{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:27:01Z","timestamp":1787232421426,"version":"build-2736575974"},"reference-count":49,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00c3\u00a7oamento de Pessoal de N\u00c3\u00advel Superior","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012950","name":"Institut national de recherche en informatique et en automatique","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012950","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002848","name":"Comisi\u00c3\u00b3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","doi-asserted-by":"publisher","award":["11140699"],"award-info":[{"award-number":["11140699"]}],"id":[{"id":"10.13039\/501100002848","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>In this work, we address time dependent wave propagation problems with strong multiscale features (in space and time). Our goal is to design a family of innovative high performance numerical methods suitable to the simulation of such multiscale problems. Particularly, we extend the multiscale hybrid-mixed (MHM) finite element method for the two- and three-dimensional time-dependent Maxwell equations with heterogeneous coefficients. The MHM method arises from the decomposition of the exact electric and magnetic fields in terms of the solutions of locally independent Maxwell problems tied together with a one-field formulation on top of a coarse-mesh skeleton. The multiscale basis functions, which are responsible for upscaling, are driven by local Maxwell problems with tangential component of the magnetic field prescribed on faces. A high-order discontinuous Galerkin method in space combined with a second-order explicit leap-frog scheme in time discretizes the local problems. This makes the MHM method effective and yields a staggered algorithm within a \u201cdivide-and-conquer\u201d framework. Several two-dimensional numerical tests assess the optimal convergence of the MHM method and its capacity to preserve the energy principle, as well as its accuracy to solve heterogeneous media problems on coarse meshes.<\/jats:p>","DOI":"10.1137\/16m110037x","type":"journal-article","created":{"date-parts":[[2018,10,25]],"date-time":"2018-10-25T13:25:46Z","timestamp":1540473946000},"page":"1648-1683","source":"Crossref","is-referenced-by-count":10,"title":["The Multiscale Hybrid-Mixed  method for the Maxwell Equations in Heterogeneous Media"],"prefix":"10.1137","volume":"16","author":[{"given":"St\u00e9phane","family":"Lanteri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Diego","family":"Paredes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Claire","family":"Scheid","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fr\u00e9d\u00e9ric","family":"Valentin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,10,25]]},"reference":[{"key":"atypb1","first-page":"1","volume":"21","author":"Abdulle A.","year":"2012","journal-title":"Numer. 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Sci. 198, Springer, Cham, 2018.","DOI":"10.1007\/978-3-319-70842-3"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/0720034"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/110835360"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2007.02.011"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/TMAG.2007.916578"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2017.04.023"},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"P. Ciarlet,\n                      Linear and Nonlinear Functional Analysis with Applications\n                      , SIAM, Philadelphia, 2013.","DOI":"10.1137\/1.9781611972597"},{"key":"atypb15","unstructured":"P. Ciarlet and F. Assous,\n                      Mod\u00e9les et m\u00e9thodes pour les \u00e9quations de Maxwell\n                      , ENSTA, 2002."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902417893"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.09.007"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.03.035"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:1999155"},{"key":"atypb20","unstructured":"R. Dautray and J.L. 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Harder and F. Valentin,\n                      Foundations of the MHM method\n                      , in Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, G. R. Barrenechea, F. Brezzi, A. Cangiani, and E. H. Georgoulis, eds., Lect. Notes Comput. Sci. Eng. 114, Springer, New York, pp. 401-433, 2016.","DOI":"10.1007\/978-3-319-41640-3_13"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1016\/S1076-5670(03)80097-6"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5682"},{"key":"atypb36","unstructured":"J. D. Joannopoulos, S. G. Johnson, and R. D. 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