Numerical Analysis of AVF Methods for Three-Dimensional Time-Domain Maxwell's Equations

We propose two schemes [AVF(2) and AVF(4)] for Maxwell's equations, by discretizing the Hamiltonian formulation with Fourier pseudospectral method for spatial discretization and average vector field method for time integration. Both AVF(2) and AVF(4) hold the two Hamiltonian energies automatically, while being energy-, momentum- and divergence-preserving, unconditionally stable, non-dissipative and spectral accurate. Rigorous error estimates are obtained for the proposed schemes. The numerical dispersion relations are also investigated. Numerical experiments support well the theoretical analysis results. The proposed schemes are valid for the regular domain, but invalid for the domain with complex geometries.