A multi-level fast multipole algorithm for low-frequency scattering from a composite object

A scheme is presented to apply the low-frequency multilevel fast. multipole algorithm (LF-MLFMA) to the scattering problem from a composite object. LF-MLFMA was applied to solving the electric field integral equation (EFIE) for the perfect electrical conductor (PEC) scattering problem by W.C. Chew et al. (see "Fast and efficient algorithms in computational electromagnetics", Artech House, p.151-202, 2001). However, for scattering from a composite object, more than one medium is involved and thus LF-MLFMA cannot be applied directly. We use contact-region-modeling (CRM) (Y. Chu et al., IEEE Trans. Antennas Propagat., vol.51, no.10, p.2837-44, 2003) to convert the composite object problem into a multi-region problem and LF-MLFMA is applied region by region. Also, in each region, LF-MLFMA is applied to different forms of the ℒ and 𝒦 operators.