# An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations

## TL;DR

This paper presents an isogeometric boundary element method using compatible B-splines for electromagnetic scattering, enabling high-order accuracy and direct CAD integration for complex geometries.

## Contribution

It introduces a novel compatible B-spline construction for electromagnetic boundary element analysis that directly utilizes CAD data, improving efficiency and accuracy.

## Key findings

- Successfully verified with Mie scattering and NASA almond problems.
- Achieves efficient computation with H-matrices and Bézier extraction.
- Handles complex geometries directly from CAD without meshing.

## Abstract

We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform Rational B-splines to represent model geometry and compatible B-splines to approximate the surface current, and adopts the isogeometric concept in which the basis for analysis is taken directly from CAD (geometry) data. The approach allows for high-order approximations and crucially provides a direct link with CAD data structures that allows for efficient design workflows. After outlining the construction of div- and curl-conforming B-splines defined over 3D surfaces we describe their use with the electric and magnetic field integral equations using a Galerkin formulation. We use B\'ezier extraction to accelerate the computation of NURBS and B-spline terms and employ H-matrices to provide accelerated computations and memory reduction for the dense matrices that result from the boundary integral discretization. The method is verified using the well known Mie scattering problem posed over a perfectly electrically conducting sphere and the classic NASA almond problem. Finally, we demonstrate the ability of the approach to handle models with complex geometry directly from CAD without mesh generation.