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

Simpson, R. N., Liu, Z. , Vazquez, R. and Evans, J.A. (2018) An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations. Journal of Computational Physics, 362, pp. 264-289. (doi: 10.1016/

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Liu, Dr Zhaowei and Simpson, Dr Robert
Authors: Simpson, R. N., Liu, Z., Vazquez, R., and Evans, J.A.
College/School:College of Science and Engineering > School of Engineering > Systems Power and Energy
College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Journal of Computational Physics
ISSN (Online):1090-2716
Published Online:02 February 2018
Copyright Holders:Copyright © 2018 Elsevier
First Published:First published in Journal of Computational Physics 362: 264-289
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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