Algorithm Studies On Unconditional-Stable Locally-One-Dimensional Finite-Difference Time-Domain Method

The time step size of locally-one-dimensional(LOD)based unconditionally-stable Finite-difference time-domain(FDTD)method is not restricted by Courant-Friedrich-Levy(CFL)condition.The LOD-FDTD solver has the potential to analyze mini-device and complex electromagnetic issue.The two questions of the LOD-FDTD method while it solveengineering practice are the larger numerical dispersion and complex simulation.The purpose of this thesis is to study the two aspects.Some optimized techniques and ameliorations are employed by LOD-FDTD method.The novel unconditionally-stable FDTD methods with low dispersion error are proposed.Then,the LOD-FDTD method are applied into the simulation of the complex mixed EM-Circuit ProblemThe basic theory of the LOD-FDTD method is expatiated in the beginning of the thesis.Then,several driving sources of calculating EMC/EMI issues are introduced.Finally,Three numerical examples are discussed and analyzed in order to validate the unconditionally-stable,effectiveness and accuracy of the LOD-FDTD method.The unconditionally stability and dispersion errors analysis of the standard LOD-FDTD method are analyzed.Several factors affecting numerical dispersion errors are discussed.There are angles of propagation,scan frequency,cells per wavelength,CFL number.The numerical dispersion error of the two order central difference is larger then the FDTD method.To circumvent the problem,higher order LOD-FDTD method is presented.Then,the unconditionally stability and high-efficiency of the higher order LOD-FDTD method are proved and numerical dispersion errors are analyzed.In order to further reduce the numerical dispersion errors,a parameter optimized LOD-FDTD method is proposed.Two different parameter optimized methods are employed,one is nonline parameter optimized method which based on local parameter optimized and the other one is simulated annealing parameter optimized method based on global parameter optimized.Then,the numerical dispersion errors of the two proposed methods and the conventional LOD-FDTD method are discussed under the same factors.Absorbing boundary conditions(ABC)of the LOD-FDTD method are analyzed.Starting with the Mur ABC of the LOD-FDTD method,a improved Mur ABC is proposed.The results show that the improved method reduces the reflection error.The reflection error increased when cell density change bigger.To resolve the problem,the Convolutional Perfectly Matched Layer ABC of the LOD-FDTD method is developed.Finally,a novel three-dimensional(3D)locally-one-dimensional unconditionally-stable FDTD method is proposed.Compared with the conventional LOD-FDTD method,the novel method provides simple algorithm implementation and low numerical dispersion.Then,reflection error of the novel unconditionally-stable LOD-FDTD improved-Mur method and LOD-FDTD-CPML are analyzed.After a theoretical study conducted algorithm,Some research works about the LOD-FDTD method for physical simulation of microwave devices are developed.LOD-FDTD algorithms of lump models are derived and applied into the simulation transient response of transmission line.Transient voltage responses of double/multi-conductor transmission line model are analyzed by some examples respectively.LOD-FDTD method is applied into the simulation of the slot structure.Shielding effectiveness of the metallic cavity with slot structure is calculated by LOD-FDTD method.The multi-arithmetic is developed which mixed LOD-FDTD method and modified nodal approach(MNA)to solve mixed EM-Circuit Problem.It is verified by dealing with typical complex EMC problem.