We present a novel, quadrature-based finite element integration method for low-order elements on GPUs, using a pattern we call thread transposition to avoid reductions while vectorizing aggressively. On the NVIDIA GTX580, which has a nominal single precision peak flop rate of 1.5 TF\/s and a memory bandwidth of 192 GB\/s, we achieve close to 300 GF\/s for element integration on first-order discretization of the Laplacian operator with variable coefficients in two dimensions, and over 400 GF\/s in three dimensions. From our performance model we find that this corresponds to 90% of our measured achievable bandwidth peak of 310 GF\/s. Further experimental results also match the predicted performance when used with double precision (120 GF\/s in two dimensions, 150 GF\/s in three dimensions). Results obtained for the linear elasticity equations (220 GF\/s and 70 GF\/s in two dimensions, 180 GF\/s and 60 GF\/s in three dimensions) also demonstrate the applicability of our method to vector-valued partial differential equations.<\/p>\n","protected":false},"excerpt":{"rendered":"
We present a novel, quadrature-based finite element integration method for low-order elements on GPUs, using a pattern we call thread transposition to avoid reductions while vectorizing aggressively. On the NVIDIA GTX580, which has a nominal single precision peak flop rate of 1.5 TF\/s and a memory bandwidth of 192 GB\/s, we achieve close to 300 […]<\/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":[11,90,3],"tags":[1655,7,1782,810,597,20,974,1634,1793,550,551,1390],"class_list":["post-16230","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-opencl","category-paper","tag-amd-firepro-w9100","tag-ati","tag-computer-science","tag-differential-equations","tag-mathematical-software","tag-nvidia","tag-nvidia-geforce-gtx-580","tag-nvidia-geforce-gtx-750-ti","tag-opencl","tag-partial-differential-equations","tag-pdes","tag-tesla-k20"],"views":2430,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/16230","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=16230"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/16230\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}