GFSAI: An Adaptive Factorized Sparse Approximate Inverse Preconditioning Algorithm on GPU

doi:10.1002/cpe.70552

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GFSAI: An Adaptive Factorized Sparse Approximate Inverse Preconditioning Algorithm on GPU

2026-01-01

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Yizhou Wang

Yige Zhang

Jiaquan Gao *

DOI：10.1002/cpe.70552

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Abstract

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The factorized sparse approximate inverse (FSAI) preconditioner has been proven to be effective in accelerating the convergence of iterative methods. Due to the high cost of constructing the FSAI preconditioner, accelerating it on graphics processing unit (GPU) has attracted considerable attention. However, despite the development of some existing FSAI preconditioning algorithms on GPU, their performance will significantly decrease when they encounter matrix types that are not suitable for them. This motivates us to investigate how to design an effective FSAI preconditioning algorithm on GPU. In this paper, we propose an adaptive FSAI preconditioning algorithm on GPU, called GFSAI-Adaptive, to address the above problem. In GFSAI-Adaptive, first, two adaptive thread allocation strategies are proposed for two special types of SPD matrices to ensure that the allocated threads can be fully utilized. Second, based on the proposed two thread allocation strategies, two FSAI kernels, called GFSAII and GFSAIII, are presented. Third, we construct a new graph convolutional network, and thus propose a search engine to select the optimal kernel from GFSAII and GFSAIII for matrices that do not belong to two special types based on it. Experimental results show that our proposed GFSAI-Adaptive is effective and outperforms a popular preconditioning algorithm in the public CUSPARSE library and a recent parallel static FSAI preconditioning algorithm on GPU.

Keywords:

CUDA

factorized sparse approximate inverse

GPU

preconditioning

symmetric positive definite matrix