Matrix-Free Multigrid with Algebraically Consistent Coarsening on Adaptive Octrees
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911610933608448 |
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| author | Wang, Mengdi Sun, Yuchen Zhu, Bo |
| author_facet | Wang, Mengdi Sun, Yuchen Zhu, Bo |
| contents | We present a matrix-free GPU multigrid preconditioner with algebraically consistent coarsening for solving Poisson equations on adaptive octree grids with irregular domains. Within uniform-resolution regions, the coarsening satisfies the Galerkin principle. At T-junctions between refinement levels, we propose a flux-consistent coarse-grid correction that restores cross-level consistency while preserving the compact matrix-free representation. The coarse operators are stored in a compact matrix-free form suitable for parallel execution on GPUs. Numerical experiments demonstrate second-order accuracy, grid-independent convergence when used with PCG, and robust performance on cut-cell problems arising in fluid simulation. On a single NVIDIA RTX 4090 GPU, the solver achieves full-solve throughputs above 200 million cells per second on analytical Poisson tests and above 70 million cells per second on pressure projection problems in fluid simulation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_18886 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Matrix-Free Multigrid with Algebraically Consistent Coarsening on Adaptive Octrees Wang, Mengdi Sun, Yuchen Zhu, Bo Numerical Analysis Graphics We present a matrix-free GPU multigrid preconditioner with algebraically consistent coarsening for solving Poisson equations on adaptive octree grids with irregular domains. Within uniform-resolution regions, the coarsening satisfies the Galerkin principle. At T-junctions between refinement levels, we propose a flux-consistent coarse-grid correction that restores cross-level consistency while preserving the compact matrix-free representation. The coarse operators are stored in a compact matrix-free form suitable for parallel execution on GPUs. Numerical experiments demonstrate second-order accuracy, grid-independent convergence when used with PCG, and robust performance on cut-cell problems arising in fluid simulation. On a single NVIDIA RTX 4090 GPU, the solver achieves full-solve throughputs above 200 million cells per second on analytical Poisson tests and above 70 million cells per second on pressure projection problems in fluid simulation. |
| title | Matrix-Free Multigrid with Algebraically Consistent Coarsening on Adaptive Octrees |
| topic | Numerical Analysis Graphics |
| url | https://arxiv.org/abs/2604.18886 |