The efficiency of boundary element methods depends crucially on the time required for setting up the stiffness matrix. The far-field part of the matrix can be approximated by compression schemes like the fast multipole method or $mathcal{H}$-matrix techniques. The near-field part is typically approximated by special quadrature rules like the Sauter-Schwab technique that can handle the singular integrals appearing in the diagonal and near-diagonal matrix elements. Since computing one element of the matrix requires only a small amount of data but a fairly large number of operations, we propose to use GPUs to handle vectorizable portions of the computation: near-field computations are ideally suited for vectorization and can therefore be handled very well by GPUs. Modern far-field compression schemes can be split into a small adaptive portion that exhibits divergent control flows and is handled by the CPU and a vectorizable portion that can again be sent to GPUs. We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPUs. Our method presented in this article is able to speedup the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.<\/p>\n","protected":false},"excerpt":{"rendered":"
The efficiency of boundary element methods depends crucially on the time required for setting up the stiffness matrix. The far-field part of the matrix can be approximated by compression schemes like the fast multipole method or $mathcal{H}$-matrix techniques. The near-field part is typically approximated by special quadrature rules like the Sauter-Schwab technique that can handle […]<\/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":[1782,723,597,20,974,1306,1793],"class_list":["post-14777","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-opencl","category-paper","tag-computer-science","tag-fast-multipole-method","tag-mathematical-software","tag-nvidia","tag-nvidia-geforce-gtx-580","tag-nvidia-geforce-gtx-680","tag-opencl"],"views":2468,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/14777","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=14777"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/14777\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}