Improved US-FDTD Method For Two-dimensional Maxwell Equations In Dissipative Medium For Maxwell’s Equations

This thesis studies the unconditionally stable finite diference time-domain scheme(US-FDTD) for the Maxwell equations with zero electrical conductivity and the un-conditionally stable finite diference time-domain scheme (US-FDTD) for the Maxwellequations with non-zero electrical conductivity.The content is divided into three chapters.The first chapter mainly introduces the background of the thesis including the math-ematical model, research methods and the significance of this research in theory andindustrial applications.In the second chapter the US-FDTD method is analyzed and found it is dissipa-tive and first order accurate. To reduce the unusual perturbation error of US-FDTDthe improved unconditionally stable finite diference time-domain scheme (IUS-FDTD)is proposed by adding a term. It is proved that the new method IUS-FDTD for the2DMaxwell equations is unconditionally stable and non-dissipative by the Fourier method.By the derivation of the truncation error it is shown that IUS-FDTD is second orderaccurate, one order higher than US-FDTD. Numerical experiments are carried out tocompare the simulation results of the two schemes, the computational results confirmthat the improved scheme IUS-FDTD has smaller numerical dispersion errors and ismore stable and accurate than the former scheme US-FDTD.The third chapter gives the unconditional stability of the improved finite diference time-domain scheme (IUS-FDTD) for the Maxwell equations in a lossy medium. Com-parison of stability, truncation error and efciency of US-FDTD with those of IUS-FDTDare presented.Numerical experiments are carried out, and the computational results showthat the accuracy in time and in space of the latter one is one order higher than that ofthe former one.