A Fast Characteristic Mode Solver for Large-Scale PEC Structures with ACA-QR-SVD Algorithm Based on SMW Formula

In this paper, a method of fast solving characteristic modes (CMs) for large-scale perfect electric conductor (PEC) structures is proposed. In this method, implicitly restarted Arnoldi method (IRAM) is used to compute CMs. In order to accelerate impedance matrix and its inverse matrix-vector products (MVPs) during the IRAM process, adaptive cross approximation (ACA) algorithm is used for impedance matrix compression. Subsequently, QR decomposition and singular value decomposition (SVD) are applied to the compressed matrix. Finally, the Sherman-Morrison-Woodbury (SMW) formula is utilized for the computation of the inverse matrix. Numerical example confirms the accuracy and effectiveness of the proposed method.