Topological asymptotic analysis of a diffusive–convective–reactive problem

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.

The topological derivative method is used to devise a simple and efficient topology design algorithm based on a level-set domain representation method.

Remarkably simple analytical expressions for the sensitivities are derived, which are useful for practical applications including heat exchange topology design and membrane eigenvalue maximization.

The topological asymptotic expansion associated with a diffusive–convective–reactive equation is rigorously derived, which is not available in the literature yet.