Dispersion analysis of triangle-based Whitney element methods for electromagnetic wave propagation

Marcella Bonazzoli 1, 2 Francesca Rapetti 1 Chiara Venturini 3
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We study the numerical dispersion/dissipation of a triangle-based edge Finite Element Method (edgeFEM) of degree r ≥ 1 when coupled with the Leap-Frog (LF) finite difference scheme to simulate the electromagnetic wave propagation over a structured triangulation of the 2D physical domain. The analysis addresses the discrete eigenvalue problem resulting from the approximation of the dispersion relation. First, we present semi-discrete dispersion graphs by varying the approximation degree r and the number of discrete points per wavelength. The fully-discrete ones are then obtained by varying also the time step. Numerical results for the edgeFEM, resp. edgeFEM-LF, are compared with those for the node Finite Element Method (nodeFEM), resp. nodeFEM-LF, applied to the considered problem.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-01949026
Contributor : Francesca Rapetti <>
Submitted on : Sunday, December 9, 2018 - 1:58:43 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:30 PM

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Marcella Bonazzoli, Francesca Rapetti, Chiara Venturini. Dispersion analysis of triangle-based Whitney element methods for electromagnetic wave propagation. Applied Mathematics and Computation, Elsevier, 2018, Recent Advances in Computing, 319, pp.274-286. ⟨10.1016/j.amc.2017.03.026⟩. ⟨hal-01949026⟩

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