Fictitious Domain Method for Unsteady Problems: Application to Electromagnetic Scattering

Francis Collino 1 Patrick Joly 1 Florence Millot
1 ONDES - Modeling, analysis and simulation of wave propagation phenomena
Inria Paris-Rocquencourt, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR2706
Abstract : In this work, we present and implement a fictitious domain method for time dependent problems of scattering by obstacles. We focus our attention on the case of 2D electromagnetic waves and perfectly conducting boundaries. Such a method allows us to work with uniform meshes for the electric field, independently of the geometry of the obstacle, the boundary condition being taken into account via the introduction of a Lagrange multiplier that can be interpreted as a surface current. After a brief description of the method and a presentation of its main properties, we show the superiority in terms of accuracy of this new method over the method that consists in using a staircase like approximation of the boundary.
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Francis Collino, Patrick Joly, Florence Millot. Fictitious Domain Method for Unsteady Problems: Application to Electromagnetic Scattering. [Research Report] RR-2963, INRIA. 1996. ⟨inria-00073735⟩

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