The mixed-form fast multipole algorithm for broadband electromagnetic simulations

Electromagnetic physics is approximately divided into three regimes: the low-frequency regime where circuit physics dominates, the mid-frequency regime where wave physics dominates, and the high-frequency regime where ray physics dominates. From conventional methods, when the frequency is low, the fast multipole algorithm (FMA) based on multipole expansion is very effective and the representation of the field is direction independent (Zhao, J.S. and Chew, W.C., 2000; Chew, 2001). On the other hand, for mid frequencies, plane-wave based fast multipole algorithms are feasible for efficient computation (Greengard, L. et al., 1998). Hence, a combination of multipoles and plane waves might provide a complete solution for broadband applications. A mixed-form FMA is implemented. The FIPWA (fast inhomogeneous plane-wave algorithm) translator (Jiang, L.J. and Chew, Micro. Opt. Tech. Lett., vol.40, no.2, p.117-22, 2004) is also introduced into the mixed-form FMA to replace the standard closed form translators from the diagonalization of the three-dimensional translation formula. As a general extension, a numerically computed translator based on singular value decomposition (SVD) is also presented.