Convergence Acceleration of Characteristic Mode-Based Basis Function Method for Connected Array Structures

Abstract

The characteristic mode (CM)-based basis function method for connected array structures has been proven to be an efficient numerical approach. However, it generates a matrix equation for which iterative methods will only slowly converge due to the truncation effect of discarding buffers. Singular value decomposition (SVD) is first implemented to enhance the orthogonality between the characteristic currents of the connected array elements. The original characteristic currents are replaced by the newly constructed global basis functions so that the condition number of resultant reduced-order matrix is greatly reduced. In addition, a preconditioner is applied for the reduced-order impedance matrix, which can greatly improve the convergence speed of iterative method. Numerical examples are given to show that the proposed methods can significantly reduce the iterative steps and the calculation time with encouraging accuracy.