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-grid 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.
|Original language||English (US)|
|Number of pages||24|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Feb 28 2018|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): CRG3 Award Ref:2281, CRG4 Award Ref:2584
Acknowledgements: Giancarlo Sangalli and Lorenzo Tamellini were partially supported by the European Research Council through the FP7 ERC consolidator grant n. 616563HIGEOM and by the GNCS 2017 project “Simulazione numerica di problemi di Interazione Fluido-Struttura (FSI) con metodi agli elementi finiti ed isogeometrici”. Lorenzo Tamellini also received support from the scholarship “Isogeometric method” granted by the Università di Pavia and by the European Union’s Horizon 2020 research and innovation program through the grant no. 680448 CAxMan. Joakim Beck received support from the KAUST CRG3 Award Ref:2281 and the KAUST CRG4 Award Ref:2584.