Efficient Characteristic Mode Analysis for PEC Objects Using Sherman–Morrison–Woodbury Formula-Based Algorithm

In characteristic mode analysis (CMA), solving the characteristic modes (CMs) from the generalized eigenvalue problem takes the main part of the workload. In this letter, the algorithm based on the Sherman–Morrison–Woodbury (SMW) formula is embedded into the implicitly restarted Arnoldi method to improve the efficiency of solving the CMs. In this method, the impedance matrix is compressed into a product of block-diagonal matrices by using the SMW formula with adaptive cross approximation algorithm. Benefiting from the efficient compression, calculating the inverse matrix of the impedance matrix and the matrix vector products related to the solution of the generalized eigenvalue problem is accelerated. Consequently, the computational time and memory requirement in CMA are both reduced. Some numerical examples are demonstrated to show the accuracy and efficiency of the proposed method.