Two Energy-Conserved Splitting Methods for Three-Dimensional Time-Domain Maxwell's Equations and the Convergence Analysis

Abstract

We devote the present paper to high-accuracy energy-preserving S-AVF(2) and S-AVF(4) schemes for the three-dimensional time-domain Maxwell's equations, based on the exponential operator splitting technique, the Fourier pseudospectral method, and the averaged vector field method. To obtain the present schemes, the key is to propose the splitting methods for Maxwell's equations, in which all subsystems should hold the same Hamiltonian. The proposed schemes are energy-preserving, high-order accurate, and unconditionally stable, while being implemented explicitly. Both schemes capture four energy invariants simultaneously. Rigorous error estimates of the schemes are established in the discrete $L^2$-norm. The theoretical results show that the S-AVF(2)/S-AVF(4) scheme converges with spectral accuracy in space and second-order/fourth-order accuracy in time, respectively. Numerical results support the theoretical analysis.