Topological asymptotic analysis of a diffusive–convective–reactive problem

Abstract

Purpose The purpose of this study is sensitivity analysis of the L2-norm and H1-seminorm of the solution of a diffusive–convective–reactive problem to topological changes of the underlying material. Design/methodology/approach The topological derivative method is used to devise a simple and efficient topology design algorithm based on a level-set domain representation method. Findings Remarkably simple analytical expressions for the sensitivities are derived, which are useful for practical applications including heat exchange topology design and membrane eigenvalue maximization. Originality/value The topological asymptotic expansion associated with a diffusive–convective–reactive equation is rigorously derived, which is not available in the literature yet.