Mathematics

Dr Ravi Prakash
Universidad de Concepcion, Concepcion, Chile

In this talk, we discuss topology optimization problem arises from inverse problem set up. We quickly review the concept of topological derivatives and it’s use in topology op- timization. To be more precise, It is well known that a huge class of inverse problems can be written in the form of overdetermined boundary value problems. Such a difficulty can be overcome by rewriting the inverse problem in the form of an optimization problem. The basic idea of this presentation consist in minimizing a functional measuring the misfit between a given data and a weak solution with respect to the parameters under consider- ation. The topological derivative concept is used. In particular, the objective functional is expanded and then truncated up to the second order term, leading to a quadratic and strictly convex form with respect to the parameters under consideration. Finally, a trivial optimization step will lead to a non-iterative second order reconstruction algorithm which does not depend on any initial guess. As a result, the reconstruction process will become very robust with respect to noisy data