A parametric convex meshfree formulation for approximating the Helmholtz solution in circular coaxial waveguide

Abstract

The application of convex meshfree approximation to the time-harmonic electromagnetic wave propagation analysis of a waveguide with non-convex cross section such as the circular coaxial waveguide remains unsolved. This paper introduces a parametric convex meshfree formulation for the circular coaxial waveguide analysis. The present method reformulates the convex meshfree approximation on the basis of a special parametric space-an extended parametric domain. The new parametric domain ensures a one-to-one geometric mapping using the convex meshfree approximation and allows the convex meshfree method to be applied to the oscillatory type of Helmholtz equation for circular coaxial waveguide analysis. Both transverse electric and transverse magnetic mode studies are conducted using the present method, and results are compared with the standard bilinear finite element method.where ∇ 2 = ∂ 2 /∂x 2 + ∂ 2 /∂y 2 denotes the two-dimensional Laplacian operator. When ϕ = E z , it represents the TE field. For this case, the field E z (x, y) is independent of z. Similarly, ϕ = H z accounts for the TM field. The symbol k c is the cutoff wavenumber. 552L.-F. WANG