A Numerical Comparison of an Isogeometric and a Classical Higher-Order Approach to the Electric Field Integral Equation

TL;DR

This paper compares a novel spline-based isogeometric boundary element method with a classical higher-order approach for solving the electric field integral equation, focusing on accuracy and computational efficiency.

Contribution

It introduces a new isogeometric boundary element method and provides a detailed numerical comparison with classical methods for electromagnetic scattering problems.

Findings

Isogeometric approach achieves high convergence orders.

Efficiency of the isogeometric method is comparable or superior to classical methods.

Accuracy per degree of freedom is favorable for the proposed approach.

Abstract

In this paper, we advocate a novel spline-based isogeometric approach for boundary elements and its efficient implementation. We compare solutions obtained by both an isogeometric approach, and a classical parametric higher-order approach via Raviart-Thomas elements to the solution of the electric field integral equation; i.e., the solution to an electromagnetic scattering problem, promising high convergence orders w.r.t. pointwise error. We discuss both, the obtained accuracy per DOF, as well as the effort required to solve the corresponding system iteratively, on three numerical examples of varying complexity.