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Coarsening of Boundary-element Spaces

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Abstract

In this paper, we will present composite boundary elements (CBE) for classical Fredholm boundary integral equations. These new boundary elements allow the low-dimensional discretisation of boundary integral equations where the minimal number of degrees of freedom is independent of the, possibly, huge number of charts which are necessary to describe a complicated surface.

The applications are threefold: (a) The coarse-grid discretisation by composite boundary elements allow the use of multigrid algorithms for solving the fine-grid discretisation independently of the number of patches which are necessary to describe the surface. (b) If the accuracy requirements are moderate, the composite boundary elements allow the low-dimensional discretisation of the integral equation. (c) A posteriori error indicators can be applied already to a low-dimensional discretisation, which do not resolve the domain, to obtain a problem-adapted discretisation.

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Authors and Affiliations

  1. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22–26, 04103, Leipzig, Germany

    W. Hackbusch

  2. Advanced Computer Vision GmbH – ACV Tech Gate Vienna, Donau-City-Strasse 1/4. Stock, 1220, Wien, Austria

    M. Löhndorf

  3. Institut für Mathematik, Universität Zürich, Winterthurerstr 190, 8057, Zürich, Switzerland

    S. A. Sauter

Authors
  1. W. Hackbusch
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  2. M. Löhndorf
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  3. S. A. Sauter
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Correspondence to W. Hackbusch.

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Hackbusch, W., Löhndorf, M. & Sauter, S.A. Coarsening of Boundary-element Spaces. Computing 77, 253–273 (2006). https://doi.org/10.1007/s00607-005-0160-0

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