The Splitting Methods Of Maxwell's Equations And Their Numerical Analysis

In this thesis, we study the splitting finite di?erence time domain methods and thefinite volume methods of two dimensional(2D) Maxwell,s equations with non-zero elec-trical conductivity. The study is divided into four parts:First ,We import the background and meanings of selected topic of the research .Introduce the model of the research problem and some numerical methods of this equa-tions.Second, we extend the splitting FDTD schemes (S-FDTD, see J. Comput. Appl.Math. 205(2007)) into the case that the conductivity is not zero. By using adding termsto the equations and the symmetry of electric and magnetic fields in computation wepropose two kinds of schemes: S-FDTDII and symmetric splitting FDTD(SS-FDTD)for the Maxwell's equations with non-zero conductivity and give the analysis of energyconservation, stability and convergence on SS-FDTD. Numerical experiments are carriedout and by comparing the computational results by S-FDTDII and ADI-FDTD, it isfound that EC-SSFDTD is more accurate than the two schemes in simulating the 2DMaxwell,s equations with non-zero electrical conductivity.Third, we derive the energy identities of the energy conserved splitting finite-di?erencetime-domain methods (EC-SSFDTD) of the two dimensional Maxwell,s equations withnonzero conductivity (σ= 0)in the discrete H1 norms. By these identities it is provedthat this scheme is unconditionally stable and convergent in the discrete H1 norms.In the fourth part, the splitting finite volume time-domain (S-FVTD) method ofthe above problems is firstly proposed by using the splitting and correcting techniques. The detailed procedure in computating the approximating solution of the 2D Maxwell,sequations is given.