Subdivision-based isogeometric analysis for axisymmetric electromagnetic problems

Abstract

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.