The Finite-difference Time-domain Method And The Finite Volume Time-domain Method For Maxwell's Equations

In this thesis,we study the finite difference method and other computation of two dimensional(2D) Maxwell's equations with non-zero electrical conductivity.The study is divided into three parts:In the first part,we consider the splitting finite-difference time-domain(S-FDTD) methods of the above problem. Two kinds of schemes,S-FDTDI and S-FDTDII are proposed by using the splitting and correcting techniques.Truncation error of the two schemes is derived and shows that S-FDTDI is first order accurate and S-FDTDII is sec-ond order accurate in time. Numerical experiments are carried out and computational results show that S-FDTDII is more accurate than S-FDTDI for simulating a wave guide problem,and that both of the two schemes are unconditionally stable.Furthermore, we give the computational results of Alternating-Direction Implicit Finite-Difference Time-Domain(ADI-FDTD)method for approximating Maxwell's equations with non-zero elec-trical conductivity. The results confirm that S-FDTDII is more accurate and costs less CPU time than ADI-FDTD.In the second part,the splitting exponential-difference time-domain(SE-FDTD) method of the above problemes is firstly proposed by using the splitting and correct-ing techniques.The detailed procedure in computating the approximating solution of the 2D Maxwell's equations with non-zero electrical conductivity is given.Numerical experiments show that SE-FDTD is of good stability and convergent.By comparing the computational results by S-FDTDII and ADI-FDTD,it is found that SE-FDTD is more accurate than the two schemes in simulating the 2D Maxwell's equations with non-zero electrical conductivity. Furthermore,another new splitting exponential finite difference (S-EDTD)method is proposed and applied in simulating a wave guide problem.Com-putational results are displayed which also confirm the efficiency of the method.In the'third part,the splitting finite volume time-domain(S-FVTD)method of the above problems is firstly proposed by using the splitting and correcting techniques. The detailed procedure in cornputating the approximating solution of the 2D Maxwell's equations is given.