LJK-Deterministic Models and Algorithms: EDP-MOISE Seminar

 

On Thursday November 20 2008 at 11h00 in Salle 1 - Tour IRMA

 

Seminary of Mr Patrick CIARLET (ENSTA)

 

Solving Maxwell's equations with the Weighted Regularization Method and a Lagrange multiplier. Application to the computation of electromagnetic eigenmodes.

 

Summary

 

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.