3-D numerical mode-matching (NMM) method for inhomogeneous media

The numerical mode-matching (NMM) method as an efficient algorithm has previously been used to model various multi-region vertically and cylindrically stratified inhomogeneous media. It has been shown that the NMM method is more efficient than direct use of the finite element method (FEM) to solve these problems. However the applications of the NMM method have been limited to two-dimensional (2-D) and two-and-a-half-dimensional (2.5-D) problems. In this work, we extend the NMM method to three-dimensional (3-D) inhomogeneous media, and apply the method to model electric impedance problems using the electrostatic approximation. Although this work models the electric potential distribution, the solution procedure presented here can be directly applied to wave problems.