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Journal of Scientific Computing
Published in: Journal of Scientific Computing 2/2019

18-08-2018

Optimal Shape Design for the p-Laplacian Eigenvalue Problem

Authors: Seyyed Abbas Mohammadi, Farid Bozorgnia, Heinrich Voss

Published in: Journal of Scientific Computing | Issue 2/2019

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Abstract

In this paper, a shape optimization problem corresponding to the p-Laplacian operator is studied. Given a density function in a rearrangement class generated by a step function, find the density such that the principal eigenvalue is as small as possible. Considering a membrane of known fixed mass and with fixed boundary of prescribed shape consisting of two different materials, our results determine the way to distribute these materials such that the basic frequency of the membrane is minimal. We obtain some qualitative aspects of the optimizer and then we determine nearly optimal sets which are approximations of the minimizer for specific ranges of parameters values. A numerical algorithm is proposed to derive the optimal shape and it is proved that the numerical procedure converges to a local minimizer. Numerical illustrations are provided for different domains to show the efficiency and practical suitability of our approach.
previous article Superconvergence Analysis and PPR Recovery of Arbitrary Order Edge Elements for Maxwell’s Equations
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Metadata
Title
Optimal Shape Design for the p-Laplacian Eigenvalue Problem
Authors
Seyyed Abbas Mohammadi
Farid Bozorgnia
Heinrich Voss
Publication date
18-08-2018
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 2/2019
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-018-0806-7

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