期刊
出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3368474.3368479
关键词
mixed precision computing; linear solver; hierarchical matrix
类别
资金
- Japan Society for the Promotion of Science (JSPS) KAKENHI Grant [JP19H04122, JP17H01749]
- Joint Usage/Research Center for Interdisciplinary Large-scale Information Infrastructures (JHPCN) in Japan [jh190042-NAH]
- High Performance Computing Infrastructure (HPCI) in Japan [jh190042-NAH]
Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time and space complexity of dense matrix vector multiplication, and hence has been applied to numerous practical problems. In this paper, we aim to accelerate the H-matrix vector multiplication by introducing mixed precision computing, where we employ both binary64 (FP64) and binary32 (FP32) arithmetic operations. We propose three methods to introduce mixed precision computing to H-matrix vector multiplication, and then evaluate them in a boundary element method (BEM) analysis. The numerical tests examine the effects of mixed precision computing, particularly on the required simulation time and rate of convergence of the iterative (BiCG-STAB) linear solver. We confirm the effectiveness of the proposed methods.
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