Topological attitude towards path following, applied to localization of complex dispersion characteristics for a lossy microwave, ferrite-coupled transmission line

We are presenting a certain simplification of the well-known PL-continuation method, applied to continuous curve tracking, for zero set of the map The presented algorithm builds a family of regular (k+1)-dimensional simplices following the set of zeros of the map F. The values of this map are calculated in the vertices of each simplex, then a decision is made as to which of the k-dimensional faces are to be taken as the faces intersected by the zero set F super(-1)(0). The method is based on sign changes of coordinate functions of the map F. The computed values of F are not used in further computations. This allows for limitation of the accuracy required to calculate values of F, i.e. the calculations may be discontinued when the signs of F values may be identified. The algorithm is less restrictive than the classical PL-continuation method and its modifications like the integer labelling. As a consequence it may be observed that in many cases the algorithm is able to follow multiple branches starting from the bifurcation point. The method is applied to the solution of practical 3D problems regarding identification of complex dispersion characteristics of microwave transmission lines. While the function F is being traced, a big computational effort is required for its value at every point of the domain. Therefore every method which can accelerate this process seems to be valuable.