Gradient-based shape optimisation of ultra-wideband antennas parameterised using splines

Methodology enabling the gradient-based optimisation of antennas parameterised using B-splines is presented. Use of the spline parametrisation allows us to obtain versatile new shapes, whereas the geometry can be represented with a small set of design variables. Moreover, good control over admissible geometries is retained. Advantages of gradient-based optimisation methods are quick convergence, and the fact that the obtained design can be guaranteed to be a local optimum. Focus of this study is to present techniques that enable the computation of exact gradients of the discrete problem, even though the complexity of the geometries does not permit establishing analytical expressions for the mesh node locations as a function of the design variables. As a numerical example the authors consider the optimisation of an ultra-wideband (UWB) antenna over the frequency band 3-10-GHz, and show that gradient-based optimisation method and spline parameterised geometries constitute an efficient design methodology for antennas. Choice of the initial shape does not seem to play a significant role in this case, since two optimisations starting from completely different initial guesses produce essentially the same results.