We outline the construction of compatible B-splines on 3D surfaces thatsatisfy the continuity requirements for electromagnetic scattering analysiswith the boundary element method (method of moments). Our approach makes use ofNon-Uniform Rational B-splines to represent model geometry and compatibleB-splines to approximate the surface current, and adopts the isogeometricconcept in which the basis for analysis is taken directly from CAD (geometry)data. The approach allows for high-order approximations and crucially providesa direct link with CAD data structures that allows for efficient designworkflows. After outlining the construction of div- and curl-conformingB-splines defined over 3D surfaces we describe their use with the electric andmagnetic field integral equations using a Galerkin formulation. We use B\'ezierextraction to accelerate the computation of NURBS and B-spline terms and employH-matrices to provide accelerated computations and memory reduction for thedense matrices that result from the boundary integral discretization. Themethod is verified using the well known Mie scattering problem posed over aperfectly electrically conducting sphere and the classic NASA almond problem.Finally, we demonstrate the ability of the approach to handle models withcomplex geometry directly from CAD without mesh generation.
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