Abstract
The scaled boundary finite element method(SBFEM) is a semi-analysis method, combing the advantages of boundary element method and finite element method. However, in solving the quadruple corner-cut ridged elliptical(QCRE) waveguide, the traditional SBFEM employ the Lagrange polynomials as the basis functions which leads to the curved boundaries cannot be exactly represented and the continuity order across element is low. In this paper, a non-uniform rational B-spline (NURBS) enhanced SBFEM is firstly extended to solve the QCRE waveguide, which can exactly describe the curved boundaries, reduce the spatial dimensions by one and obtain analytically results in the radial direction. According to its symmetry, only a quarter of the ridged elliptical waveguide needs to be simulated and subdivided into several subdomains. The curved boundaries and straight boundaries of the subdomains are described and discretized by the NURBS and Lagrange basis functions, respectively. The side-face boundaries do not need to be discretized. Then, the NURBS enhanced SBFEM governing equation of the waveguide eigenvalue problem is derived based on the vibrational principle and scaled boundary coordinate transforming. Finally, a generalized eigenvalue equation respecting to the cut-off wave numbers is established by introducing the boundary dynamic stiffness and employing a continued fraction solution. Numerical results verify the high computational efficiency and accuracy of the NURBS enhanced SBFEM with exactly describing the curved boundaries. The influence of the corner-cut on the cut-off wave numbers of several modes and single-mode bandwidth are investigated in details.
Highlights
In order to meet the performance requirements of micro-wave and millimeter-wave communication systems, it is necessary to continuously explore and research new waveguides with special cross-section shapes
The traditional SBFEM employ the Lagrange polynomials as the basis functions which leads to the curved boundaries cannot be exactly represented and the continuity order across element is low
In the traditional SBFEM, the whole outer boundary b is discretized by the Lagrange basis function
Summary
In order to meet the performance requirements of micro-wave and millimeter-wave communication systems, it is necessary to continuously explore and research new waveguides with special cross-section shapes. The traditional SBFEM employ the Lagrange polynomials as the basis functions which leads to the curved boundaries cannot be exactly represented and the continuity order across element is low.
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