Splines over regular triangulations in numerical simulation |
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Affiliation: | 1. Department of Mathematics, University of Rome “Tor Vergata”, Italy;2. Department of Mathematics and Computer Science, University of Florence, Italy;3. Department of Information Engineering and Mathematics, University of Siena, Italy |
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Abstract: | 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. |
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Keywords: | Isogeometric analysis Galerkin methods Box splines Three-directional meshes Weak boundary conditions |
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