{"id":14254,"date":"2015-07-13T23:40:47","date_gmt":"2015-07-13T20:40:47","guid":{"rendered":"http:\/\/hgpu.org\/?p=14254"},"modified":"2015-07-13T23:40:47","modified_gmt":"2015-07-13T20:40:47","slug":"gpu-accelerated-discontinuous-galerkin-methods-on-hybrid-meshes","status":"publish","type":"post","link":"https:\/\/hgpu.org\/?p=14254","title":{"rendered":"GPU-accelerated discontinuous Galerkin methods on hybrid meshes"},"content":{"rendered":"<p>We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius of the DG operator using order-dependent constants in trace and Markov inequalities. Computational efficiency is achieved under a combination of element-specific kernels (including new quadrature-free operators for the pyramid), multi-rate timestepping, and acceleration using Graphics Processing Units.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius [&hellip;]<\/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":[89,157,90,3],"tags":[14,1796,628,20,1650,1793,252,240,328],"class_list":["post-14254","post","type-post","status-publish","format-standard","hentry","category-nvidia-cuda","category-mathematics","category-opencl","category-paper","tag-cuda","tag-mathematics","tag-numerical-analysis","tag-nvidia","tag-nvidia-geforce-gtx-980","tag-opencl","tag-openmp","tag-spectral-elements","tag-wave-equation"],"views":2733,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/14254","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=14254"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/14254\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}