Hierarchical Pattern Exploitation for Fast Solving Finite Periodic Arrays Scattering Problems

The hierarchical pattern exploitation (HPE) is utilized for fast solving electro-magnetic problems of finite periodic composite arrays. The classical framework of the $\mathcal{H}$ -matrix ignores the spatial location of the sub-array to which the basis functions belong. To exploit the periodicity fully, the interaction blocks denoting patterns are characterized and hashed to create a dictionary between patterns and the corresponding sub-matrices. Thanks to large repeated calculations being pruned, the system matrix assembly is accelerated and the required memory is reduced significantly. Numerical examples illustrate the competitive performance of the proposed method.