Multigrid methods for the Stokes problem on GPU systems - Cui, Cu; Kanschat, Guido (Computers & fluids, 2025)
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.
Online verfügbar: 12. Juni 2025, Artikelversion: 17. Juni 2025
Gesehen am 27.10.2025