Splines over regular triangulations in numerical simulation. (January 2017) - Pelosi, Francesca; Giannelli, Carlotta; Manni, Carla; Sampoli, Maria Lucia; Speleers, Hendrik
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. Highlights: We propose an isogeometric method based on box splines over three-directional meshes. The use of box splines instead of tensor-product B-splines has several advantages. Box splines enable flexible geometries and improve the sparsity of related matrices. A weak form in connection with a geometric map is used to enforce boundary conditions. A selection of examples illustrates the effectiveness of the approach.