Analysis And Simulation Of Leapfrog ADI Scheme For Electromagnetic Wave Propagation In Metamaterials

N umerical simulation of electromagnetic wave propagation in metamaterials is of great help to the research and analysis of metamaterials.In this paper,two kinds of unconditionally stable schemes for simulating electromagnetic wave propagation in metamaterials are studied,one of them is the Leapfrog ADI-FDTD scheme,the other is a new scheme which based on the idea of Leapfrog scheme.Firstly,energy stability of the existing Leapfrog ADI-FDTD scheme for Maxwell's equation is analyzed,it is proved that the scheme is unconditionally stable and second-order convergent in time and space,and the scheme is extended to the simulation of metamaterials.Then,a new scheme which can be combined with the finite element method easily is constructed by using the idea of Leapfrog method,it is proved that the new scheme is unconditionally stable and second-order convergent in time and space,and the new scheme is extended to the simulation of metamaterials.Finally,some numerical experiments are designed to test the properties of these two schemes and their simulation effect of electromagnetic wave propagation in metamaterials.The experimental results agree with the theoretical results and the simulation effect of these two schemes are well.The main innovations of this paper are as follows:1.Energy equation of the Leapfrog ADI-FDTD scheme for the Maxwell equation is found,it is proved that the scheme is unconditionally stable and second order convergent by using the energy equation.2.The Leapfrog ADI-FDTD scheme is extended to the simulation of metamaterials.3.A new unconditionally stable scheme for Maxwell's equation is constructed,the new scheme can be combined with the finite element method easily.4.Theoretical analysis and numerical experiments are prove the unconditional stability and convergence of the new scheme5.The new scheme is extended to the simulation of metamaterials.6.Numerical experiments show that the new algorithm is about 50% faster than the traditional crank-Nicolson(CN)scheme under the same conditions.