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About this paper
Mengdi Wang, Yuchen Sun, Bo Zhu
Researchers at Georgia Tech developed a GPU-accelerated, matrix-free multigrid preconditioner for solving Poisson equations on adaptive octree grids with irregular cut-cell domains. The method implements algebraically consistent coarsening and a flux-consistent coarse-grid correction at T-junctions, achieving second-order accuracy and grid-independent convergence with throughputs over 200 million cells per second.
Key insights
- Algebraically consistent coarsening can be effectively achieved in a matrix-free manner on adaptive octrees, providing robust convergence on irregular domains with discontinuous coefficients.
- An FAS-style coarse-grid correction is crucial for addressing flux deviation and maintaining cross-level consistency at T-junctions in adaptive octree multigrid, which improves overall convergence.
- Optimizing multigrid operations for GPU architectures through tile-based processing, shared memory utilization, and on-the-fly ghost cell reconstruction significantly enhances computational throughput and memory efficiency for large-scale adaptive simulations.
Summary by alphaXiv.
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