In this paper, we develop and analyze efficient energy-conserved splitting finitedifference 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.
Introduction.The main aim of numerical methods is to solve scientific and engineering problems effectively and accurately. Among them, one kind of successful method is the alternating direction implicit (ADI) methods, which decompose the original multidimensional problem into some one-dimensional subproblems to reduce the computational complexities and CPU time (see, e.g., [3,5,20,21,25] and more recent works [4, 6, 12, 19], etc.). The technique has been applied to solve high-dimensional large scale problems, and the procedure can be solved by a parallel computing system.The numerical computation of Maxwell's equations has recently been playing an important role in electromagnetic science and in many application areas such as the microelectronic field and microwave, radio frequency, wireless, optical circuit, and antenna techniques. The famous finite-difference time-domain (FDTD) method, also called Yee's scheme and first proposed by Yee in 1966 (see [26]), has been one important numerical algorithm for solving Maxwell's equations in three dimensions. The convergence analysis of the method was strictly carried out in later papers [14,16]. Yee's scheme employs a fully staggered space-time grid, is explicit and of second order convergence in both time and spatial steps, and has been widely used in computational