^{1}, Carsten Unverzagt

^{1}, Andrea Walther

^{2}and Bernd Henning

^{1}

^{1}Measurement Engineering Group, University Paderborn, Warburger Str. 100, 33098 Paderborn, Germany.

^{2}Institute of Mathematics, University Paderborn, Warburger Str. 100, 33098 Paderborn, Germany.

Modeling and simulation of wave propagation may be realized using analytical, semi-analytical or even numerical approaches. In geometrically simple waveguides such as rods, it is still a quite elegant way to employ the analytical Global Matrix Method, firstly presented by Lowe, as no spatial discretization is needed. Therefore, no approximations and no constraints regarding spatial aliasing must be considered. Semi-analytic approaches (such as SAFE, see Bartoli et al. (2006) or SB-FEM, see Gravenkamp et al. (2012)) result in an eigenvalue problem to be solved numerically. For every given frequency one is able to compute a set of corresponding wavenumber solutions. On the other hand, the analytical way ends in a root-finding problem, which is more difficult in a mathematical sense, as you need to compute a complete set of roots within a given interval. Thus, the most concerning restriction of this analytical approach is the root-finding problem. Existing approaches, based on so called mode-tracers, use the physical phenomenon that solutions (roots) appear in a certain pattern (waveguide modes) and thus use known solutions to limit the root finding algorithms search space with respect to consecutive solutions. The limitation of the search space might be uncertain in certain cases. Hence, we propose to replace the mode-tracer with a suitable version of an Interval-Newton method based on INTLAB, see Rump (1999). We extended the interval and automatic derivative computation provided by INTLAB such that this information is also available for ordinary and modified Bessel functions. Results, based on cylindrical waveguides, of the described Interval-Newton approach will be shown and compared to a mode-tracing approach. Pros and cons will be discussed.