GPU Preconditioning for Block Linear Systems Using Block Incomplete Sparse Approximate Inverses

Solving sparse triangular systems is the building block for incomplete LU- (ILU-) based preconditioning, but parallel algorithms, such as the level-scheduling scheme, are sometimes limited by available parallelism extracted from the sparsity pattern. In this study, the block version of the incomplet...

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Bibliographic Details
Published in:Mathematical problems in engineering 2021, Vol.2021, p.1-13
Main Authors: Ma, Wenpeng, Hu, Yiwen, Yuan, Wu, Liu, Xiazhen
Format: Article
Language:English
Subjects:
Accelerators
Algorithms
Engineering
Graphics processing units
Linear systems
Performance assessment
Preconditioning
Sparsity
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Summary:Solving sparse triangular systems is the building block for incomplete LU- (ILU-) based preconditioning, but parallel algorithms, such as the level-scheduling scheme, are sometimes limited by available parallelism extracted from the sparsity pattern. In this study, the block version of the incomplete sparse approximate inverses (ISAI) algorithm is studied, and the block-ISAI is considered for preconditioning by proposing an efficient algorithm and implementation on graphical processing unit (GPU) accelerators. Performance comparisons are carried out between the proposed algorithm and serial and parallel block triangular solvers from PETSc and cuSPARSE libraries. The experimental results show that GMRES (30) with the proposed block-ISAI preconditioning achieves accelerations 1.4 × –6.9 × speedups over that using the cuSPARSE library on NVIDIA Tesla V100 GPU.
ISSN:1024-123X
1563-5147
DOI:10.1155/2021/5558508