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The topological asymptotic expansion for the quasi-Stokes problem. (English) Zbl 1072.49027

Summary: We propose a topological sensitivity analysis for the quasi-Stokes equations. It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors in an eutrophized lake.

MSC:

49Q10 Optimization of shapes other than minimal surfaces
49Q12 Sensitivity analysis for optimization problems on manifolds
74P15 Topological methods for optimization problems in solid mechanics
76D55 Flow control and optimization for incompressible viscous fluids
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