Ralf Hiptmair

Finite elements in computational electromagnetism

This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinate-independent statement of Maxwells equations in the calculus of differential forms. The asymptotic convergence of discrete solutions is investigated theoretically. As discrete differential forms represent a genuine generalization of conventional Lagrangian finite elements, the analysis is based upon a judicious adaptation of established techniques in the theory of finite elements. Risks and difficulties haunting finite element schemes that do not fit the framework of discrete differential forms are highlighted.

Multigrid Method for Maxwell's Equations

In this paper we are concerned with the efficient solution of discrete variational problems related to the bilinear form ({\bf curl}\!

Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces

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Canonical construction of finite elements

, {\bf curl}\!

Symmetric Coupling for Eddy Current Problems

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Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the

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p

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-Version

defined on \textbf{\textit{H}}

Discrete Hodge operators

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Galerkin Boundary Element Methods for Electromagnetic Scattering

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