An Interpolating Element-free Galerkin Scaled Boundary Method For Waveguide Eigenvalue Problem

As a newly-developed semi-analytical method,the scaled boundary element method is very powerful to deal with singular and unbounded problems.The interpolating element-free Galerkin scaled boundary method(IEFG-SBM)has combined the advantages of the elementfree Galerkin(EFG)method and the scaled boundary method in the frame of improved interpolating moving least-squares(IIMLS)method.In the IEFG-SBM,the solution is analytical in the radial direction and only requires the information of nodes on the boundary,which reduces the spatial dimension by one and greatly decreases the workload of preprocessing.The improved interpolation moving least-squares(IIMLS)method adopts nonsingular weight function,which not only overcomes difficulty of the calculation inconvenience that caused by the singularity of the weight function in the interpolation moving least-squares method by Lancaster,but also overcomes the difficulty in applying the essential boundary conditions.In addition,the number of undetermined coefficients is one less than that in the traditional moving least square method,which can simplify the calculation and improve the calculation precision and efficiency.Based on the improved continued-fraction technique,the interpolation element-free Galerkin proportional boundary method is applied for the first time to the analysis of waveguide eigenvalue problems.The corresponding calculation formulas are derived and the MATLAB programs are compiled.The influence of different order of continuous fractions and different nodal arrangement for the computational accuracy is analyzed.Based on the IEFG-SBM,several typical numerical examples of waveguide eigenvalue problem are analyzed to verify the effectiveness and accuracy of the proposed method for waveguide eigenvalue problem.