Fast wavelet BEM for 3d electromagnetic shaping

Authors:
Karsten Eppler;Helmut Harbrecht
Affiliations:
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr., Berlin, Germany;Institute of Computer Science and Applied Mathematics, Christian-Albrechts-University of Kiel, Kiel, Germany
Venue:
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Year:
2005

Citing 3
Cited 1

A fast algorithm for particle simulations

Journal of Computational Physics
Numerical approximation of a free boundary problem arising in electromagnetic shaping

SIAM Journal on Numerical Analysis
Adaptive low-rank approximation of collocation matrices

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A new fictitious domain method in shape optimization

Computational Optimization and Applications

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Abstract

In the present paper we combine an energy variational approach with shape optimization techniques to compute numerically free surfaces in electromagnetic shaping and levitation of liquid metals in three dimensions. Assuming the domains to be starshaped, the surfaces are represented via an ansatz by spherical harmonics, which generalizes the approximation by Fourier series in two dimensions. We will show that all ingredients of the shape optimization algorithm, particularly the shape gradient and the cost functional, can be computed by boundary integrals. A wavelet based fast boundary element method of optimal complexity is employed for the computation of the exterior magnetic field and its Neumann-to-Dirichlet map.