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Splines over regular triangulations in numerical simulation
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DOI：10.1016/j.cad.2016.08.002.png)
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摘要
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We investigate the use of smooth spline spaces over regular triangulations as a tool in (isogeometric) Galerkin methods. In particular, we focus on box splines over three-directional meshes. Box splines are multivariate generalizations of univariate cardinal B-splines sharing the same properties. Tensor-product B-splines with uniform knots are a special case of box splines. The use of box splines over three-directional meshes has several advantages compared with tensor-product B-splines, including enhanced flexibility in the treatment of the geometry and stiffness matrices with stronger sparsity. Boundary conditions are imposed in a weak form to avoid the construction of special boundary functions. We illustrate the effectiveness of the approach by means of a selection of numerical examples. (C) 2016 Elsevier Ltd. All rights reserved.
Keyword:
Isogeometric analysis
Galerkin methods
Box splines
Three-directional meshes
Weak boundary conditions
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