Overlapping subspaces and singular systems with application to Isogeometric Analysis
Numerical Analysis
2024-09-02 v1 Numerical Analysis
Abstract
We propose a framework for solving partial differential equations (PDEs) motivated by isogeometric analysis (IGA) and local tensor-product splines. Instead of using a global basis for the solution space we use as generators the disjoint union of subspace bases. This leads to a potentially singular linear system, which is handled by a Krylov linear solver. The framework may offer computational advantages in dealing with spaces like Hierarchical B-splines, T-splines, and LR-splines.
Cite
@article{arxiv.2408.17273,
title = {Overlapping subspaces and singular systems with application to Isogeometric Analysis},
author = {Andrea Bressan and Massimiliano Martinelli and Giancarlo Sangalli},
journal= {arXiv preprint arXiv:2408.17273},
year = {2024}
}