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

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 Bézier 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. •An isogeometric boundary element method for electromagnetic scattering is proposed.•Compatible B-spline approximations used to discretize the electric and magnetic field integral equations are detailed.•The superior accuracy of high order compatible B-spline approximations over traditional approximations is demonstrated.•The approach is verified with the classical Mie scattering and NASA almond problems and validated against experimental data.•The ability to determine radar cross section profiles directly from CAD data without meshing is demonstrated.