Efficient AMG reduction-based preconditioners for structural mechanics

Structural problems play a critical role in many areas of science and engineering. Their efficient and accurate solution is essential for designing and optimising civil engineering, aerospace, and materials science applications, to name a few. When appropriately tuned, Algebraic Multigrid (AMG) methods exhibit a convergence that is independent of the problem size, making them the preferred option for solving structural problems. Nevertheless, AMG faces several computational challenges, including its remarkable memory footprint, costly setup, and the relatively low arithmetic intensity of the sparse linear algebra operations. This work presents AMGR, an enhanced variant of AMG that mitigates such limitations. Its name arises from the AMG reduction framework it introduces, and its flexibility allows for leveraging several features that are common in structural problems. Namely, periodicities, spatial symmetries, and localised non-linearities. For such cases, we show how to reduce the memory footprint and setup costs of the standard AMG, as well as increase its arithmetic intensity. Despite being lighter than the standard AMG, AMGR exhibits comparable scalability and convergence rates. Numerical experiments on several industrial applications prove AMGR's effectiveness, resulting in up to 3.7x overall speed-ups compared to the standard AMG.