A sparse-grid isogeometric solver

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 90s 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.

updated version after review

References in corpus (4)

• Fast formation of isogeometric Galerkin matrices by weighted quadrature
• Nonlinear static isogeometric analysis of arbitrarily curved Kirchhoff-Love shells
• Matrix-free weighted quadrature for a computationally efficient isogeometric $k$-method
• A Robust Multigrid Method for Isogeometric Analysis using Boundary Correction

Cited by in corpus (2)

• IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains
• Compressive Isogeometric Analysis