Multigrid methods for the Stokes problem on GPU systems
This paper presents a matrix-free multigrid method for solving the Stokes problem, discretized using Hdiv-conforming discontinuous Galerkin methods. Our method operates directly on both the velocity and pressure spaces, eliminating the need for a global Schur complement approximation. We employ a mu...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
30 August 2025
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| In: |
Computers & fluids
Year: 2025, Volume: 299, Pages: 1-11 |
| ISSN: | 1879-0747 |
| DOI: | 10.1016/j.compfluid.2025.106703 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.compfluid.2025.106703 Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S004579302500163X 
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| Author Notes: | Cu Cui, Guido Kanschat |
| Summary: | This paper presents a matrix-free multigrid method for solving the Stokes problem, discretized using Hdiv-conforming discontinuous Galerkin methods. Our method operates directly on both the velocity and pressure spaces, eliminating the need for a global Schur complement approximation. We employ a multiplicative Schwarz smoother with vertex-patch subdomains and the Schur complement method combined with the fast diagonalization for the efficient evaluation of the local solvers. By leveraging the tensor product structure of Raviart-Thomas elements and an optimized, conflict-free shared memory access pattern, the matrix-free operator evaluation demonstrates excellent performance, reaching over one billion degrees of freedom per second on a single NVIDIA A100 GPU. Numerical results indicate efficiency comparable to that of the three-dimensional Poisson problem. |
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| Item Description: | Online verfügbar: 12. Juni 2025, Artikelversion: 17. Juni 2025 Gesehen am 27.10.2025 |
| Physical Description: | Online Resource |
| ISSN: | 1879-0747 |
| DOI: | 10.1016/j.compfluid.2025.106703 |