LJK-Deterministic Models and Algorithms: EDP-MOISE Seminar
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On Thursday November 20 2008 at 11h00 in Salle 1 - Tour IRMA
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Seminary of Mr Patrick CIARLET (ENSTA)
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Solving Maxwell's equations with the Weighted Regularization Method and a Lagrange multiplier. Application to the computation of electromagnetic eigenmodes.
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Summary
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The Weighted Regularization Method was introduced and analyzed a few years ago by Martin Costabel and Monique Dauge. It allows one to solve numerically Maxwell's equations, set in a domain with a boundary that possesses reentrant corners and/or edges. We consider the extension of their method, to the case where the constraint on the divergence of the fields is enforced with the help of a Lagrange multiplier. We present and analyze a couple of Finite Elements which allows us to solve the problem, with a uniform discrete inf-sup condition. Among others, one can check that the use of the plain Taylor-Hood Finite Element yields sub-optimal results in terms of the inf-sup condition. Finally, we illustrate the methods by a series of 2D and 3D computations of electromagnetic eigenmodes.
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