New aspects of the method of lines

Analysis of microstrip patch antennas on arbitrarily shaped multilayers

“…For absorbing boundaries, the exact eigenvalues of the wave equation for the discretized space differ from the analytical values calculated in [10]. They can easily be derived by means of where is the discretization distance and are the eigenvalues given by the finite difference approximation of the operators used in the MoL [5], [12].…”

“…The numerical procedure presented in this paper is an extension of the discrete mode-matching (DMM) method, which originally has been developed to overcome some disadvantages in the method of lines (MoL) [5]. It has already been applied successfully to the analysis of 2-D structures like dielectric waveguides and microstrip lines with planar and non-planar layers as well as planar 3-D structures (planar MPAs) [6]- [9].…”

The Discretized MIE-Formalism for Electromagnetic Scattering

“…The MoL is a special FD technique which allows the analytical incorporation of the radiation condition. In the last years, this mathematical tool has been applied very successfully to guided wave problems with separable but inhomogeneous boundary conditions [38][39][40][41][42]. In this paper it is demonstrated that it can be used also for non-separable boundary value problems.…”

Applying the method of lines and discrete mode‐matching method to non‐planar structures

“…This method has certainly shown its efficiency and accuracy when laterally homogeneous (homogeneous along directions normal to the planar interfaces) structures and separable variable boundaries (SVB) are involved [2]. According to [3,4], the MoL can be equivalently viewed as a variant, with further approximations, of the mode-matching technique. References [3] and [4] also provide a new numerical technique, discrete mode matching (DMM), that closely resembles the MoL (although similar schemes were previously used [5,6]).…”