17034

Decoupled Block-Wise ILU(k) Preconditioner on GPU

Bo Yang, Hui Liu, He Zhong, Zhangxin Chen
University of Calgary
arXiv:1703.01325 [cs.NA], (3 Mar 2017)

@article{yang2017decoupled,

   title={Decoupled Block-Wise ILU(k) Preconditioner on GPU},

   author={Yang, Bo and Liu, Hui and Zhong, He and Chen, Zhangxin},

   year={2017},

   month={mar},

   archivePrefix={"arXiv"},

   primaryClass={cs.NA}

}

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This research investigates the implementation mechanism of block-wise ILU(k) preconditioner on GPU. The block-wise ILU(k) algorithm requires both the level k and the block size to be designed as variables. A decoupled ILU(k) algorithm consists of a symbolic phase and a factorization phase. In the symbolic phase, a ILU(k) nonzero pattern is established from the point-wise structure extracted from a block-wise matrix. In the factorization phase, the block-wise matrix with a variable block size is factorized into a block lower triangular matrix and a block upper triangular matrix. And a further diagonal factorization is required to perform on the block upper triangular matrix for adapting a parallel triangular solver on GPU.We also present the numerical experiments to study the preconditioner actions on different k levels and block sizes.
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