A geometric multigrid preconditioner for Shifted Boundary Method
The Shifted Boundary Method (SBM) trades some part of the burden of body-fitted meshing for increased algebraic complexity. While the resulting linear systems retain the standard O(h−2) conditioning of second-order operators, the non-symmetry and non-local boundary coupling render them resistant to...
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| Autori principali: | , |
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| Natura: | Article (Journal) |
| Lingua: | inglese |
| Pubblicazione: |
26 May 2026
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| In: |
Computer methods in applied mechanics and engineering
Year: 2026, Volume: 460, Pages: 1-15 |
| ISSN: | 1879-2138 |
| DOI: | 10.1016/j.cma.2026.119043 |
| Accesso online: | Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.cma.2026.119043 Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S0045782526003166 
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| Note sull'autore: | Michał Wichrowski, Ajay Ajith |
| Riassunto: | The Shifted Boundary Method (SBM) trades some part of the burden of body-fitted meshing for increased algebraic complexity. While the resulting linear systems retain the standard O(h−2) conditioning of second-order operators, the non-symmetry and non-local boundary coupling render them resistant to standard Algebraic Multigrid (AMG) and simple smoothers for high-order discretizations. We present a geometric multigrid preconditioner that effectively tames these systems. At its core lies the Full-Residual Shy Patch smoother: a subspace correction strategy that filters out some patches while capturing the full physics of the shifted boundary. Unlike previous cell-wise approaches that falter at high polynomial degrees, our method delivers convergence with low mesh dependence. We demonstrate performance for Continuous Galerkin approximations, maintaining low and stable iteration counts up to polynomial degree p=3 in 3D, proving that SBM can be both geometrically flexible and algebraically efficient. |
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| Descrizione del documento: | Gesehen am 13.08.2026 |
| Descrizione fisica: | Online Resource |
| ISSN: | 1879-2138 |
| DOI: | 10.1016/j.cma.2026.119043 |