Discontinuous Galerkin boundary element methods for complex electromagnetic applications

Summary form only given. This work investigates the use of discontinuous Galerkin (DG) methods for the integral equation based solution of the time-harmonic Maxwell equations. It allows the solution of the combined field integral equation using discontinuous Galerkin boundary element spaces. Namely, square-integrable, L², vector function spaces will be employed for both trial and testing functions. Therefore, it supports various types and shapes of elements, non-conformal discretizations and non-uniform orders of approximation. Initial work has been done to examine the possibility of developing a discontinuous Galerkin boundary element method for solving the electromagnetic wave scattering problem from non-penetrable objects. It is based on the interior penalty formulation and a novel derivation of the weak formulation is introduced. This research will further investigate the IEDG method for penetrable composite objects composed of piecewise homogeneous materials. Two further topics to be discussed in this work are: (i) the application of domain decomposition methods as effective preconditioners for the solution of IEDG matrix equations, and (ii) the uniqueness, stability and quasi-optimal convergence of the discrete solutions. The merits of proposed method are justified through challenge real-world applications including an electromagnetic wave scattering from an electrically large multi-scale aircraft, and a high-definition composite unmanned aerial vehicle.