Abstract
Recently, cloaking devices have collected a lot of attentions as an aplication of metamaterials. The cloaking is a technology to hide an object by arranging cloaking materials around the object. The light goes around the object by the cloaking materials and the object will be invisible. Many researchers have been trying to develop the cloaking devices by periodical arrangement of micro structures, which is not necessarily "optimal" since the arrangement is often designed by trial and error prcess. To realise an "optimal" cloaking device, the topology optimisation is considered to be a promissing design tool. The topology optimisation is the most flexible configuration optimisation method and can find an optimal configuration based on mathematical verification. In this method, the finite element method (FEM) is generally used. The FEM, however, takes a lot of numerical costs to generate a mesh and cannot treat an open domain strictly. From these points of view, the boundary element method (BEM) can be said more suitable for the topology optimisation for cloaking devices. In the BEM, mesh is generated only on the boundary and open domain can be evaluated exactly. In this study, we apply a BEM-based topology optimisation to the design problem of carpet cloaking devices. In the optimisation problem, an objective function is defined on a lot of observation points around the object to be hidden. The configuratin will therefore be complicated, which causes the large number of optimisation steps and accumulation of analysis error. In order to avoid this problem we employ the quadratic element to discretize the boundary. Through numerical examples, we confirmed the efficiencly of the proposed method.
