Algebraic Multigrid

Algebraic multigrid (AMG) methods efficiently solve large systems of equations arising from partial differential equations (PDEs), primarily by constructing a hierarchy of coarser grids to accelerate convergence. Current research focuses on improving AMG's performance and adaptability through machine learning techniques, such as neural networks and graph neural networks, to optimize parameters (e.g., strong thresholding), automate grid coarsening (e.g., agglomeration), and design more efficient coarse-grid operators. These advancements aim to reduce computational cost and enhance the robustness of AMG solvers across diverse PDE problems and complex geometries, impacting fields reliant on high-fidelity numerical simulations.