Showing papers by "Antoine Laurain published in 2010"

On a Bernoulli problem with geometric constraints

Abstract: A Bernoulli free boundary problem with geometrical constraints is studied. The domain $\Om$ is constrained to lie in the half space determined by $x_1\geq 0$ and its boundary to contain a segment of the hyperplane $\{x_1=0\}$ where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed and this paper is devoted first to the study of geometric and asymptotic properties of the solution and then to the numerical treatment of the problem using a shape optimization formulation. The major difficulty and originality of this paper lies in the treatment of the geometric constraints.

A shape and topology optimization technique for solving a class of linear complementarity problems in function space

Abstract: A shape and topology optimization driven solution technique for a class of linear complementarity problems (LCPs) in function space is considered. The main motivating application is given by obstacle problems. Based on the LCP together with its corresponding interface conditions on the boundary between the coincidence or active set and the inactive set, the original problem is reformulated as a shape optimization problem. The topological sensitivity of the new objective functional is used to estimate the "topology" of the active set. Then, for local correction purposes near the interface, a level set based shape sensitivity technique is employed. A numerical algorithm is devised, and a report on numerical test runs ends the paper.