An introduction to the topological derivative

Abstract

PurposeThis paper provides a self-contained introduction to the mathematical aspects of the topological derivative.Design/methodology/approachFull justifications are given on simple model problems following a modern approach based on the averaged adjoint state technique. Extensions are discussed in relation with the literature on the field.FindingsClosed expressions of topological derivatives are obtained and commented.Originality/valueSeveral cases are covered in a unified and didactic presentation. Some elements of proof are novel.