Computing electromagnetic eigenmodes with continuous Galerkin approximations

Patrick Ciarlet (1) , Grace Hechme (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

Costabel and Dauge proposed a variational setting to solve numerically the time-harmonic Maxwell equations in 3D polyhedral geometries, with a continuous approximation of the electromagnetic field. In order to remove spurious eigenmodes, three computational strategies are then possible. The original method, which requires a parameterization of the variational formulation. The second method, which is based on an a posteriori filtering of the computed eigenmodes. And the third method, which uses a mixed variational setting so that all spurious modes are removed a priori. In this paper, we discuss the relative merits of the approaches, which are illustrated by a series of 3D numerical examples. © 2008 Elsevier B.V. All rights reserved.

Mots clés: Electromagnetism; Continuous Galerkin discretization; Eigenvalues and eigenvectors computations

Domaines: Analyse numérique [math.NA]; Electromagnétisme

Patrick Ciarlet, Grace Hechme. Computing electromagnetic eigenmodes with continuous Galerkin approximations. Computer Methods in Applied Mechanics and Engineering, 2008, 198 (2), pp.358-365. ⟨10.1016/j.cma.2008.08.005⟩. ⟨hal-00873075⟩