Topological optimization method for a geometric control problem in Stokes flow

We consider a geometric control problem in Stokes flow. We propose a simple and fast algorithm using topological optimization techniques. Our approach consists in studying the variation of a cost function with respect to the insertion of a small obstacle in the domain. Theoretical results are derived in two and three dimensional case and valid for large class of cost functions. Some numerical experiments are presented in 2D and 3D showing the efficiency of our approach.