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

Abstract

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. KEYWORDScomputational electromagnetics, domain decomposition, frequency-domain Maxwell equations, high performance computing, hybridizable discontinuous Galerkin *https://www.ansys.com/products/electronics/ansys-hfss † https://www.comsol.com Int J Numer Model. 2020;33:e2678. wileyonlinelibrary.com/journal/jnm

Advanced Numerical Modeling Methods for the Characterization and Optimization of Metasurfaces

“…A paper describing our work and results is under review [15]. In the future, we plan to enable this GSTC-based modeling in our high order HDGFD (Hybridizable Discontinuous Galerkin Frequency-Domain) [1].…”

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

“…Starting from the work in [203], research on timeharmonic Maxwell's equations tackled the analysis and development of HDG formulations [186], including methods suitable for simulations at large wave numbers [189] and Schwarz-type domain decomposition (DD) strategies designed for HDG [18,185]. Recent applications of HDG to time-harmonic Maxwell's equations focus on wave propagation in heterogeneous media modelling photovoltaic cells [41], coupling with nonlocal hydrodynamic Drude and generalised nonlocal optical response models [184] and with hydrodynamic models for metals [257][258][259]271] to simulate plasmonic nanostructures.…”

HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB

“…Starting from the work in [203], research on time-harmonic Maxwell's equations tackled the analysis and development of HDG formulations [186], including methods suitable for simulations at large wave numbers [189] and Schwarz-type domain decomposition (DD) strategies designed for HDG [18,185]. Recent applications of HDG to time-harmonic Maxwell's equations focus on wave propagation in heterogeneous media modelling photovoltaic cells [41], coupling with nonlocal hydrodynamic Drude and generalised nonlocal optical response models [184] and with hydrodynamic models for metals [257][258][259]271] to simulate plasmonic nanostructures.…”