Topological asymptotic analysis of a diffusive–convective–reactive problem

Abstract

PurposeThe 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/approachThe topological derivative method is used to devise a simple and efficient topology design algorithm based on a level-set domain representation method.FindingsRemarkably simple analytical expressions for the sensitivities are derived, which are useful for practical applications including heat exchange topology design and membrane eigenvalue maximization.Originality/valueThe topological asymptotic expansion associated with a diffusive–convective–reactive equation is rigorously derived, which is not available in the literature yet.