Locally implicit discontinuous Galerkin method for time domain electromagnetics

Victorita Dolean Maini, Hassan Fahs, Loula Fezoui, Stephane Lanteri

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

In the recent years, there has been an increasing interest in discontinuous Galerkin time domain (DGTD) methods for the solution of the unsteady Maxwell equations modeling electromagnetic wave propagation. One of the main features of DGTD methods is their ability to deal with unstructured meshes which are particularly well suited to the discretization of the geometrical details and heterogeneous media that characterize realistic propagation problems. Such DGTD methods most often rely on explicit time integration schemes and lead to block diagonal mass matrices. However, explicit DGTD methods are also constrained by a stability condition that can be very restrictive on highly refined meshes and when the local approximation relies on high order polynomial interpolation. An implicit time integration scheme is a natural way to obtain a time domain method which is unconditionally stable but at the expense of the inversion of a global linear system at each time step. A more viable approach consists of applying an implicit time integration scheme locally in the refined regions of the mesh while preserving an explicit time scheme in the complementary part, resulting in an hybrid explicit–implicit (or locally implicit) time integration strategy. In this paper, we report on our recent efforts towards the development of such a hybrid explicit–implicit DGTD method for solving the time domain Maxwell equations on unstructured simplicial meshes. Numerical experiments for 3D propagation problems in homogeneous and heterogeneous media illustrate the possibilities of the method for simulations involving locally refined meshes.
LanguageEnglish
Pages512-526
Number of pages15
JournalJournal of Computational Physics
Volume229
Issue number2
DOIs
Publication statusPublished - 20 Jan 2010

Fingerprint

Galerkin method
Discontinuous Galerkin Method
Galerkin methods
Time Domain
Discontinuous Galerkin
electromagnetism
Maxwell equations
Time Integration
Mesh
Heterogeneous Media
Electromagnetic wave propagation
mesh
Maxwell's equations
Linear systems
Interpolation
Propagation
Explicit Time Integration
Polynomials
Local Approximation
Inhomogeneous Media

Keywords

  • computational electromagnetics
  • time domain Maxwell's equations
  • discontinuous Galerkin method
  • unstructured tetrahedral meshes
  • hybrid explicit-implicit scheme

Cite this

Dolean Maini, Victorita ; Fahs, Hassan ; Fezoui, Loula ; Lanteri, Stephane. / Locally implicit discontinuous Galerkin method for time domain electromagnetics. In: Journal of Computational Physics. 2010 ; Vol. 229, No. 2. pp. 512-526.
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Locally implicit discontinuous Galerkin method for time domain electromagnetics. / Dolean Maini, Victorita; Fahs, Hassan; Fezoui, Loula; Lanteri, Stephane.

In: Journal of Computational Physics, Vol. 229, No. 2, 20.01.2010, p. 512-526.

Research output: Contribution to journalArticle

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