IsoGeometric Approximations for Electromagnetic Problems in Axisymmetric Domains

TL;DR

This paper introduces a novel numerical method combining spectral Fourier approximation and IsoGeometric Analysis for efficient and accurate electromagnetic simulations in axisymmetric domains, reducing computational costs while maintaining high accuracy.

Contribution

The paper presents a new combined Fourier and IsoGeometric Analysis approach for electromagnetic problems in axisymmetric domains, with proven stability and high-order convergence.

Findings

High order convergence demonstrated through numerical benchmarks

Significant reduction in computational cost due to mode decoupling

Method maintains stability and accuracy in complex geometries

Abstract

We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the radial and axial directions. This combination allows to blend the flexibility and accuracy of IGA approaches with the advantages of a Fourier representation on axisymmetric domains. It also allows to reduce significantly the computational cost by decoupling of the computations required for each Fourier mode. We prove that the discrete approximation spaces employed functional space constitute a closed and exact de Rham sequence. Numerical simulations of relevant benchmarks confirm the high order convergence and other computational advantages of the proposed method.