The Topological-shape Sensitivity Method and Its Applications in Topology Design and Inverse Problems

Abstract. The topological derivative gives the sensitivity of a cost function when the domain under consideration is perturbed by the introduction of a hole. In particular, the topological derivative was already applied for solving topology design of several engineering problems. Alternatively, this same idea can also be used to calculate the sensitivity of the problem when, instead of a hole, a small incrustation is introduced at a point in the domain. Therefore, the topological derivative concept is wider. In fact, it also can be applied to inverse problems and to simulate physical phenomena with changes on their configuration. Thus, in the present paper, the topological derivative computed through the novel Topological-Shape Sensitivity Method is applied in a to 2D and 3D heat conduction, torsion with creep and inverse conductivity problem.