A Low-Frequency-Stable Higher-Order Isogeometric Discretization of the Augmented Electric Field Integral Equation

TL;DR

This paper introduces a spline-based higher-order isogeometric discretization for the augmented electric field integral equation, achieving low-frequency stability and high accuracy without meshing.

Contribution

It presents a novel higher-order isogeometric discretization method for the augmented electric field integral equation that avoids low-frequency breakdown and enhances accuracy.

Findings

Method maintains stability at low frequencies.

Numerical experiments show high accuracy.

Extension to higher-order basis functions improves convergence.

Abstract

This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an exact representation of the model geometry described in terms of non-uniform rational B-splines without meshing. This is particularly useful when high accuracy is required or when meshing is cumbersome for instance during optimization of electric components. The augmented electric field integral equation is adopted and the deflation method is applied, so the low-frequency breakdown is avoided. The extension to higher-order basis functions is analyzed and the convergence rate is discussed. Numerical experiments on academic and realistic test cases demonstrate the high accuracy of the proposed approach.