Non-uniform grid based fast direct solver for quasi-planar scatterers

The computational analysis of electromagnetic scattering from quasi-planar objects is of great practical interest. There is especially growing interest in fast integral equations-based direct solvers since they facilitate repeated solutions for various excitations/incident fields. An efficient direct solver for elongated geometries has been proposed. Also fast direct solvers for quasi-static and moderately high frequency regimes have been developed. Following many ideas of these earlier works, we present an algorithm based on the non-uniform grid (NG) approach for the analysis of scattering from quasi-planar objects and provide a derivation of the computational complexity for the dynamic quasi-planar case. The proposed algorithm is applicable to arbitrary frequency regimes and can be employed to accelerate existing method of moments (MoM) codes.