This paper applies a subdivision-based isogeometric method to solve the axisymmetric Maxwell eigenvalue problem. The reduction to an $H^1$-formulation allows to use a Catmull-Clark construction for both geometry and field discretization. The approach yields a numerical solution for the electric field, which is $C^1$-continuous everywhere except at extraordinary vertices. This is demonstrated by computing the eigenmodes of a TESLA 9-cell cavity, showing smoother fields with less numerical noise than conventional methods. The convergence rate of the method is numerically analyzed and is in agreement with rates observed in the literature.

翻译：本文提出一种基于细分的等几何方法，用于求解轴对称麦克斯韦特征值问题。通过将问题简化为$H^1$公式，可采用Catmull-Clark构造同时处理几何与场离散。该方法求得的电场数值解在奇异顶点处连续，而在其余区域满足$C^1$连续性。通过计算TESLA九腔腔体的特征模式验证了该方法，结果表明其场分布更平滑，数值噪声低于传统方法。对收敛率进行了数值分析，所得结果与文献中观测到的收敛率一致。