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

hierarchical basis functions

mass-lumping

higer-order basis functions

finite element method

maxwell's equations

Author

JOHAN WINGES

Chalmers, Signals and Systems, Signalbehandling och medicinsk teknik, Signal Processing

Thomas Rylander

Chalmers, Signals and Systems, Signalbehandling och medicinsk teknik, Signal Processing

AntennEMB, 11-12 March, Göteborg

Subject Categories

Computational Mathematics

Electrical Engineering, Electronic Engineering, Information Engineering

Roots

Basic sciences

Infrastructure

C3SE (Chalmers Centre for Computational Science and Engineering)

More information

Created

10/7/2017