A modified MoL algorithm with faster convergence and improved computational efficiency

Appendix A: Discretisation Schemes and Difference Operators

“…A fourth-order approximation for planar microwave structures is first investigated in [14]. The authors of [15] and [16] explicitly give higher-order approximations for the necessary first derivative. These authors claim that different transformation matrices are necessary for the second-and fourth-order approximations.…”

“…The authors of [15] and [16] explicitly give higher-order approximations for the necessary first derivative. In fact, in [15] and [16] the same matrices are used in both cases. It will be shown in this section that this is not the case.…”

A modified method of lines for open and shielded structures

“…In order to find relevant criteria for their First, the shielded microstrip transmission line shown in Fig. 1 is considered [7], and its propagation characteristics are solved using both the original MOL and the MMOL. The relative error in the effective dielectric constant is plotted in Figs.…”

“…To overcome this problem, nonequidistant discretization schemes have been considered [5][6], but they are not systematically applicable. Another approach was pn~posed by Xiao et al [7], however, it is more complicated than the co:nventional MOL. In this paper, a Modified MOL M O L ) is studied that satisfies efficiently the edge condition through the use of transformation functions [8-91.…”