On the detection of several obstacles in 2D Stokes flow: topological sensitivity and combination with shape derivatives

Fabien Caubet (1) , Carlos Conca (2) , Matías Godoy (1, 2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

We consider the inverse problem of detecting the location and the shape of several obstacles immersed in a fluid flowing in a larger bounded domain Ω from partial boundary measurements in the two dimensional case. The fluid flow is governed by the steady-state Stokes equations. We use a topological sensitivity analysis for the Kohn-Vogelius functional in order to find the number and the qualitative location of the objects. Then we explore the numerical possibilities of this approach and also present a numerical method which combines the topological gradient algorithm with the classical geometric shape gradient algorithm; this blending method allows to find the number of objects, their relative location and their approximate shape.

Mots clés: Geometric inverse problem; topological sensitivity analysis; topological gradient; shape gradient; Stokes equations; Kohn-Vogelius functional

Domaines: Optimisation et contrôle [math.OC]

Fabien Caubet, Carlos Conca, Matías Godoy. On the detection of several obstacles in 2D Stokes flow: topological sensitivity and combination with shape derivatives. Inverse Problems and Imaging , 2016, 10 (2), pp.327--367. ⟨hal-01191099⟩