Hybrid non-uniform grid based fast global boundary conditions for electromagnetic simulations for concave scatterers

Differential equation based techniques, such as finite element and finite difference methods [1] are often preferred for analyzing electromagnetic scattering by targets involving inhomogeneous media. Customarily, truncation of the computational domain, as required in these methods, is achieved using local Absorbing Boundary Conditions (ABCs) such as the Mur or the Perfectly Matched Layer (PML) type as long as the boundary surface is convex. The convexity requirement translates into a sizeable "white space" when treating an essentially concave geometry and hence implies a significant additional computational cost. Alternatively, boundary integral formulations allow for arbitrary shaped exterior boundaries at the expense of global, rather than local, formulation. It has been shown in [2,3], though, that the combination of global ABCs with suitable fast integration algorithms provides a viable alternative to local formulations. The method relies on surface integration with the added benefit of a two level Non-uniform Grid (NG) algorithm, introduced in [4]. This algorithm is shown to reduce the computational cost of evaluating the boundary integrals from O(N²)to O(NL^1.5), while a multilevel algorithm will ultimately attain an asymptotic complexity of O(NlogN), N being the number of boundary unknowns. In this work, the method presented in [3] is hybridized with a local ABC for enhanced accuracy.