In this paper, an efficient approach is proposed to analyse the interior boundary value problem in a spheroidal cavity with perfectly conducting wall. Since the vector wave equations are not fully separable in spheroidal coordinates, it becomes necessary to double-check validity of the vector wave functions employed in analysis of the vector boundary problems. In this paper, a closed-form solution has been obtained for the eigenfrequencies f{sub}(ns0) based on TE and TM cases. From a series of numerical solutions for these elgenfrequencies, it is observed that the f{sub}(ns0) varies with the coordinates of the parameter f in the form of f{sub}(ns0)(ζ)=f{sub}(ns)(0) [1+g{sup}(1)/ζ{sup}2+g{sup}(2)/ζ{sup}4+g{sup}(3)/ζ{sup}6+...]. By means of least squares fitting technique, the values of the coefficients, g{sup}(1), g{sup}(2), g{sup}(3), ..., are determined numerically. It provides analytical results, and fast computations, of the eigenfrequencies and the results are valid although ζ is large (e.g., ζ≥100).
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机译：本文提出了一种有效的方法来分析具有完美导电壁的球腔内的内部边界值问题。由于载体波方程在球形坐标中不完全可分离，因此需要在分析矢量边界问题时双重检查矢量波函数的有效性。本文基于TE和TM案例获得了针对特征频率f {sub}（ns0）的闭合形式解决方案。从一系列用于这些ELGENFREQUECERIES的数值解决方案，观察到F {sub}（ns0）与参数f的参数f的坐标以f {sub}（ns0）（ns0）（ns0）= f}（ ns）（0）[1 + g {sup}（1）/ζ{sup} 2 + g {sup}（2）/ζ{sup} 4 + g {sup}（3）/ζ{sup} 6+ ......]。通过最小二乘拟合技术，数值确定系数G {sup}（1），g {sup}（1），g {sup}（3），g {sup}（3），g {sup}（3），......。它提供了分析结果，并且快速计算，虽然ζ大（例如，ζ≥100），但结果是有效的。
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