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arXiv · 1404.7155

B\'{e}zier projection: a unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis

Derek C. Thomas·Michael A. Scott·John A. Evans·Kevin Tew·Emily J. Evans
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Abstract

We introduce B\'{e}zier projection as an element-based local projection methodology for B-splines, NURBS, and T-splines. This new approach relies on the concept of B\'{e}zier extraction and an associated operation introduced here, spline reconstruction, enabling the use of B\'{e}zier projection in standard finite element codes. B\'{e}zier projection exhibits provably optimal convergence and yields projections that are virtually indistinguishable from global $L^2$ projection. B\'{e}zier projection is used to develop a unified framework for spline operations including cell subdivision and merging, degree elevation and reduction, basis roughening and smoothing, and spline reparameterization. In fact, B\'{e}zier projection provides a \emph{quadrature-free} approach to refinement and coarsening of splines. In this sense, B\'{e}zier projection provides the fundamental building block for $hpkr$-adaptivity in isogeometric analysis.

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Derek C. Thomas, Michael A. Scott, John A. Evans, Kevin Tew, Emily J. Evans. 2014-04-28. B\'{e}zier projection: a unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis. https://doi.org/10.1016/j.cma.2014.07.014

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