The demand for dense matrix computation in large scale and complex simulations is increasing; however, the memory capacity of current computer system is insufficient for such simulations. Hierarchical matrix method (H-matrices) is attracting attention as a computational method that can reduce the memory requirements of dense matrix computations. However, the computation of H-matrices is more complex than that of dense and sparse matrices; thus, accelerating the H-matrices is required. We focus on H-matrix – vector multiplication (HMVM) on a single NVIDIA Tesla P100 GPU. We implement five GPU kernels and compare execution times among various processors (the Broadwell-EP, Skylake-SP, and Knights Landing) by OpenMP. The results show that, although an HMVM kernel can compute many small GEMV kernels, merging such kernels to a single GPU kernel was the most effective implementation. Moreover, the performance of BATCHED BLAS in the MAGMA library was comparable to that of the manually tuned GPU kernel.<\/p>\n","protected":false},"excerpt":{"rendered":"
The demand for dense matrix computation in large scale and complex simulations is increasing; however, the memory capacity of current computer system is insufficient for such simulations. Hierarchical matrix method (H-matrices) is attracting attention as a computational method that can reduce the memory requirements of dense matrix computations. However, the computation of H-matrices is more […]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[11,89,3],"tags":[1782,14,1483,37,20,252,1931],"class_list":["post-18098","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-nvidia-cuda","category-paper","tag-computer-science","tag-cuda","tag-intel-xeon-phi","tag-linear-algebra","tag-nvidia","tag-openmp","tag-tesla-p100"],"views":2263,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/18098","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=18098"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/18098\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=18098"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=18098"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=18098"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}