Numerical investigation of a 3D hybrid high-order method for the indefinite time-harmonic Maxwell problem

Discontinuous Galerkin; Hybrid high-order method; Maxwell equations; Class of methods; Discontinuous galerkin; High-order; High-order methods; Higher-order; Higher-order methods; Maxwell's problems; Numerical investigations; Time-harmonic; Analysis; Engineering (all); Computer Graphics and Computer-Aided Design; Applied Mathematics

Abstract :

[en] 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.

Disciplines :

Mathematics
Computer science

Author, co-author :

Cicuttin, Matteo ; Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, Italy

Geuzaine, Christophe ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE)

Language :

English

Title :

Numerical investigation of a 3D hybrid high-order method for the indefinite time-harmonic Maxwell problem

Publication date :

June 2024

Journal title :

Finite Elements in Analysis and Design

ISSN :

0168-874X

eISSN :

1872-6925

Publisher :

Elsevier

Volume :

233

Pages :

104124

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0168874X24000180?httpAccept=text/xml

Funders :

INRIA - Institut National de Recherche en Informatique et en Automatique

Funding text :

The authors wish to express their gratitude to S. Lemaire (INRIA), Z. Dong (INRIA) and T. Chaumont-Frelet (INRIA) for the useful discussions about some of the theoretical aspects of the HHO method.

Available on ORBi :

since 04 June 2025

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