Efficient 3D-FEM-calculation of electromagnetic wave propagation processes

The aim of this investigation was to develop a more efficient alternative to the conventional approach of calculating three-dimensional electromagnetic wave propagation processes – implemented in the finite element method (FEM).

This has been achieved by a bicomplex formulation of boundary value problems in conjunction with a conformal discretization of the electromagnetic wave field. Here, an extension of modern discretization techniques within the framework of geometric algebra proved helpful. The investigation of the bicomplex formulation was carried out in the software MATLAB® and – like a formulation based on commonly used Helmholtz equations – compared to the exact analytical solutions. In all examples discussed, an improvement in numerical accuracy over the Helmholtz equation approach was achieved with the same discretization of the solution space.

The presented approach represents a profitable alternative for certain problems. Furthermore, the techniques used to discretize the field quantities and to complexify the differential equation can be advantageously applied to other physical problems.

T. Reum, H. Toepfer
Investigation of electromagnetic wave propagation in the bicomplex 3D-FEM using a wavenumber Whitney Hodge operator
COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. ahead-of-print, No. ahead-of-print, 2022
doi.org/10.1108/COMPEL-03-2021-0078

Contact: M.Sc. Thomas Reum