The gradient based topological optimization tools introduced during the
last ten years tend naturally to modify the topology of a domain by
creating small holes inside the domain.
Once these holes have been created, they usually remain
unchanged, at least during the topological phase of the optimization
algorithm. In this paper, a new asymptotic expansion is introduced which
allows to decide whether an existing hole must be removed or not for
improving the cost function. Then, two numerical examples are presented:
the first one compares topological optimization with standard shape
optimization, and the second one, issued from a lake oxygenation
problem, illustrates the use of the new asymptotic expansion.