{"id":5918,"date":"2011-10-16T16:12:22","date_gmt":"2011-10-16T13:12:22","guid":{"rendered":"http:\/\/hgpu.org\/?p=5918"},"modified":"2011-10-16T16:12:22","modified_gmt":"2011-10-16T13:12:22","slug":"high-performance-finite-difference-pde-solvers-on-gpus","status":"publish","type":"post","link":"https:\/\/hgpu.org\/?p=5918","title":{"rendered":"High performance finite difference PDE solvers on GPUs"},"content":{"rendered":"<p>We show how to implement highly efficient GPU solvers for one dimensional PDEs based on finite difference schemes. The typical use case is to price a large number of similar or related derivatives in parallel. Application scenarios include market making, real time pricing, and risk management. The tridiagonal systems in the backward propagation of a finite difference scheme are solved with parallel cyclic reduction. This is a fine-grained parallel tridiagonal solver, which is well adapted to the hierarchical architecture of a modern GPU. We explain in detail the calculation work flow and study the performance of the solver relative to a well optimized CPU implementation. Our timings demonstrate performance improvement factors 25 on a single GPU and 38 on two GPUs.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We show how to implement highly efficient GPU solvers for one dimensional PDEs based on finite difference schemes. The typical use case is to price a large number of similar or related derivatives in parallel. Application scenarios include market making, real time pricing, and risk management. The tridiagonal systems in the backward propagation of a [&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":[89,576,3],"tags":[14,1804,327,20,550,551,599,199],"class_list":["post-5918","post","type-post","status-publish","format-standard","hentry","category-nvidia-cuda","category-finance","category-paper","tag-cuda","tag-finance","tag-finite-difference","tag-nvidia","tag-partial-differential-equations","tag-pdes","tag-risk-management","tag-tesla-c1060"],"views":3801,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/5918","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=5918"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/5918\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5918"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5918"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5918"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}