{"id":6504,"date":"2011-12-07T11:50:38","date_gmt":"2011-12-07T09:50:38","guid":{"rendered":"http:\/\/hgpu.org\/?p=6504"},"modified":"2011-12-07T11:50:38","modified_gmt":"2011-12-07T09:50:38","slug":"towards-a-complete-fem-based-simulation-toolkit-on-gpus-geometric-multigrid-solvers","status":"publish","type":"post","link":"https:\/\/hgpu.org\/?p=6504","title":{"rendered":"Towards a complete FEM-based simulation toolkit on GPUs: Geometric Multigrid solvers"},"content":{"rendered":"<p>We describe a GPU- and multicore-oriented implementation technique for a key component of finite element based simulation toolkits for partial differential equations on unstructured grids: Geometric Multigrid solvers. We use efficient sparse matrix-vector multiplications throughout the solver pipeline: within the coarse-grid solver, smoothers and even grid transfers. Our implementation can handle several low- and high-order finite element spaces in 2D and 3D, and for representative benchmark problems, we achieve close to an order of magnitude speedup on a single GPU over a multithreaded CPU code. In addition we present preliminary results for experiments with strong smoothers for unstructured problems on the GPU, aiming at augmenting numerical and computational efficiency simultaneously.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We describe a GPU- and multicore-oriented implementation technique for a key component of finite element based simulation toolkits for partial differential equations on unstructured grids: Geometric Multigrid solvers. We use efficient sparse matrix-vector multiplications throughout the solver pipeline: within the coarse-grid solver, smoothers and even grid transfers. Our implementation can handle several low- and high-order [&hellip;]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"open","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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[89,104,3],"tags":[451,14,810,1037,212,1795,20,251,550,551,421],"class_list":["post-6504","post","type-post","status-publish","format-standard","hentry","category-nvidia-cuda","category-fluid-dynamics","category-paper","tag-benchmarking","tag-cuda","tag-differential-equations","tag-fem","tag-finite-element-method","tag-fluid-dynamics","tag-nvidia","tag-nvidia-geforce-gtx-285","tag-partial-differential-equations","tag-pdes","tag-sparse-matrix"],"views":2132,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/6504","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=6504"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/6504\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6504"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6504"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}