
| Title | A sparse-grid isogeometric solver | 
| Publication Type | Report Series | 
| Year of Publication | 2017 | 
| Authors | Beck J., Sangalli G., Tamellini L. | 
| Series | IMATI Report Series | 
| Number | 17-13 | 
| Pagination | 24 | 
| Date Published | 09/2017 | 
| Place Published | Pavia | 
| Publisher | CNR-IMATI | 
| Type of Work | Preprint | 
| Abstract | Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations. | 
| Keywords | B-splines, Combination technique, Isogeometric analysis, NURBS, Sparse grids | 
| URI | http://irs.imati.cnr.it/reports/irs17-13 | 
| Citation Key | irs17-13 | 
