A Modified HODLR Solver Based on Higher Order Basis Functions for Solving Electromagnetic Scattering Problems

In this letter, we present a novel fast direct solver based on a modified hierarchically off-diagonal low-rank (M-HODLR) matrix format with higher order basis functions for analyzing electromagnetic scattering by electrically large objects. The M-HODLR matrix compresses the far-group submatrices by an extended admissibility condition, which enhances the efficiency and accuracy of the original HODLR. To further alleviate the burden of the fast direct solution of the conventional surface integral equation (SIE), the higher order hierarchical vector basis (HOHVB) functions defined over a curved surface are employed. To account for HOHVB, an efficient assembly scheme based on patch coupling is developed to accelerate the adaptive across approximation implementation in M-HODLR. The proposed method can significantly reduce the computational time and memory cost of a conventional SIE solver. Several numerical examples are presented to validate the accuracy and efficiency of the proposed method in solving electrically large objects. Owing to the characteristics of HOHVB, different patch sizes or basis functions with different orders can be chosen according to the local geometry of the object. Therefore, the proposed method is very appealing for large- and multiscale simulations.