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Scaled boundary finite element approach for waveguide eigenvalue problem

机译：波导特征值问题的尺度边界有限元方法

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摘要

The scaled boundary finite element method (SBFEM) is developed for the solution of waveguide eigenvalue problems, which combines the advantages of the finite element method and the boundary element method. A new variational principle formulation to derive the SBFEM equations for waveguide is developed. An equation of the dynamic stiffness matrix for waveguide representing the relationship between the `flux?? and the longitudinal field components at the discretised boundary is established. A continued fraction solution in terms of eigenvalue is obtained. By using the continued fraction solution and introducing auxiliary variables, the flux??longitudinal field relationship is formulated as a system of linear equations in eigenvalue then a generalised eigenvalue equation is obtained. The eigenvalues of rectangular, L-shaped, vaned rectangular and quadruple corner-cut ridged square waveguides are calculated and compared with analytical solution and other numerical methods. The results show that the present method yields excellent results, high precision and less computational time and rapid convergence is observed.
机译：针对波导特征值问题，提出了比例边界有限元方法（SBFEM），该方法结合了有限元方法和边界元方法的优点。提出了一种新的变分原理公式来推导波导的SBFEM方程。波导动态刚度矩阵方程，表示“通量”之间的关系并建立了离散边界处的纵向场分量。获得关于特征值的连续分数解。通过使用连续分数解并引入辅助变量，将通量-纵向场关系公式化为特征值线性方程组，然后得到一个广义的特征值方程。计算了矩形，L形，叶片矩形和四角切角脊形方形波导的特征值，并将其与解析解和其他数值方法进行了比较。结果表明，该方法取得了良好的效果，精度高，计算时间短，收敛速度快。

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