Institute of High Performance Computing

Mesh-Free Methods in Computational Electromagnetics

Established simulation methods for electromagnetic fields generally rely on subdividing the computational domain into elementary cells. These cells – often hexa- or tetrahedral – constitute a mesh that establishes a topological relation between the points in the computational domain at which the fields are computed. While these methods have been successfully used in a wide range of applications and have continuously evolved over the last decades, the fixed topological relation between the computational nodes introduces an inherent disadvantage for several applications such as moving charges and boundaries as well as automatic discretization refinement. These cases often require a re-meshing of the computational domain in conventional simulation methods, which prohibits changes during the simulation.

We anticipate mesh-free methods to bridge this shortcoming. In those methods the fields are computed at more or less random locations in the computational domain that are free to interact with each other. While relatively established in the realm of computational mechanics and astrophysics, mesh-free methods have yet to find their way into electromagnetics. Our initial results are promising. We have implemented a mesh-free code based on the smoothed particle hydrodynamics method (We term our method ‘SPEM – Smoothed Particle Electromagnetics’) for two-dimensional problems.

Transversal Electric Field in a rectangular waveguide cavity that has been excited with a broad-band Gaussian pulse as computed with SPEM.