A multi-objective topology optimisation for 2D electro-magnetic wave problems with the level set method and BEM

We have been investigating applications of a level set-based topology optimisation for wave devices with the boundary element method. For two-dimensional electro-magnetic wave problems, we have, so far, proposed a topology optimisation which can find a configuration of dielectric materials to locally minimise an objective functional such as the intensity of transverse electric (TE) or transverse magnetic (TM) polarised wave with a specific frequency. As an extension of our methodology, this paper presents a multi-objective topology optimisation, which can deal with some objective functionals simultaneously. The present method, for instance, can find a material distribution which can locally minimise the intensity of both TM and TE waves with multiple frequencies. The basic idea of the proposed method is to use the weighted sum or the Kreisselmeier–Steinhause function of the original objective functionals as a new objective functional. We present a derivation of the topological derivative for the new objective functional, and a detailed algorithm of the optimisation process with the derived topological derivative. We also present some numerical examples to illustrate the validity and efficiency of the proposed method.