of sharp corners and sign-changing coefficients are carefully examined. For each method, the convergence of the eigenvalues with respect to the mesh refinement and the shape function order, as well as computation time and memory requirements are investigated. The open-source template model used to obtain the numerical results is provided. Details of the implementation of polynomial and rational eigenvalue problems in GetDP are given in the appendix. Program summary Program title: NonLinearEVP.pro CPC Library link to program files: http://dx.doi.org/10.17632/r57nxxtc62.1 Licensing provisions: GNU General Public License 3 Programming language: Gmsh (http://gmsh.info), GetDP (http://getdp.info) Nature of problem: Computing the eigenvalues and eigenvectors of electromagnetic wave problems involving frequency-dispersive materials. The resulting eigenvalue problem is non-linear and non-hermitian. Solution method: Finite element method coupled to efficient non-linear eigenvalue solvers: Relevant SLEPc solvers were interfaced to the Finite Element software GetDP. Several linearization schemes are benchmarked. (C) 2020 Elsevier B.V. All rights reserved. es_ES
dc.description.sponsorship The work was partly supported by the French National Agency for Research (ANR) under the project "Resonance" (ANR-16-CE240013). The authors acknowledge the members of the project "Resonance'' for fruitful discussions. C. Campos and J. E. Roman were supported by the Spanish Agencia Estatal de Investigacion (AEI) under project SLEPc-HS (TIN2016-75985-P), which includes European Commission ERDF funds. C. Geuzaine was supported by ARC grant for Concerted Research Actions (ARC WAVES 15/19-03), financed by the Wallonia-Brussels Federation of Belgium. The authors thank Christian Engström from Ume¿ Universitet for helpful comments. Maxence Cassier from Institut Fresnel is acknowledged. Finally, the authors address special thanks to Anne-Sophie Bonnet Ben-Dhia and Camille Carvalho from INRIA (POEMS) for their motivating remarks and insights. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Computer Physics Communications es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Electromagnetism es_ES
dc.subject Photonics es_ES
dc.subject Frequency-dispersion es_ES
dc.subject Non-linear eigenvalue problem es_ES
dc.subject Finite elements es_ES
dc.subject.classification CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL es_ES
dc.title Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.cpc.2020.107509 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//TIN2016-75985-P/ES/SOLVERS DE VALORES PROPIOS ALTAMENTE ESCALABLES EN EL CONTEXTO DE LA BIBLIOTECA SLEPC/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/ANR//ANR-16-CE24-0013/FR/Theory and numerical modeling of optical resonance/Resonance/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/Fédération Wallonie-Bruxelles//ARC WAVES 15%2F19-03/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107379RB-I00/ES/ALGORITMOS PARALELOS Y SOFTWARE PARA METODOS ALGEBRAICOS EN ANALISIS DE DATOS/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Sistemas Informáticos y Computación - Departament de Sistemes Informàtics i Computació es_ES
dc.description.bibliographicCitation Demesy, G.; Nicolet, A.; Gralak, B.; Geuzaine, C.; Campos, C.; Roman, JE. (2020). Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures. Computer Physics Communications. 257:1-15. https://doi.org/10.1016/j.cpc.2020.107509 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1016/j.cpc.2020.107509 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 15 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 257 es_ES
dc.relation.pasarela S\425589 es_ES
dc.contributor.funder Fédération Wallonie-Bruxelles es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.contributor.funder Agence Nationale de la Recherche, Francia es_ES
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