Splines over regular triangulations in numerical simulation. (January 2017)

• Record Type: Journal Article
• Authors: Pelosi, Francesca; Giannelli, Carlotta; Manni, Carla; Sampoli, Maria Lucia; Speleers, Hendrik
• Is Part Of: Computer aided design. Volume 82(2017)
• Page Start: 100
• Page End: 111
• Publication Date: 2017-01
• Subjects: Isogeometric analysis -- Galerkin methods -- Box splines -- Three-directional meshes -- Weak boundary conditions; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2016.08.002
• Languages: English
• ISSNs: 0010-4485

Abstract

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.