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arXiv · 2408.17273

Overlapping subspaces and singular systems with application to Isogeometric Analysis

Andrea Bressan·Massimiliano Martinelli·Giancarlo Sangalli
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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.

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Andrea Bressan, Massimiliano Martinelli, Giancarlo Sangalli. 2024-08-30. Overlapping subspaces and singular systems with application to Isogeometric Analysis. https://arxiv.org/abs/2408.17273

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