A Direct Solution for Fine Structures Combining the Characteristic Basis Function Method and the Accelerated Cartesian Expansion Algorithm

A direct scheme for the rigorous computation of electromagnetic scattering problems involving finely structured targets is presented. This scheme integrates the characteristic basis function method (CBFM) with the accelerated Cartesian expansion (ACE) algorithm. Due to the convergence difficulties of the impedance matrix in the iterative solution caused by the fine structure, the CBFM is employed to compress the unknowns for direct solution; while the ACE algorithm is utilized to accelerate the construction of the reduced matrix. Given that ACE is based on Taylor series expansion, the proposed method can avoid the low-frequency breakdown problem. Moreover, compared to purely algebraic operations, the ACE is rooted in physical principles, leading to significant improvements in computational efficiency. Numerical results are provided to validate the proposed method.