Computing roots for the analytic modeling of guided waves in acoustic waveguides

Computer aided simulation of guided acoustic waves in single- or multilayered waveguides is an essential tool for several applications of acoustics and ultrasonics (i.e. pipe inspection, noise reduction). To simulate wave propagation in geometrically simple waveguides (plates or rods), one may employ the analytical global matrix method [1]. This requires the computation of all roots of the determinate of a certain submatrix. The evaluation of all real or even complex roots is actually the methods most concerning restriction. Previous approaches base on so called mode-tracers which 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 searchspace with respect to consecutive solutions. As the limitation of searchspace might be unstable in some cases, we propose to replace the mode-tracer with a suitable version of an interval Newton method based on Intlab [2]. To apply this interval based method, we extended the interval and derivative computation provided by Intlab such that corresponding information is also available for Bessel functions used in the circular model (rods) of acoustic waveguides. We present numerical results of a simple acoustic waveguide and discuss extensions required for more realistic scenarios.