Energy-Conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations in Three Dimensions

In this paper, we develop and analyze efficient energy-conserved splitting finite-difference time-domain (FDTD) schemes for solving three dimensional Maxwell's equations in electromagnetic computations. All proposed energy-conserved splitting finite-difference time-domain (EC-S-FDTD) algorithms are strictly proved to be energy-conserved and unconditionally stable, and they can be computed efficiently. Rigorous convergence results are obtained for the schemes. The EC-S-FDTDII schemes are proved to have second order in both time step and spatial steps, while the EC-S-FDTDI schemes have second order in spatial steps and first order in time step. The error estimates are optimal, and especially the constant in the error estimates is proved to be only $O(T)$. Numerical experiments confirm the theoretical analysis results.