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.
Pelosi, F., Giannelli, C., Manni, C., Sampoli, M.l., Speleers, H. (2017). Splines over regular triangulations in numerical simulation. COMPUTER AIDED DESIGN, 82, 100-111 [10.1016/j.cad.2016.08.002].
Splines over regular triangulations in numerical simulation
Pelosi, Francesca;Manni, Carla;Speleers, Hendrik
2017-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.