A Basis-Free Loop-Star Preconditioned Reduced-Domain Layered-Medium Integral-Equation Solver

Layered-medium integral-equation (LMIE) solvers that incorporate large metallizations into Green's functions can significantly accelerate electromagnetic analysis of electronic packages. Similar to their counterparts for homogeneous backgrounds, however, these reduced-domain LMIE solvers are limited by the low-frequency breakdown of the electric-field integral-equation (EFIE) operator. To combat the breakdown and keep iteration counts low when solving the system of equations resulting from reduced-domain LMIE formulations, a basis-free loop-star decomposition, combined with a frequency-scaled sparse preconditioner, is applied to the diagonal blocks of the impedance matrix corresponding to the EFIE operator in a blockwise manner. The accuracy and efficiency of the preconditioned LMIE solver are validated using a benchmark packaging problem.