Optimising stop-bands in periodic waveguides using genetic algorithms and wave finite element method

Abstract

In this paper, we propose using the wave finite element method and genetic algorithms to design periodic waveguide structures with optimal stop-bands. Instead of modelling waveguides using the standard finite element method, we use the wave finite element method to model the waveguides. The wave and finite element method is based on using periodic structure theory and the finite element model of a unit cell of the waveguide to describe the waveguide's motion in terms of wave amplitudes rather than in terms of physical degrees of freedom. This results in a numerically efficient model of the waveguide which can be used in optimisation studies. In particular, the focus of this paper is on the optimisation of stop-bands in the waveguides which leverage this property of periodic structures. Genetic algorithms will be used to optimise the stop-bands. A numerical example where analytical models can be obtained will be used to demonstrate the efficacy of the proposed approach and its potential.