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Toward Generalized Finite Element Difference Methods for Electro- and Magnetostatics

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Scientific Computing in Electrical Engineering

Part of the book series: Mathematics in Industry ((MATHINDUSTRY,volume 4))

Abstract

The paper explores a class of “Finite Element Difference” (FED) schemes with Finite Difference-type data structures but based on Finite Element — variational principles. Curved material boundaries are approximated algebraically on relatively coarse regular rectangular or hexahedral grids by a judicious choice of local approximating functions, rather than geometrically on conforming meshes. The grids do not have to resolve small geometric details. The proposed approach combines the ideas of the Generalized Finite Element — Partition of Unity methods, Discontinuous Galerkin Methods and Finite Difference / Finite Volume / Finite Integration Techniques.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Akron, Akron, OH, 44325-3904, USA

    Igor Tsukerman

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  1. Igor Tsukerman
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Editors and Affiliations

  1. Digital Design and Test, Philips Research Laboratories IC Design, Building WAY, Room 4.77 Prof. Holstlaan 4, 5656, AA, Eindhoven, The Netherlands

    Wilhelmus H. A. Schilders

  2. Electronic Design and Tools, Philips Research Laboratories IC Design, Building WAY, Room 3.073 Prof. Holstlaan 4, 5656, AA, Eindhoven, The Netherlands

    E. Jan W. ter Maten

  3. TU/e Dommelgebouw, Magma Design Automation, Den Dolech 2, 5612, AZ, Eindhoven, The Netherlands

    Stephan H. M. J. Houben

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Tsukerman, I. (2004). Toward Generalized Finite Element Difference Methods for Electro- and Magnetostatics. In: Schilders, W.H.A., ter Maten, E.J.W., Houben, S.H.M.J. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55872-6_5

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  • DOI: https://doi.org/10.1007/978-3-642-55872-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21372-7

  • Online ISBN: 978-3-642-55872-6

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