Scaled boundary finite element method for the eigen analysis of waveguide
Received:November 01, 2011  Revised:February 14, 2012
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KeyWord:scaled boundary finite element method  waveguide  eigenvalue  variational principle
林皋 大连理工大学 建设工程学部,大连 ;大连理工大学 海岸和近海工程国家重点实验室,大连
刘俊 大连理工大学 建设工程学部,大连 ;大连理工大学 海岸和近海工程国家重点实验室,大连
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      Scaled boundary finite element method (SBFEM) is used for determining waveguide eigenva-lue.The key characteristic of SBFEM is that governing equations are discretized on boundary of computational domain by SBFEM,which reduces spatial dimension by one,and analytical procedure is applied in the reduced direction.A weighted residual approach and coordinate transformation between scaled and cartesian coordinate are used to derive the SBFEM equations for both TE and TM mode cases of waveguide based on Helmholtz Equation.The dynamic stiffness matrix of waveguide is also obtained as a continued fraction solution.By using this solution and introducing auxiliary variables,the standard procedures can be applied to perform eigen analysis of waveguide.The eigenvalues of rectangular,L-shaped and vaned rectangular waveguide are calculated and compared with analytic solution and other numerical methods.The results show that the present method yields excellent results,high precision and less amount of computation time. And rapid convergence is observed as the order of continued fraction increases.The transmission characteristics of a quadruple corner-cut ridged square waveguide have been analyzed.