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A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems.

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Title: A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems.
Authors: Xu, Tianshi1 (AUTHOR) tianshi.xu@emory.edu, Li, Rui Peng2 (AUTHOR), Osei-Kuffuor, Daniel2 (AUTHOR)
Source: International Journal of High Performance Computing Applications. May2025, Vol. 39 Issue 3, p424-442. 19p.
Subjects: Algebraic multigrid methods, Sparse matrices, Krylov subspace, Parallel processing, Linear systems
Abstract: 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 by targeting an algebraically smooth vector. 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. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract: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 by targeting an algebraically smooth vector. 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. [ABSTRACT FROM AUTHOR]
ISSN:10943420
DOI:10.1177/10943420251319334