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

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  • 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 $\Omega$ 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.
    Mathematics Subject Classification: Primary: 49Q10, 35R30, 49Q12; Secondary: 76D55.


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