  Topological sensitivities are a very useful tool for determining optimal
designs. The topological derivative of a domain-dependent functional represents
the sensitivity with respect to the insertion of an infinitesimally small hole.
In the gradient-based ON/OFF method, proposed by M. Ohtake, Y. Okamoto and N.
Takahashi in 2005, sensitivities of the functional with respect to a local
variation of the material coefficient are considered. We show that, in the case
of a linear state equation, these two kinds of sensitivities coincide. For the
sensitivities computed in the ON/OFF method, the generalization to the case of
a nonlinear state equation is straightforward, whereas the computation of
topological derivatives in the nonlinear case is ongoing work. We will show
numerical results obtained by applying the ON/OFF method in the nonlinear case
to the optimization of an electric motor.
