A Novel Sixth Order Energy-Conserved Method for Three-Dimensional Time-Domain Maxwell's Equations
This work provides a high-accuracy, structure-preserving numerical method for computational electromagnetics, addressing the need for long-time stable simulations.
The paper proposes a novel sixth-order energy-conserved method for 3D time-domain Maxwell's equations that preserves multiple conservation laws and achieves sixth-order accuracy in time and spectral accuracy in space, with an error constant of O(T).
In this paper, a novel sixth order energy-conserved method is proposed for solving the three-dimensional time-domain Maxwell's equations. The new scheme preserves five discrete energy conservation laws, three momentum conservation laws, symplectic conservation law as well as two divergence-free properties and is proved to be unconditionally stable, non-dissipative. An optimal error estimate is established based on the energy method, which shows that the proposed method is of sixth order accuracy in time and spectral accuracy in space in discrete $L^{2}$-norm. The constant in the error estimate is proved to be only $O(T)$. Furthermore, the numerical dispersion relation is analyzed in detail and a fast solver is presented to solve the resulting discrete linear equations efficiently. Numerical results are addressed to verify our theoretical analysis.