Online from: 1982
Subject Area: Electrical & Electronic Engineering
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|Title:||An implicit discontinuous Galerkin time-domain method for two-dimensional electromagnetic wave propagation|
|Author(s):||Adrien Catella, (NACHOS Project-Team, INRIA, Sophia Antipolis, France), Victorita Dolean, (J.A. Dieudonné Mathematics Laboratory, University of Nice-Sophia Antipolis, Nice, France), Stéphane Lanteri, (NACHOS Project-Team, INRIA, Sophia Antipolis, France)|
|Citation:||Adrien Catella, Victorita Dolean, Stéphane Lanteri, (2010) "An implicit discontinuous Galerkin time-domain method for two-dimensional electromagnetic wave propagation", COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 29 Iss: 3, pp.602 - 625|
|Keywords:||Differential equations, Electromagnetism, Galerkin method, Meshes, Wave propagation|
|Article type:||Research paper|
|DOI:||10.1108/03321641011028215 (Permanent URL)|
|Publisher:||Emerald Group Publishing Limited|
|Acknowledgements:||The authors gratefully acknowledge support from CEA DAM (Military Application Division), CESTA Center, under Grant No. 4600 118950.|
Purpose – The purpose of this paper is to develop a time implicit discontinuous Galerkin method for the simulation of two-dimensional time-domain electromagnetic wave propagation on non-uniform triangular meshes.
Design/methodology/approach – The proposed method combines an arbitrary high-order discontinuous Galerkin method for the discretization in space designed on triangular meshes, with a second-order Cranck-Nicolson scheme for time integration. At each time step, a multifrontal sparse LU method is used for solving the linear system resulting from the discretization of the TE Maxwell equations.
Findings – Despite the computational overhead of the solution of a linear system at each time step, the resulting implicit discontinuous Galerkin time-domain method allows for a noticeable reduction of the computing time as compared to its explicit counterpart based on a leap-frog time integration scheme.
Research limitations/implications – The proposed method is useful if the underlying mesh is non-uniform or locally refined such as when dealing with complex geometric features or with heterogeneous propagation media.
Practical implications – The paper is a first step towards the development of an efficient discontinuous Galerkin method for the simulation of three-dimensional time-domain electromagnetic wave propagation on non-uniform tetrahedral meshes. It yields first insights of the capabilities of implicit time stepping through a detailed numerical assessment of accuracy properties and computational performances.
Originality/value – In the field of high-frequency computational electromagnetism, the use of implicit time stepping has so far been limited to Cartesian meshes in conjunction with the finite difference time-domain (FDTD) method (e.g. the alternating direction implicit FDTD method). The paper is the first attempt to combine implicit time stepping with a discontinuous Galerkin discretization method designed on simplex meshes.
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