Scalability of Classical Algebraic Multigrid for Elasticity to Half a Million Parallel Tasks

The parallel performance of several classical Algebraic Multigrid (AMG) methods applied to linear elasticity problems is investigated. These methods include standard approaches such as the unknown approach, the hybrid approach as well the global matrix (GM) and the local neighborhood (LN) approach, which improve AMG convergence by incorporating rigid body modes (RBMs) into the interpolation. Numerical experiments for twoand three-dimensional elasticity problems using up to 131 072 cores with up to 262 144 MPI processes on the Vulcan supercomputer (LLNL, USA) and up to 262 144 cores and 524 288 MPI processes on the JUQUEEN supercomputer (JSC, Jülich, Germany) are presented. It is demonstrated that incorporating all RBMs into the interpolation leads generally to better convergence and scalability.