The spatial fourth-order energy-conserved S-FDTD scheme for Maxwell%26apos;s equations

作者：Liang Dong^*; Yuan Qiang

来源：Journal of Computational Physics, 2013, 243: 344-364.

DOI：10.1016/j.jcp.2013.02.040

• Energy-conserved
• S-FDTD
• Spatial fourth-order
• Maxwell%26apos
• s equations

In this paper we develop a new spatial fourth-order energy-conserved splitting finite-difference time-domain method for Maxwell%26apos;s equations. Based on the staggered grids, the splitting technique is applied to lead to a three-stage energy-conserved splitting scheme. At each stage, using the spatial fourth-order difference operators on the strict interior nodes by a linear combination of two central differences, one with a spatial step and the other with three spatial steps, we first propose the spatial high-order near boundary differences on the near boundary nodes which ensure the scheme to preserve energy conservations and to have fourth-order accuracy in space step. The proposed scheme has the important properties: energy-conserved, unconditionally stable, non-dissipative, high-order accurate, and computationally efficient. We first prove that the scheme satisfies energy conversations and is in unconditional stability. We then prove the optimal error estimates of fourth-order in spatial step and second-order in time step for the electric and magnetic fields and obtain the convergence and error estimate of divergence-free as well. Numerical dispersion analysis and numerical experiments are presented to confirm our theoretical results.

• 出版日期2013-6-15