High order HDG method and domain decomposition solvers for frequency‐domain electromagnetics

This work is concerned with the numerical treatment of the system of three‐dimensional frequency‐domain (or time‐harmonic) Maxwell equations using a high order hybridizable discontinuous Galerkin (HDG) approximation method combined with domain decomposition (DD) on the basis of hybrid iterative‐dire...

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Bibliographic Details
Published in:International journal of numerical modelling 2020-03, Vol.33 (2), p.n/a
Main Authors: Agullo, Emmanuel, Giraud, Luc, Gobé, Alexis, Kuhn, Matthieu, Lanteri, Stéphane, Moya, Ludovic
Format: Article
Language:English
Subjects:
computational electromagnetics
Computer Science
Computer simulation
Distributed, Parallel, and Cluster Computing
domain decomposition
Domain decomposition methods
frequency‐domain Maxwell equations
Galerkin method
high performance computing
hybridizable discontinuous Galerkin
Iterative methods
Mathematical analysis
Mathematics
Maxwell's equations
Model testing
Numerical Analysis
Solvers
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Summary:This work is concerned with the numerical treatment of the system of three‐dimensional frequency‐domain (or time‐harmonic) Maxwell equations using a high order hybridizable discontinuous Galerkin (HDG) approximation method combined with domain decomposition (DD) on the basis of hybrid iterative‐direct parallel solution strategies. The proposed HDG method preserves the advantages of classical DG methods previously introduced for the time‐domain Maxwell equations, in particular, in terms of accuracy and flexibility with regards to the discretization of complex geometrical features, while keeping the computational efficiency at the level of the reference edge element‐based finite element formulation widely adopted for the considered PDE system. We study in details the computational performances of the resulting DD solvers in particular in terms of scalability metrics by considering both a model test problem and more realistic large‐scale simulations performed on high performance computing systems consisting of networked multicore nodes.
ISSN:0894-3370
1099-1204
DOI:10.1002/jnm.2678