Fast simulation of complicated 3-D structures above lossy magnetic media

A fast numerical method is presented for the simulation of complicated 3-D structures, such as inductors constructed from Litz or stranded wires, above or sandwiched between the planar lossy magnetic media. Making use of its smoothness, the quasi-static multilayer Green's function is numerically computed using finite differences, and its source height dependence is computed using an optimal Toeplitz-plus-Hankel decomposition. We show that a modified precorrected fast Fourier transform method can be applied to reduce the dense linear algebra problem to near-linear time, and that frequency-dependent setups can be avoided to result in a considerable speed-up. Experimental verifications are made for a 16-strand Litz wire coil realistically modeled down to each individual strand. Results are obtained in 2-3 h, showing an excellent agreement to measurements, and can be used to study the impact of transposition patterns in Litz wire construction.