Detection of point-forces location using topological algorithm in Stokes flows

We consider a viscous incompressible fluid under the action of a finite number of particles located inside the flow domain. Each particle exerts a pointwise force on the fluid. The main objective is the detection of point-forces locations through minimization of a given performance functional. The regularity-lack of the state does not allow to derive optimalities conditions and build numerical algorithms. To overcome this difficulty, a relaxation technique is used and the detection problem is formulated as a topological optimization one. A topological sensitivity analysis is derived and efficient numerical algorithms are proposed.