A hybridizable discontinuous Galerkin method combined to a Schwarz algorithm for the solution of 3d time-harmonic Maxwell's equation

Authors:
Liang Li;Sté/phane Lanteri;Ronan Perrussel
Affiliations:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, PR China;INRIA, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France;CNRS/ LAPLACE (Laboratoire Plasma et Conversion dEnergie)/ F-31071 Toulouse, France and Université/ de Toulouse/ INP, UPS/ LAPLACE/ F-31071 Toulouse, France
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

A Schwarz-type domain decomposition method is presented for the solution of the system of 3d time-harmonic Maxwell@?s equations. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of the problem based on a tetrahedrization of the computational domain. The discrete system of the HDG method on each subdomain is solved by an optimized sparse direct (LU factorization) solver. The solution of the interface system in the domain decomposition framework is accelerated by a Krylov subspace method. The formulation and the implementation of the resulting DD-HDG (Domain Decomposed-Hybridizable Discontinuous Galerkin) method are detailed. Numerical results show that the resulting DD-HDG solution strategy has an optimal convergence rate and can save both CPU time and memory cost compared to a classical upwind flux-based DD-DG (Domain Decomposed-Discontinuous Galerkin) approach.