Algebraic Schwarz preconditioning for the Schur complement: application to the time-harmonic Maxwell equations discretized by a discontinuous Galerkin method - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2011

Algebraic Schwarz preconditioning for the Schur complement: application to the time-harmonic Maxwell equations discretized by a discontinuous Galerkin method

Abstract

we primary study parallel algebraic additive Schwarz preconditioning technique for the Schur complement in the context of frequency domain electromagnetic wave propagation problems. For that purpose, the system of 2D and 3D time-harmonic Maxwell equations in first order (or mixed) form is discretized using a discontinuous Galerkin method formulated on an unstructured tetrahedral mesh. The resulting large sparse non-Hermitian complex coefficient linear system is solved by a parallel algebraic domain decomposition. More precisely, we will consider numerical techniques based on a non-overlapping decomposition of the graph associated with the sparse matrix to solve a condensed system. Although the Schur complement system is usually more tractable than the original problem by an iterative Krylov subspace technique, preconditioning treatment is still required. The numerical and parallel performance of different variants of algebraic Additive Schwarz parallel preconditioners for the Schur complement will be illustrated on a set of test problems. Furthermore, preliminary comparisons of this purely algebraic approach with continuous discrete Schwarz approach will be presented.
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Dates and versions

inria-00577639 , version 1 (17-03-2011)

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  • HAL Id : inria-00577639 , version 1

Cite

Emmanuel Agullo, Luc Giraud, Abdou Guermouche, Azzam Haidar, Jean Roman, et al.. Algebraic Schwarz preconditioning for the Schur complement: application to the time-harmonic Maxwell equations discretized by a discontinuous Galerkin method. The Twentieth International Conference on Domain Decomposition Methods, Feb 2011, San Diego La Jolla, United States. ⟨inria-00577639⟩
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