A Geometric Multigrid Preconditioner for Shifted Boundary Method
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909991487668224 |
|---|---|
| author | Wichrowski, Michał Ajith, Ajay |
| author_facet | Wichrowski, Michał Ajith, Ajay |
| contents | 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 $\mathcal{O}(h^{-2})$ 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 discretisations. We present a geometric multigrid preconditioner that effectively tames these systems. At its core lies the \emph{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10399 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Geometric Multigrid Preconditioner for Shifted Boundary Method Wichrowski, Michał Ajith, Ajay Numerical Analysis 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 $\mathcal{O}(h^{-2})$ 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 discretisations. We present a geometric multigrid preconditioner that effectively tames these systems. At its core lies the \emph{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. |
| title | A Geometric Multigrid Preconditioner for Shifted Boundary Method |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.10399 |