This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods, on challenging anisotropic diffusion problems and a collection of general sparse matrices.

翻译：本文提出了一种基于区域分解框架下不完全LU分解的并行预条件方法，用于求解通用稀疏线性系统。我们重点关注分布式内存并行架构，特别是配备图形处理单元的系统。除了块雅可比方法外，我们提出了通用两级ILU舒尔补方法，其中给出了求解粗级缩减系统的不同策略。这些策略在构造粗级算子时与改进的ILU方法相结合，以有效消除光滑误差。我们利用基于GPU的稀疏矩阵核来加速所提ILU预条件子的设置与求解阶段。在具有挑战性的各向异性扩散问题和通用稀疏矩阵集合上，我们评估了所提方法作为代数多重网格光滑器和Krylov子空间方法预条件子的效率。