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A new fictitious domain method in shape optimization

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Abstract

The present paper is concerned with investigating the capability of the smoothness preserving fictitious domain method from Mommer (IMA J. Numer. Anal. 26:503–524, 2006) to shape optimization problems. We consider the problem of maximizing the Dirichlet energy functional in the class of all simply connected domains with fixed volume, where the state equation involves an elliptic second order differential operator with non-constant coefficients. Numerical experiments in two dimensions validate that we arrive at a fast and robust algorithm for the solution of the considered class of problems. The proposed method can be applied to three dimensional shape optimization problems.

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Authors and Affiliations

  1. Institut für Numerische Mathematik, Technische Universität Dresden, Zellescher Weg 12–14, 01062, Dresden, Germany

    Karsten Eppler

  2. Institut für Numerische Mathematik, Universität Bonn, Wegelerstr. 6, 53115, Bonn, Germany

    Helmut Harbrecht

  3. Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Mario S. Mommer

Authors
  1. Karsten Eppler
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  2. Helmut Harbrecht
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  3. Mario S. Mommer
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Correspondence to Helmut Harbrecht.

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Eppler, K., Harbrecht, H. & Mommer, M.S. A new fictitious domain method in shape optimization. Comput Optim Appl 40, 281–298 (2008). https://doi.org/10.1007/s10589-007-9076-2

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  • DOI: https://doi.org/10.1007/s10589-007-9076-2

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