We discuss an approach for solving sparse or dense banded linear systems ${bf A} {bf x} = {bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${bf A} in {mathbb{R}}^{N times N}$ is possibly nonsymmetric and moderately large; i.e., $10000 leq N leq 500000$. The ${it split and parallelize}$ (${tt SaP}$) approach seeks to partition the matrix ${bf A}$ into diagonal sub-blocks ${bf A}_i$, $i=1,ldots,P$, which are independently factored in parallel. The solution may choose to consider or to ignore the matrices that couple the diagonal sub-blocks ${bf A}_i$. This approach, along with the Krylov subspace-based iterative method that it preconditions, are implemented in a solver called ${tt SaP::GPU}$, which is compared in terms of efficiency with three commonly used sparse direct solvers: ${tt PARDISO}$, ${tt SuperLU}$, and ${tt MUMPS}$. ${tt SaP::GPU}$, which runs entirely on the GPU except several stages involved in preliminary row-column permutations, is robust and compares well in terms of efficiency with the aforementioned direct solvers. In a comparison against Intel’s ${tt MKL}$, ${tt SaP::GPU}$ also fares well when used to solve dense banded systems that are close to being diagonally dominant. ${tt SaP::GPU}$ is publicly available and distributed as open source under a permissive BSD3 license.<\/p>\n","protected":false},"excerpt":{"rendered":"
We discuss an approach for solving sparse or dense banded linear systems ${bf A} {bf x} = {bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${bf A} in {mathbb{R}}^{N times N}$ is possibly nonsymmetric and moderately large; i.e., $10000 leq N leq 500000$. The ${it split and parallelize}$ (${tt SaP}$) approach seeks […]<\/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":[11,89,3],"tags":[1782,14,37,20,176,341,1390],"class_list":["post-14619","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-nvidia-cuda","category-paper","tag-computer-science","tag-cuda","tag-linear-algebra","tag-nvidia","tag-package","tag-sparse-direct-solvers","tag-tesla-k20"],"views":2471,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/14619","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=14619"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/14619\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14619"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}