Electron Cyclotron Resonance simulations on unstructured meshes using Vector Finite Elements

An elegant algorithm for solving Maxwell’s equations is the finite difference time domain (FDTD) algorithm, sometimes referred to as “Yee’s algorithm”. With some simple adaptations, this algorithm can be used both in the time domain and in the frequency domain. It is extremely easy to implement, and has second order convergence out of the box. However, simulation domains with complex shapes are often easier to model using an unstructured triangular mesh, for which the FDTD algorithm is not well designed.

Vector finite elements on the other hand can easily be used to discretize Maxwell’s equations on such meshes. They allow for anisotropic and inhomogeneous media, are easy to expand to three dimensions, and they satisfy the no-divergence condition from Maxwell’s laws by design. Additionally, they have as advantage over traditional nodal based finite elements that it is easier to work with sharp conducting edges, material interfaces and discontinuities, and spurious solutions are less of an issue.

A proof-of-concept two-dimensional solver for the transverse magnetic polarization using vector elements is implemented in MATLAB. The solver is validated with test cases for which analytic solutions are available, showing convergence speed matching predictions from literature. The code is then applied to a cold, magnetized plasma, in order to study a simple Electron Cyclotron Resonance (ECR) scenario, and the results are compared with PLASIMO, a plasma modelling software package.