2022-10-03T18:07:54Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:001064502017-03-31T05:36:57Z05471:07431:07702
Parallel Hierarchical Matrices with Adaptive Cross Approximation on Symmetric Multiprocessing ClustersParallel Hierarchical Matrices with Adaptive Cross Approximation on Symmetric Multiprocessing Clusterseng[Regular Papers] boundary element method, matrix approximation, hierarchical matrices, adaptive cross approximation, parallel scalability, symmetric multiprocessing clustershttp://id.nii.ac.jp/1001/00106426/Articlehttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=106450&item_no=1&attribute_id=1&file_no=1Copyright (c) 2014 by the Information Processing Society of JapanACCMS, Kyoto University / JST CRESTJST CREST / Information Initiative Center, Hokkaido UniversityJST CREST / Department of Electrical Engineering, Kyoto UniversityJST CREST / Department of Electrical Engineering, Doshisha UniversityAkihiro, IdaTakeshi, IwashitaTakeshi, MifuneYasuhito, TakahashiWe discuss a scheme for hierarchical matrices with adaptive cross approximation on symmetric multiprocessing clusters. We propose a set of parallel algorithms that are applicable to hierarchical matrices. The proposed algorithms are implemented using the flat-MPI and hybrid MPI+OpenMP programming models. The performance of these implementations is evaluated using an electric field analysis computed on two symmetric multiprocessing cluster systems. Although the flat-MPI version gives better parallel scalability when constructing hierarchical matrices, the speed-up reaches a limit in the hierarchical matrix-vector multiplication. We succeeded in developing a hybrid MPI+OpenMP version to improve the parallel scalability. In numerical experiments, the hybrid version exhibits a better parallel speed-up for the hierarchical matrix-vector multiplication up to 256 cores.We discuss a scheme for hierarchical matrices with adaptive cross approximation on symmetric multiprocessing clusters. We propose a set of parallel algorithms that are applicable to hierarchical matrices. The proposed algorithms are implemented using the flat-MPI and hybrid MPI+OpenMP programming models. The performance of these implementations is evaluated using an electric field analysis computed on two symmetric multiprocessing cluster systems. Although the flat-MPI version gives better parallel scalability when constructing hierarchical matrices, the speed-up reaches a limit in the hierarchical matrix-vector multiplication. We succeeded in developing a hybrid MPI+OpenMP version to improve the parallel scalability. In numerical experiments, the hybrid version exhibits a better parallel speed-up for the hierarchical matrix-vector multiplication up to 256 cores.AA00700121Journal of information processing2246426502014-10-151882-66522014-10-20