Energy-conserved splitting FDTD methods for Maxwell's equations

In this paper, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell's equations in two dimensions are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the discrete divergence of electric fields for these two schemes. For the EC-S-FDTDII scheme, we prove that the discrete divergence is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes are non-dissipative. Numerical experiments confirm well the theoretical analysis results.