Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Optimal shape design in three-dimensional Brinkman flow using asymptotic analysis techniques

Author: Houcine Meftahi
Journal: Quart. Appl. Math. 75 (2017), 525-537
MSC (2010): Primary 65M32, 76B75, 49Q10, 74S30
DOI: https://doi.org/10.1090/qam/1464
Published electronically: March 16, 2017
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Abstract: The aim of this paper is to reconstruct an obstacle $ \omega $ immersed in a fluid governed by the Brinkman equation in a three-dimensional bounded domain $ \Omega $ from internal data. We reformulate the inverse problem in an optimization one by using a least square functional. We prove the existence of an optimal solution for the optimization problem. We perform the asymptotic expansion of the cost function using a straightforward way based on a penalization technique. An important advantage of this method is that it avoids the truncation method used in the literature. Finally, we make some numerical results, exploring the efficiency of the method.

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Houcine Meftahi
Affiliation: Technical University of Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany
Email: meftahi@math.tu-berlin.de

DOI: https://doi.org/10.1090/qam/1464
Received by editor(s): December 10, 2016
Received by editor(s) in revised form: February 3, 2017
Published electronically: March 16, 2017
Article copyright: © Copyright 2017 Brown University