抄録
In this paper, we present a rigorous derivation of the topological derivative related to non-linear eigenvalue problems, which can be extended to design problems for photonic/phononic structures. It is shown that the topological derivative of the eigenvalue is associated with the eigenpair of the relevant eigenvalue. The validity of the topological derivative is confirmed with numerical examples by the SS method, in which a fast direct solver with the fast multipole representation of the boundary integral equation is utilised. Also, an example of material configuration design by the topological derivative in which the eigenfrequency is manipulated is shown.
