New energy identities and super convergence analysis of the energy conserved splitting FDTD methods for 3D Maxwell's equations

作者：Gao, Liping; Li, Xingjie; Chen, Wenbin^*

来源：Mathematical Methods in the Applied Sciences, 2013, 36(4): 440-455.

DOI：10.1002/mma.2605

• finite-difference time-domain(FDTD) method
• Maxwell's equations
• energy conservation
• super-convergence

The energy-conserved splitting finite-difference time-domain (EC-S-FDTD) method has recently been proposed to solve the Maxwell equations with second order accuracy while numerically keep the L2 energy conservation laws of the equations. In this paper, the EC-S-FDTD scheme for the 3D Maxwell equations is proved to be energy-conserved and unconditionally stable in the discrete H1 norm. The EC-S-FDTD scheme is of second-order accuracy both in time step and spatial steps, which suggests the super-convergence of this scheme in the discrete H1 norm. And the divergence of the electric field of the EC-S-FDTD scheme in the discrete L2 norm is second-order accurate. Numerical experiments confirm our theoretical analysis.

• 出版日期2013-3-15
• 单位中国石油大学（北京）; 复旦大学