Gauge techniques in time and frequency domain TLM

Typical features of the Transmission Line Matrix (TLM) algorithm in connection with stub loading techniques and prone to be hidden by common frequency domain formulations are elucidated within the propagator approach. In particular, the latter reflects properly the perturbative character of the TLM scheme and its relation to gauge field models. Internal ‘gauge’ degrees of freedom are made explicit in the frequency domain by introducing the complex nodal Smatrix as a function of operators that act on external or internal fields or virtually couple the two. As a main benefit, many techniques and results gained in the time domain thus generalize straight away. The recently developed deflection method for algorithm synthesis, which is extended in this paper, or the non-orthogonal node approximating Maxwell’s equations, for instance, become so at once available in the frequency domain. In view of applications in computational plasma physics, the TLM model of a relativistic charged particle current coupled to the Maxwell field is traced out as a prototype. MSC-classes: 65C20, 65M06, 76D05