Numerical investigation of a 3D hybrid high-order method for the indefinite time-harmonic Maxwell problem
Hybrid High-Order (HHO) methods are a recently developed class of methods belonging to the broader family of Discontinuous Sketetal methods. Other well known members of the same family are the well-established Hybridizable Discontinuous Galerkin (HDG) method, the nonconforming Virtual Element Method...
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| Published in: | Finite elements in analysis and design Vol. 233; p. 104124 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.06.2024
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| ISSN: | 0168-874X, 1872-6925, 1872-6925 |
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| Abstract | Hybrid High-Order (HHO) methods are a recently developed class of methods belonging to the broader family of Discontinuous Sketetal methods. Other well known members of the same family are the well-established Hybridizable Discontinuous Galerkin (HDG) method, the nonconforming Virtual Element Method (ncVEM) and the Weak Galerkin (WG) method. HHO provides various valuable assets such as simple construction, support for fully-polyhedral meshes and arbitrary polynomial order, great computational efficiency, physical accuracy and straightforward support for hp-refinement. In this work we propose an HHO method for the indefinite time-harmonic Maxwell problem and we evaluate its numerical performance. In addition, we present the validation of the method in two different settings: a resonant cavity with Dirichlet conditions and a parallel plate waveguide problem with a total/scattered field decomposition and a plane-wave boundary condition. Finally, as a realistic application, we demonstrate HHO used on the study of the return loss in a waveguide mode converter. |
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| AbstractList | Hybrid High-Order (HHO) methods are a recently developed class of methods belonging to the broader family of Discontinuous Sketetal methods. Other well known members of the same family are the well-established Hybridizable Discontinuous Galerkin (HDG) method, the nonconforming Virtual Element Method (ncVEM) and the Weak Galerkin (WG) method. HHO provides various valuable assets such as simple construction, support for fully-polyhedral meshes and arbitrary polynomial order, great computational efficiency, physical accuracy and straightforward support for hp-refinement. In this work we propose an HHO method for the indefinite time-harmonic Maxwell problem and we evaluate its numerical performance. In addition, we present the validation of the method in two different settings: a resonant cavity with Dirichlet conditions and a parallel plate waveguide problem with a total/scattered field decomposition and a plane-wave boundary condition. Finally, as a realistic application, we demonstrate HHO used on the study of the return loss in a waveguide mode converter. |
| ArticleNumber | 104124 |
| Author | Cicuttin, Matteo Geuzaine, Christophe |
| Author_xml | – sequence: 1 givenname: Matteo orcidid: 0000-0001-5485-2493 surname: Cicuttin fullname: Cicuttin, Matteo email: matteo.cicuttin@polito.it organization: Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, I-10129, Italy – sequence: 2 givenname: Christophe surname: Geuzaine fullname: Geuzaine, Christophe organization: Montefiore Institute B28, University of Liège, Allée de la Découverte 10, Liège, B-4000, Belgium |
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| Cites_doi | 10.1007/s10915-016-0272-z 10.1007/s00211-005-0604-7 10.1007/s10915-020-01195-z 10.1002/nme.6137 10.1093/imanum/drz038 10.1016/j.cma.2020.113178 10.1007/s00466-018-1538-0 10.1109/TMAG.2015.2494062 10.1109/TAP.2005.861524 10.1142/S0218202522500051 10.1016/j.cma.2018.08.037 10.1007/s10915-014-9964-4 10.1080/02726340701818147 10.1109/TMAG.2014.2358701 10.1016/j.jcp.2018.05.017 10.1007/s10915-018-0745-3 10.1108/03321641311306196 10.1137/19M1285901 10.1007/s10915-021-01492-1 10.1016/j.cam.2017.09.017 10.1051/m2an/2015090 10.1016/j.jcp.2011.05.018 10.1109/TMAG.2017.2679341 10.1016/j.crma.2014.10.013 10.1186/s40323-015-0032-x 10.1093/imanum/draa059 10.1137/070706616 10.1016/j.cma.2014.09.009 10.1515/cmam-2014-0018 10.1016/j.cpc.2017.05.012 10.1090/S0025-5718-10-02334-3 10.1016/j.cam.2012.10.003 |
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| Keywords | Discontinuous Galerkin Maxwell equations Hybrid high-order method |
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| Snippet | Hybrid High-Order (HHO) methods are a recently developed class of methods belonging to the broader family of Discontinuous Sketetal methods. Other well known... |
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| SubjectTerms | Analysis Applied Mathematics Class of methods Computer Graphics and Computer-Aided Design Computer science Discontinuous Galerkin Engineering (all) Engineering, computing & technology High-order High-order methods Higher-order Higher-order methods Hybrid high-order method Ingénierie, informatique & technologie Mathematics Mathématiques Maxwell equations Maxwell's problems Numerical investigations Physical, chemical, mathematical & earth Sciences Physique, chimie, mathématiques & sciences de la terre Sciences informatiques Time-harmonic |
| Title | Numerical investigation of a 3D hybrid high-order method for the indefinite time-harmonic Maxwell problem |
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