The shape and topological optimizations connection Original Research Article

In 1973, Jean Céa introduced a topological shape optimization algorithm based on a fixed point method. The recent topological gradient concept provides a mathematical justification of Céaʹs powerful method. The aim of the topological gradient is to compute the sensitivity of a cost function when we drill a little hole in the domain. Some optimality conditions are derived when classical shape gradient and topological gradient are used simultaneously, and numerical results are shown both in Mechanics and Electromagnetics.