极坐标系中的B样条有限元法解波导本征值问题

本文提出了用极坐标系中的Ｂ样条有限元法解波导本征值问题，该方法有两个突出优点：（１）避免某些含曲线边界的波导截面的剖分误差；（２）改善尖角波导的计算精度，本文首先建立了极坐标系中Ｂ样条有限元方程，然后通过对圆形，扇形，双脊加圆形和心形波导本征值问题的实际计算，表明方法的有效性和实有价值。

The Solution of Waveguide Eigenvalue Problems Using the B-Spline Finite Element Method in Polar Coordinates

The B-spline finite element method in polar coordinates for solving some waveguide eigenvalue problems is described. The technique has two main advantages: (1)Avoiding thesubdivision errors at some curved boundaries 1 (2)Improvement on the computational accuracy for asharp corner existed in the waveguide cross section. The B-spline finite element equations in the 0p coordinate system are established. The method is used to solve the eigenvalue problems in circular,sector,double-ridged circular,and heart waveguides. The numerical results are compared withthe exact solutions and those obtained by the traditional finite element method in polar coodinates,which demonstrates that the present method is convenient to implement,and leads to a high computational accuracy and substantial saving in computer storage and time.