Analysis Of Waveguide Propagation Characteristics By Generalized Finite Difference Method

The generalized finite difference method is a regional meshless method that has become popular in recent years.This algorithm uses multivariate function Taylor series expansion and least squares fitting technology to convert the derivative values of the function at any node of the computational domain into the form of the weighted sum of the function values of adjacent nodes,which overcomes the dependence of the traditional finite difference method on the grid.The thesis mainly studies the following aspects:Firstly,this thesis derives the numerical discrete process of the generalized finite difference method when solving nonlinear partial differential equations,analyzes three important factors that affect the accuracy of the method,and proposes improvements to the construction of the point cluster in the method.Then the generalized finite difference method is used to solve the static electromagnetic field problem,and the actual engineering situation is simulated by adding random point disturbance and data error disturbance.Secondly,this thesis applies the generalized finite difference method to analyze the propagation characteristics of the waveguide and gives the general steps to solve the eigenvalue problem of the waveguide.The good performance of this method is proved by comparison with other common waveguide problem solving methods.In addition,the propagation characteristics of various waveguides with complex cross sections and the cutoff wavenumbers of three-dimensional resonators are calculated accurately.Thirdly,this thesis introduces an improved version of the generalized finite difference method.This method neither relies on a weighting function,nor is it based on the least squares fitting technique.This thesis also gives the method to deal with the matrix singularity in the actual calculation and an ingenious way to deal with the second type of boundary conditions.Finally,this thesis extends the improved generalized finite method to the three dimensions.