Higher-Order Finite Element Solver for Maxwell’s Equations

Conference poster, 2014

We present a finite element formulation equipped with higher-order basis functions for the electric and magnetic field, which are used together to approximate the electromagnetic field in Maxwell’s equations. The first type of basis functions are formulated on hexahedral elements, where mass lumping is feasible for the special case of brick-shaped elements. Our implementation allows for automatic generation of arbitrary order p for the field approximation, where the lowest-order approximation is the linear representation with p = 1. The second type of basis functions are formulated on tetrahedral elements, which allows for meshing of arbitrary geometries. These basis functions are of hierarchical type and are implemented for orders p=1 to 4 for complete order spaces as well as incomplete (gradient reduced) order spaces. We test our basis functions on eigenvalue problems and find that the eigenvalues are i. reproduced with the correct multiplicity ii. converge towards the analytical result with an error that is proportional to ℎ^2p where ℎ is the element size