A Topology Optimisation of Wave Absorbers in Two-Dimentional Electro-Magnetic Field with an Accelerated BEM by the \({\mathscr {H}}\)-Matrix Method

In this study, we propose a new topology optimisation for electro-magnetic wave absorbers. We define an objective function as the amount of time-averaged inward Poynting’s vector on boundary of absorbing material, and consider to maximise the objective function. The sensitivity of the objective function is strictly derived as a variation of the objective function when an infinitesimal hole is created in the design domain by using the adjoint variable method. For the efficient and accurate computation of the topological derivative, we employ the boundary element method and the \({\mathscr {H}}\)-matrix method. In the boundary element method, radiation condition is automatically satisfied with the help of the Green function, which enables us to treat problems defined in the infinite domain strictly. Also, by using the accelerated LU decomposition with the \({\mathscr {H}}\)-matrix method to solve the algebraic equations derived by the BEM, we achieve the fast computation of the sensitivity. We apply the sensitivity analysis to the level-set based topology optimisation.