ILU Smoothers for C-AMG with Scaled Triangular Factors

ILU smoothers can be effective in the algebraic multigrid $V$-cycle. However, direct triangular solves are comparatively slow on GPUs. Previous work by Chow and Patel \cite{ChowPatel2015} and Antz et al. \cite{Anzt2015} proposed an iterative approach to solve these systems. Unfortunately, when the Jacobi iteration is applied to highly non-normal upper or lower triangular factors, the iterations will diverge. An ILU smoother is introduced for classical Ruge-St\"uben C-AMG that applies row and/or column scaling to mitigate the non-normality of the upper triangular factor. Our approach facilitates the use of Jacobi iteration in place of the inherently sequential triangular solve. Because the scaling is applied to the upper triangular factor, it can be done locally for a diagonal block of the global matrix. An ILUT Schur complement smoother, that solves the Schur system along subdomain (MPI rank) boundaries using GMRES, maintains a constant iteration count and improves strong-scaling. Numerical results and parallel performance are presented for the Nalu-Wind and PeleLM \cite{PeleLM} pressure solvers. For large problem sizes, GMRES$+$AMG with iterative triangular solves executes at least five times faster than when using direct solves on the NREL Eagle supercomputer.