Abstract-The lowering and raising operators of cylindrical harmonics are used to derive the general fast multipole expressions of arbitrary order Hankel functions. These expressions are then employed to transform the dense matrix in the scattering matrix method (SMM) into a combination of sparse matrices (aggregation, translation and disaggregation matrices). The novel method is referred to as fast multipole accelerated scattering matrix method (FMA-SMM). Theoretical study shows FMA-SMM has lower complexity O(N 1.5 ) instead of SMM's O(N 2 ), where N stands for total harmonics number used. An empirical formula is derived to relate the minimum group size in FMA-SMM to the highest order Hankel functions involved. The various implementation parameters are carefully investigated to guarantee the algorithm's accuracy and efficiency. The impact of the cylinders density on convergence rate of iterative solvers (BiCGStab(2) here), memory cost as well as CPU time is also investigated. Up to thousands of cylinders can be easily simulated and potential applications in photonic crystal devices are illustrated. 106 Zhang and Li

Abstract-The finite element hybridized with the boundary integral method is a powerful technique to solve the scattering problem, especially when the fast multipole method is employed to accelerate the matrix-vector multiplication in the boundary integral method. In this paper, the multifrontal method is used to calculate the triangular factorization of the ill conditioned finite element matrix in this hybrid method. This improves the spectral property of the whole matrix and makes the hybrid method converge very fast. Through some numerical examples including the scattering from a real-life aircraft with an engine, the accuracy and efficiency of this improved hybrid method are demonstrated.

Abstract-A novel coupled T-matrix and microwave network approach is proposed for the multiple scattering from parallel semicircular channels. First, an equivalent network is set up to derive the T-matrix of a single channel, in which the S-parameters are derived for the semicircular boundary and the T-matrix of the inclusive cylinders is served as loading matrix of s-parameters. In addition, the T-matrix of the inclusive cylinders is obtained from the T-matrix of each cylinder in its local coordinates using the addition theorem of cylindrical harmonics. Thus, the T-matrix description of semicircular channels could be obtained steadily by the equivalent microwave network theory. Second, the addition theorems in half space are derived and utilized to take account of multiple scattering from several parallel channels. Comparing with previous dual-series eigenfunction solutions, the coupled method simplifies the analysis and could handle much more complex structures step by step. The method is verified by comparison with previous publications and both TM and TE wave illumination are considered.

Abstract-The T-matrix method is used to model semicircular channels filled with chiral materials in a conducting plane. The coupling of both TM and TE polarizations is represented explicitly. Addition theorems in half space are derived and used to take account of the multiple scattering of parallel channels. The boundary conditions are checked for chiral channels to verify the algorithm proposed. Coand cross-polarization effects of chiral materials are investigated by varying several physical and geometrical parameters of the parallel channels.