An introduction to the topological derivative

Samuel Amstutz (1, 2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

This paper provides a self-contained introduction to the mathematical aspects of the topological derivative. Full justifications are given on simple model problems following a modern approach. Methodological aspects and extensions are discussed, in relation with the literature on the field.

Mots clés: topological derivative; topology optimization; shape optimization

Domaines: Optimisation et contrôle [math.OC]

Samuel Amstutz. An introduction to the topological derivative. Engineering Computations, 2021. ⟨hal-03311517v2⟩