Overlapping subspaces and singular systems with application to Isogeometric Analysis
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929479620755456 |
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| author | Bressan, Andrea Martinelli, Massimiliano Sangalli, Giancarlo |
| author_facet | Bressan, Andrea Martinelli, Massimiliano Sangalli, Giancarlo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_17273 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Overlapping subspaces and singular systems with application to Isogeometric Analysis Bressan, Andrea Martinelli, Massimiliano Sangalli, Giancarlo Numerical Analysis 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. |
| title | Overlapping subspaces and singular systems with application to Isogeometric Analysis |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2408.17273 |