A sparse-grid isogeometric solver

Joakim Beck, Giancarlo Sangalli, Lorenzo Tamellini

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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-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 languageEnglish (US)
Pages (from-to)128-151
Number of pages24
JournalComputer Methods in Applied Mechanics and Engineering
Volume335
DOIs
StatePublished - Feb 28 2018

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