The adaptive cross approximation algorithm for general half-space scattering problems

The general half-space scattering problems (i.e., the scatterers are straddling the interface of a half-space) are analyzed using the algebraic adaptive cross approximation (ACA) algorithm. As the object is naturally separated into two parts by the interface, two different mesh densities are required due to the contrast of the two background materials. Therefore, two multilevel tree structures are set up individually in the two regions. For the same-side interactions, the grouping strategy is the same as that for free-space problems; while for the different-side couplings, we present a z-dependent grouping scheme. The numerical example is demonstrated to validate the proposed method.