Electron. J. Diff. Equ., Vol. 2016 (2016), No. 152, pp. 1-8.

High-order topological asymptotic expansion for Stokes equations

Mohamed Abdelwahed, Montassar Barhoumi, Nejmeddine Chorfi

Abstract:
We use the topological sensitivity analysis method to solve various optimization problems. It consists of studying the asymptotic expansion of the objective function relative to a perturbation of the domain topology. This expansion becomes insufficient in some applications when it is limited to the first order topological derivative. We present a new topological sensitivity analysis for the Stokes equations based on a high order asymptotic expansion. The derived result is valid for different class of shape functions.

Submitted February 27, 2016. Published June 20, 2016.
Math Subject Classifications: 35A15, 35B25, 35B40, 49K40.
Key Words: Stokes equations; topology optimization; sensitivity analysis; topological derivative; high order asymptotic expansion.

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Mohamed Abdelwahed
Department of Mathematics
College of Sciences, King Saud University
Riyadh, Saudi Arabia
email: mabdelwahed@ksu.edu.sa
Montassar Barhoumi
Department of Mathematics
ESSTHS, Sousse University, Tunisia
email: montassar.barhoumi2014@gmail.com
Nejmeddine Chorfi
Department of Mathematics
College of Sciences, King Saud University
Riyadh, Saudi Arabia
email: nchorfi@ksu.edu.sa

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