Conformal and multi-scale time-domain methods: From tetrahedral mesh to meshless discretisation

Numerical methods applied in Cartesian grids have become workhorses for general purpose time-domain electromagnetic simulations because of their simplicity, efficiency and scalability. Implementations often consider specific treatments for curved and slanted boundaries, as well as sub-cell models and sub-gridding schemes. As alternative, methods based on unstructured discretisation, such as a tetrahedral mesh, have never truly become mainstream techniques despite their remarkable capabilities for accurate multi-scale and conformal modelling. This paper firstly reviews the development of a particular conformal time-domain method applied in tetrahedral meshes, namely the Finite-Volume Time-Domain method, and illustrates its potential for multi-scale problems in a selected example. The second part of the paper points out a novel class of methods which are amenable to conformal time-domain implementation on clouds of points. These so-called “meshless methods” do not require an explicit mesh definition, and open new perspectives towards future applications involving multi-scale multi-physics problems.