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An efficient sparse approximate inverse preconditioning algorithm on GPU
Author(s) -
He Guixia,
Yin Renjie,
Gao Jiaquan
Publication year - 2019
Publication title -
concurrency and computation: practice and experience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.309
H-Index - 67
eISSN - 1532-0634
pISSN - 1532-0626
DOI - 10.1002/cpe.5598
Subject(s) - preconditioner , thread (computing) , computer science , parallel computing , graphics processing unit , inverse , cuda , graphics , algorithm , mathematical optimization , iterative method , computational science , mathematics , computer graphics (images) , geometry , operating system
Summary The sparse approximate inverse (SPAI) preconditioner has proven to be effective in accelerating the convergence of iterative methods. Recently, accelerating it on the graphics processing unit (GPU) has attracted considerable attention due to the fact that the cost of constructing it is high. This motivates us to investigate how to accelerate the construction of SPAI preconditioners on GPU in this paper. We propose an efficient sparse approximate inverse algorithm on GPU, called SPAI‐Adaptive. For our proposed SPAI‐Adaptive, there are the following novelties: (1) an adaptive thread allocation strategy for SPAI‐Adaptive is proposed to assign the optimal thread number for each column of the preconditioner, and (2) Each component of the preconditioner, which includes finding indices I and J , constructing local submatrix, decomposing the local matrix into QR, and solving the upper triangular linear system, is computed in parallel inside a thread group of GPU. Experimental results show that the proposed SPAI‐Adaptive is effective, and has good performance and high parallelism.