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Maxwell and Lamé eigenvalues on polyhedra

✍ Scribed by Martin Costabel; Monique Dauge

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
249 KB
Volume
22
Category
Article
ISSN
0170-4214

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✦ Synopsis

In a convex polyhedron, a part of the Lame´eigenvalues with hard simple support boundary conditions does not depend on the Lame´coefficients and coincides with the Maxwell eigenvalues. The other eigenvalues depend linearly on a parameter s linked to the Lame´coefficients and the associated eigenmodes are the gradients of the Laplace-Dirichlet eigenfunctions. In a non-convex polyhedron, such a splitting of the spectrum disappears partly or completely, in relation with the non-H singularities of the Laplace-Dirichlet eigenfunctions. From the Maxwell equations point of view, this means that in a non-convex polyhedron, the spectrum cannot be approximated by finite element methods using H elements. Similar properties hold in polygons. We give numerical results for two L-shaped domains.

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