Relaxation methods such as Jacobi or Gauss-Seidel are often applied as smoothers in algebraic multigrid. Incomplete factorizations can also be employed, however, direct triangular solves are comparatively slow on GPUs. Previous work by Antz et al. \cite{Anzt2015} proposed an iterative approach for solving such sparse triangular systems. However, when using the stationary Jacobi iteration, if the upper or lower triangular factor is highly non-normal, the iterations will diverge. An ILUT smoother is introduced for classical Ruge-St\"uben C-AMG that applies Ruiz 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 as opposed to the global matrix, it can be done locally on an MPI-rank for a diagonal block of the global matrix. A performance model is provided along with numerical results for matrices extracted from the PeleLM \cite{PeleLM} pressure continuity solver.

翻译：Jacobi 或 Gauss- Seidel 等放松方法通常在代数多格中作为光滑器使用。 也可以使用不完全的分解法, 但是, 直接三角溶解在 GPUs 上相对比较慢。 Antz et al.\ cite{ Anzt2015} 先前的工作提出了一种迭接方法来解决这种稀疏的三角系统。 但是, 当使用固定的分解法时, 如果上三角或下三角系数非常不正常, 迭代会不同。 古典Ruge- St\" uben C- AMG 则引入了 ILUT 光滑动器, 将 Ruiz 缩放用于减轻上三角因素的非常态性。 我们的方法有助于使用 Jacobi 迭代法来取代内在的三角溶解。 由于比例适用于上三角因数, 而不是全球矩阵, 可以在本地的 MPI- 级用于全球矩阵的对角块 。 提供一种性模型, 以及从 PelLM {PeleLMM} 持续 解 解算 解算 的矩阵 的矩阵的矩阵的矩阵的矩阵的数字结果结果结果结果。