Subdivision-based isogeometric analysis for axisymmetric electromagnetic problems

2026-06-11

AI Summary

This study addresses the challenge of high-accuracy solution of axisymmetric Maxwell eigenvalue problems by introducing, for the first time, Catmull–Clark subdivision-based isogeometric analysis to this domain. By reformulating the problem in an H¹ variational setting and leveraging subdivision surfaces to unify geometric representation and electric field discretization, the proposed method achieves globally C¹-continuous electric field approximations everywhere except at singular points. The approach substantially suppresses numerical noise and successfully computes the eigenmodes of a TESLA 9-cell superconducting cavity, yielding smoother electric field distributions than conventional finite element methods. Numerical experiments confirm the theoretically predicted convergence rates, highlighting the method’s advantages for simulating electromagnetic fields requiring high continuity.

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.

Problem

• axisymmetric electromagnetic problems
• Maxwell eigenvalue problem
• isogeometric analysis
• subdivision surfaces
• electric field continuity

Innovation

• subdivision-based isogeometric analysis
• axisymmetric Maxwell eigenvalue problem
• Catmull-Clark subdivision
• C¹-continuous electric field
• numerical convergence