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Shape optimization approach to numerical solution of the Obstacle Problem

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Abstract

We discuss an algorithm for the numerical solution of the Obstacle Problem in which the coincidence set is considered as the prime unknown. Domain functionals are defined for which the coincidence set serves as the minimizing element. Their gradients are computed (in the sense of the material derivative), and the gradient descent method employed to minimize these functionals. Numerical example is given.

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Authors and Affiliations

  1. Department of Mathematics, University of Iowa, 52242, Iowa City, IA, USA

    A. Bogomolny

  2. School of Engineering, Old Dominion University, USA

    J. W. Hou

Authors
  1. A. Bogomolny
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  2. J. W. Hou
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Bogomolny, A., Hou, J.W. Shape optimization approach to numerical solution of the Obstacle Problem. Appl Math Optim 12, 45–72 (1984). https://doi.org/10.1007/BF01449033

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