Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples

TL;DR

This paper introduces a rigorous isogeometric boundary element method for 3D electromagnetic scattering, including a fast multipole acceleration and industrial-scale numerical examples demonstrating its effectiveness.

Contribution

It provides a novel theoretical analysis and a fast computational approach for electromagnetic boundary problems using isogeometric techniques.

Findings

Proves existence, uniqueness, and quasi-optimality of the isogeometric approach.

Develops a tailored fast multipole method with competitive complexity.

Demonstrates effectiveness through industrial-scale numerical examples.

Abstract

We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within the isogeometric framework, we show existence, uniqueness, and quasi-optimality of the isogeometric approach. For a fast and efficient computation, we then introduce and analyze an interpolation-based fast multipole method tailored to the isogeometric setting, which admits competitive algorithmic and complexity properties. This is followed by a series of numerical examples of industrial scope, together with a detailed presentation and interpretation of the results.