Overlapping subspaces and singular systems with application to Isogeometric Analysis

TL;DR

This paper introduces a framework for solving PDEs using overlapping subspaces in isogeometric analysis, enabling efficient handling of complex spline spaces and potentially improving computational performance.

Contribution

It proposes a novel approach using disjoint union of subspace bases for PDE solutions, addressing singular systems in IGA with Krylov solvers.

Findings

Framework effectively handles singular systems.

Applicable to hierarchical and local spline spaces.

Potential computational advantages in IGA applications.

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.