Study On Alternative Direction Implicit Finite Difference Time Domain Method For Solving Maxwell's Equations

Maxwell's equations are very impoytant theoretical achievements in physics from the 19th century,They are highly summarized and generalized in the theory of electromagnetic field and play a fundamen-tal role in the application of electromagnetic field.Maxwell's equations reveal the symmetrical beauty in the process of electric and magnetic field transformation,which is fully expressed in modern math-ematical form.With the continuous development of the Maxwell equations,it has been widely used in modern power technology and electronic technology,electromagnetic scattering,antenna simulation,seismic wave detection and other practical problems.Methods for solving Maxwell equations have also been developed,such as Finite Element Time Domain Method,Discontinuous Galerkin Method,Finite Difference Time Domain Method,etc.In this paper,the Maxwell equations are solved based on Finite Difference Time Domain Method,Firstly,the Finite Difference Time Domain Method is introduced and the one-dimensional and two-dimensional differential dispersion scheme is derived;Because the electromagnetic field is distributed in the whole space,the solution space is always finite in practice.In order to transform the infinite s-pace into a finite space and reduce the reflection generated by Wave propagation,the absorption boundary conditions are introduced and introduced accordingly;Its numerical stability and numerical dispersion characteristics are discussed and analyzed.Because the time step and space step must satisfy the stability condition when using Finite Differ-ence Time Domain Method to solve Maxwell equations,which makes the solution of practical problems have certain limitations.Therefore,in order to overcome the limitation of stability conditions,a new difference scheme is constructed in this paper,that is,an implicit difference scheme based on alternat-ing directions,called the alternating direction implicit time-domain finite difference method,the implicit difference scheme for one-dimensional and two-dimensional problems is derived,and the introduced ab-sorption boundary is improved on the basis of the Finite Difference Time Domain Method to make it have better absorption effect on electromagnetic waves,and its stability is analyzed at the same time.Finally,the numerical calculation formulas obtained by these two methods are verified and numerically simulated.