Guest editorial
Antônio André Novotny, Sebastián M. Giusti, Samuel Amstutz
Abstract
On the topological derivative method and its applications in computational engineering The topological derivative (or topological gradient) concept has been designed in order to give a precise and quantitative information on the sensitivity of a user-given shape functional with respect to topological domain perturbations. Specifically, it appears in the first term of the asymptotic expansion of the shape functional with respect to a small parameter measuring the size of the perturbation under consideration, typically a hole, an inclusion, a source-term or a crack. It naturally complements the more classical notion of shape derivative that accounts for smooth shape variations. As a matter of fact, the two concepts can be explicitly related through the expression of the topological derivative as the singular limit of the shape gradient