| In this thesis, the splitting finite diference time domain method (S-FDTDsee[11,12]) and the symmetric energy-conserved splitting finite diference time domain method(EC-S-FDTD, see [13,14,15]) are extended to Maxwell’s equations in polar coordinates.Two methods for Maxwell equations in polar coordinates are proposed: splitting finitediference time domain method (PS-FDTD) and symmetric splitting finite diferencetime domain method (PSS-FDTD). The computational procedures of the splitting finitediference time domain method in polar coordinates with the perfectly electric conduct-ing boundary conditions are given. The extrapolated method is used to deal with thesingularity. The equivalent scheme of PS-FDTD is derived and the truncation error isanalyzed. By the energy methods it is proved that PS-FDTD is unconditionally sta-ble and convergent. To validate the method, numerical experiments are provided andconfirm the efciency of the PS-FDTD method. In addition, how to use the symmetricsplitting finite diference time domain method to solve the Maxwell equations in polarcoordinate system and how to treat the values of the field at the singular point are pro-vided. Numerical examples verified the theoretical analysis.The text is divided into three chapters.In the first chapter, we describes the background and significance of the researchproject, including introduction to some splitting finite diference methods for solvingMaxwell’s equations in the Cartesian coordinate system, and the model in polar coordi-nate system. In the second chapter, the splitting FDTD method for Maxwell equations in Carte-sian coordinate system is extended to the two dimensional Maxwell equations in polarcoordinates and a new finite diference method, called PS-FDTD, is proposed. The sys-tems of linear equations for PS-FDTD to solve the Maxwell equations in polar coordinateswith the perfectly electric conducting boundary conditions are derived. The extrapola-tion method is used to deal with the singularity. To analyze PS-FDTD the equivalentscheme of it is derived and the truncation error is obtained by Taylor theorem. It isproved by the energy methods that PS-FDTD is unconditionally stable and convergent.Finally, numerical experiments are provided to confirm the efciency of the PS-FDTDmethod by simulating the circular waveguide problem.In the third chapter, the symmetric energy-conserved splitting finite diference timedomain method are used in simulating the Maxwell’s equations in polar coordinates, andthe computational procedure of solving a circular waveguide problem with the perfectlyelectric conducting boundary conditions is presented. The singularity of the field is dealtwith by the extrapolation method. Finally, numerical examples verified the efectivenessof the method. |
