Discussions on numerical accuracy of the vector finite element methods using the vector‐shape function

Abstract

AbstractWith respect to the vector finite element method for analysis of the electromagnetic waveguide, the numerical accuracy and the numerical efficiency are investigated for three types of variational expressions with which spurious‐free vector finite element analyses are possible. For the linear, isotropic, and lossless waveguide, these methods are compared with regard to the physical and mathematical properties and the electromagnetic field construction of the guided mode using vector‐shape functions represented by complete polynomials of identical form. Two of the variational expressions use different‐order shape functions for the two transverse components and the longitudinal component. Four types of computation methods can be constructed by selection of the electromagnetic field components. Another method uses the shape functions with identical orders in four transverse components.Numerical computations have been carried out for various waveguides. From the results of the computations, it is shown that the physical and mathematical properties of the two variational expressions using the three transverse and longitudinal components are equivalent and that the numerical accuracy of the propagation constant of each guided mode depends on the magnitude of the longitudinal field components used in an actual computation method unlike the method using four transverse components. By using the results, optimum selection of computation methods can be realized.