Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica (Mar 2020)

Kohn-Vogelius formulation and high-order topological asymptotic formula for identifying small obstacles in a fluid medium

  • Barhoumi Montassar

DOI
https://doi.org/10.2478/auom-2020-0003
Journal volume & issue
Vol. 28, no. 1
pp. 35 – 59

Abstract

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This paper concerns the identification of a small obstacle immersed in a Stokes flow from boundary measurements. The proposed approach is based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. We derive a high order asymptotic formula describing the variation of a Kohn-Vogelius type functional with respect to the insertion of a small obstacle inside the fluid flow domain. The obtained asymptotic formula will serve as very useful tools for developing accurate and robust numerical reconstruction algorithms.

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