Iterative Calculation of Characteristic Modes Using Arbitrary Full-Wave Solvers

An iterative algorithm is adopted to construct approximate representations of matrices describing the scattering properties of arbitrary objects. The method is based on the implicit evaluation of scattering responses from iteratively generated excitations. The method does not require explicit knowledge of any system matrices (<italic>e.g.</italic>, stiffness or impedance matrices) and is well-suited for use with matrix-free and iterative full-wave solvers, such as FDTD (Finite-difference time-domain method), FEM (Finite element method), and MLFMA (Multilevel Fast Multipole Algorithm). The proposed method allows for significant speed-up compared to the direct construction of a full transition matrix or scattering dyadic. The method is applied to the characteristic mode decomposition of arbitrarily shaped obstacles of arbitrary material distribution. Examples demonstrating the speed-up and complexity of the algorithm are studied with several commercial software packages.