The energy conservative splitting FDTD scheme and its energy identities for metamaterial electromagnetic Lorentz system

Abstract In this paper, we develop a new energy conservative splitting FDTD scheme for solving the metamaterial electromagnetic Lorentz system. The electromagnetic Lorentz model in metamaterials is to describe the resonance of nuclei-bounded electrons in dielectrics by the damped oscillation with a restoring force. Investigating the energy properties for metamaterial electromagnetic Lorentz system is important. The new energy identities of the metamaterial electromagnetic Lorentz system are obtained, which illustrate the conservations of the global energy in Lorentz medium. An efficient energy conservative splitting FDTD scheme is proposed to solve the Lorentz dispersive system in metamaterials. The advantages of the developed scheme lie in energy conservation, unconditional stability, easy implementation, second-order convergence both in time and space as well as superconvergence, which are demonstrated rigorously in the paper. Numerical experiments show the performance of the scheme for modeling the Lorentz models.

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