Research Of The Conservation Of Finite Difference Methods For Maxwell Equations

Since energy conservation is an important property of electromagnetic fields,derivation of numerical energy identities and study energy conservation of a numerical scheme are then significant in numerical methods of Maxwell equations.Among them,the finite difference method(called FDTD)is one of the earliest methods to apply Maxwell equations.For different boundary conditions,the energy conservation study of this numerical method plays an important role in solving electromagnetic problems.In this paper,we study the new conservation of the Yee scheme under this condition based on the periodic boundary conditions.The numerical identity of the two dimensions is derived,and the conservation,error estimation and numerical verification of the scheme are analyzed.The detailed contents of the thesis are listed as follows:The numerical conservation of the three-dimensional Yee scheme under periodic boundary conditions(PBD)is derived.In the sense of new conservation,the convergence of the Yee scheme is studied and the error estimation formula is given.The proof scheme is second-order convergence and approximately conservation under discrete H~1,H~2 norm.It is revealed that the curl and the second curl of the electromagnetic field have conservation under the L~2norm.Numerical experiments are carried out and computational results demonstrated the analysis on new conservation and super convergence.