Research On Mixed Conditionally Stable Finite-Difference Time-Domain Method

Recently,to overcome the limitation of Courant-Friedrichs-Lewy(CFL)time stability conditions of finite-difference time-domain(FDTD)method,unconditionally stable FDTD methods and weakly conditionally stable FDTD methods have been proposed.The computational efficiency is improved,and the application of the FDTD method in complex problems with fine structure is broadened.However,the improvement of computational efficiency is accompanied by the decrease of computational accuracy.Therefore,the structural optimization and the increase of computational accuracy for unconditionally stable FDTD methods and weakly conditionally stable FDTD methods have become important research directions in the field of FDTD method.Based on the characteristics of unconditionally stable FDTD methods and weakly conditionally stable FDTD methods,two unconditionally stable FDTD algorithms for loading lumped elements are proposed firstly,then a novel four-step weakly conditionally stable method is proposed in this dissertation,and several optimized weakly conditionally FDTD methods are proposed to improve the computational accuracy,and expand the application of weakly conditionally stability methods in electromagnetic problems with absorbing boundaries.The work in this dissertation is mainly divided into the following aspects:(?)Based on the five-step LOD(Locally-One-Dimensional)-FDTD method,a five-step LOD-FDTD method including lumped capacitors is proposed,and then a six-step SS-FDTD method including the lumped resistances is proposed,which extends the application of the unconditionally stable FDTD method.(?)By applying the split-step scheme of unconditionally stable FDTD methods to the hybrid implicit-explicit(HIE)FDTD method,a novel four-step three-dimensional(3D)HIE-FDTD algorithm is proposed.Compared with the HIE-FDTD method,the proposed method increases the max value of the time step,thereby improving the computational efficiency.In order to further improve the computational accuracy of the four-step HIE-FDTD algorithm,the four-step HIE-FDTD method is optimized in this dissertation by introducing artificial anisotropic parameters,and an optimized four-step HIE-FDTD method is proposed.The accuracy of the optimized method is greatly improved.In addition,in order to further broaden the application of the four-step HIE-FDTD algorithm,a four-step HIE-FDTD method for loading the NPML(nearly perfect match layer)absorption boundary is proposed.(?)By introducing artificial anisotropic parameters,an optimized weaker HIE-FDTD method is proposed.Under the value of high time step,the numerical dispersion error of the algorithm is significantly reduced.At the same time,the weaker HIE-FDTD method for loading NPML absorption boundary is also studied,which extends the application of the algorithm.(?)By introducing articicial anisotropic parameters,an optimized leapfrog HIE-FDTD method is proposed.The time stability condition of the proposed method is close to that of the leapfrog HIE-FDTD method,and the numerical accuracy of the proposed method is better than that of the leapfrog HIE-FDTD algorithm,which is close to the traditional FDTD algorithm and has higher computational efficiency.Besides,the proposed algorithm very suitable for electromagnetic problems with fine structure in only one direction.