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Special Radon Semester on Computational Mechanics
Linz, October-December 2005
Abstract - Schwarz Methods for Maxwell Equations

Author: Joachim Schöberl

Title of the contribution: Schwarz Methods for Maxwell Equations

Abstract:
Electromagnetic phenomena are described by Maxwell equations. The weak formulation is discretized by Nedelec finite elements. Since real problems are usually 3D, one obtains huge systems of equations, which must be solved by efficient iterative methods. Hiptmair as well as Arnold, Falk and Winther have proposed and analyzed special multigrid methods tuned to the properties of the underlying function space H(curl). We will discuss their methods, and I will present a new technique to prove robust multigrid convergence on non-convex domains. The new analysis is based on commuting interpolation operators, and is very similar to the scalar case.

In the second part of the talk, I will present a new basis for high order H(curl) elements. It includes gradient basis functions explicitely, which allows to use simple Schwarz methods.

Practical examples including the simulation of a power transformer are presented.

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