Unstructured Block Meshing in Time-Domain TLM Method with Local Time-Step

Many problems in nature and engineering are multiscale. Thus, for adequately representing structure geometrical details, one has to use small cell sizes which impose small time-step values. In addition, if the mesh is irregular but structured it might lead to exhaustive computer expenditure and higher dispersion. The alternate approach is to use block-meshing techniques which allow fine discretization in regions with fine details and coarse discretization in regions with smoothly-varying details. However, the mesh is said "unstructured" in this case and beside spatial interpolation that provokes some additional error, the choice of time-steps is of crucial importance when time-domain methods are considered. The main consequence is the long-term stability of the process. In this article, we present an algorithm that allows the use of local time-steps unlike the global time-step approach usually considered. Some experiments are presented to show the behavior and performances of a block-meshing algorithm used in time-domain TLM computation with local time-step.