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Fast Evaluation of Eddy Current Integral Operators

In: Numerical Mathematics and Advanced Applications

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  • Steffen Börm

    (Max-Planck-Institute für Mathematik in den Naturwissenschaften)

Abstract

Summary Boundary element formulations for eddy current problems are based on non-local operators. Discretizing these operators by standard Galerkin techniques leads to large dense matrices. In order to treat the discretized system efficiently, we cannot store these dense matrices directly, but use data-sparse approximations. We present an approach based on piecewise polynomial interpolation of the underlying kernel functions. The resulting H 2-matrix approximation can be stored using only O(nm 3) units of storage, where n is the number of degrees of freedom and m is the order of the interpolation. Construction and evaluation of the approximated matrix requires only O(nm 3) operations. This paper presents joint work with Jörg Ostrowski.

Suggested Citation

  • Steffen Börm, 2004. "Fast Evaluation of Eddy Current Integral Operators," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 151-158, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_12
    DOI: 10.1007/978-3-642-18775-9_12
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