On the Treatment of Arbitrary Boundary Conditions Using a Fast Direct ${\mathcal {H}}$ -Matrix Solver in MoM

This communication adapts the formalism of hierarchical (H-) matrices to the direct solution process (LU decomposition) of the method of moments (MoM) in the frequency domain. A novel clustering approach based on physical constraints is presented and extended to treat dielectric bodies as well as arbitrary boundary conditions. Comparisons with other numerical methods are provided. The analyses show a considerable speedup of the computation times and a significant reduction of required memory compared with the traditional MoM solution process, especially for highly resonant structures where iterative solvers like the multilevel fast multipole algorithm show poor convergence.