{"id":"https://openalex.org/W2997945685","doi":"https://doi.org/10.1145/882262.882364","title":"Sparse matrix solvers on the GPU: conjugate gradients and multigrid","display_name":"Sparse matrix solvers on the GPU: conjugate gradients and multigrid","publication_year":2003,"publication_date":"2003-07-01","ids":{"openalex":"https://openalex.org/W2997945685","doi":"https://doi.org/10.1145/882262.882364","mag":"2997945685"},"language":"en","primary_location":{"id":"doi:10.1145/882262.882364","doi":"https://doi.org/10.1145/882262.882364","is_oa":false,"landing_page_url":"https://doi.org/10.1145/882262.882364","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-a","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2997945685"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073007257","display_name":"Jeff Bolz","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeff Bolz","raw_affiliation_strings":["Caltech"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000833932","display_name":"Ian Farmer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ian Farmer","raw_affiliation_strings":["Caltech"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049319779","display_name":"Eitan Grinspun","orcid":"https://orcid.org/0000-0003-4460-7747","observed_orcids":["https://orcid.org/0000-0003-4460-7747"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eitan Grinspun","raw_affiliation_strings":["Caltech"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":null,"display_name":"Peter Schr\u00f6der","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Schr\u00f6der","raw_affiliation_strings":["Caltech"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":30.0845,"has_fulltext":false,"cited_by_count":559,"citation_normalized_percentile":{"value":0.99814849,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"22","issue":"3","first_page":"917","last_page":"924"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.8130000233650208,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.8130000233650208,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.14720000326633453,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.03400000184774399,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sparse-matrix-solvers","display_name":"sparse matrix solvers","score":0.902999997138977},{"id":"https://openalex.org/keywords/gpu-computing","display_name":"GPU computing","score":0.9890000224113464},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"conjugate gradient method","score":0.9139999747276306},{"id":"https://openalex.org/keywords/multigrid-solver","display_name":"multigrid solver","score":0.8650000095367432},{"id":"https://openalex.org/keywords/mesh-smoothing","display_name":"mesh smoothing","score":0.6290000081062317},{"id":"https://openalex.org/keywords/surface-parameterization","display_name":"surface parameterization","score":0.9179999828338623},{"id":"https://openalex.org/keywords/fluid-simulation","display_name":"fluid simulation","score":0.9639999866485596},{"id":"https://openalex.org/keywords/solid-mechanics","display_name":"solid mechanics","score":0.7820000052452087},{"id":"https://openalex.org/keywords/geometric-flows","display_name":"geometric flows","score":0.875},{"id":"https://openalex.org/keywords/parallel-numerical-simulation","display_name":"parallel numerical simulation","score":0.38999998569488525}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7928091287612915},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.744143545627594},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7013987898826599},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6898863315582275},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6670733094215393},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5723194479942322},{"id":"https://openalex.org/C50630238","wikidata":"https://www.wikidata.org/wiki/Q971505","display_name":"General-purpose computing on graphics processing units","level":3,"score":0.5691180229187012},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5357540845870972},{"id":"https://openalex.org/C2778119891","wikidata":"https://www.wikidata.org/wiki/Q477690","display_name":"CUDA","level":2,"score":0.511391818523407},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.5000317096710205},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.47932207584381104},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46657121181488037},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.4549630582332611},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.4518796503543854},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.4422542154788971},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4202575385570526},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.4141750931739807},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3421202003955841},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.16491597890853882},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.12617617845535278},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11524549126625061},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.09458670020103455},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.09013772010803223},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1145/882262.882364","doi":"https://doi.org/10.1145/882262.882364","is_oa":false,"landing_page_url":"https://doi.org/10.1145/882262.882364","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-a","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:119123","doi":null,"is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/119123/1/cit-asci-tr175.pdf","pdf_url":"https://authors.library.caltech.edu/119123/1/cit-asci-tr175.pdf","source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Report or Paper"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.112.5723","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.5723","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.stevens.edu/~quynh/courses/cs638-papers/bolz_gpu_conj_grad.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.61.9009","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.9009","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://csdrm.caltech.edu/publications/cit-asci-tr/cit-asci-tr175.pdf","raw_type":"text"},{"id":"pmh:oai:authors.library.caltech.edu:69209","doi":null,"is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/69209/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"},{"id":"pmh:oai:authors.library.caltech.edu:69521","doi":null,"is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/69521/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:authors.library.caltech.edu:69522","doi":null,"is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/69522/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W40887843","https://openalex.org/W69766967","https://openalex.org/W581389087","https://openalex.org/W1603142303","https://openalex.org/W1967321130","https://openalex.org/W1976584051","https://openalex.org/W1985787666","https://openalex.org/W1995932740","https://openalex.org/W1997542937","https://openalex.org/W1999294962","https://openalex.org/W2000214666","https://openalex.org/W2023237845","https://openalex.org/W2034147186","https://openalex.org/W2058880116","https://openalex.org/W2106439303","https://openalex.org/W2112708371","https://openalex.org/W2118688057","https://openalex.org/W2127091535","https://openalex.org/W2144837273","https://openalex.org/W2175441551","https://openalex.org/W2232710831","https://openalex.org/W2237109911","https://openalex.org/W2295821368","https://openalex.org/W2912424718","https://openalex.org/W2997712422","https://openalex.org/W2999104210","https://openalex.org/W4230055019","https://openalex.org/W4230252700","https://openalex.org/W4238834011","https://openalex.org/W4241730892","https://openalex.org/W4245886800","https://openalex.org/W4253118614","https://openalex.org/W4254019281","https://openalex.org/W4301491118","https://openalex.org/W6683006921","https://openalex.org/W6945029233"],"related_works":["https://openalex.org/W114513664","https://openalex.org/W1982358758","https://openalex.org/W632376272","https://openalex.org/W2005061189","https://openalex.org/W2167567393","https://openalex.org/W1523532434","https://openalex.org/W2023024657","https://openalex.org/W2605235102","https://openalex.org/W2324243098","https://openalex.org/W7164740774"],"abstract_inverted_index":{"Many":[0],"computer":[1],"graphics":[2],"applications":[3,55,76],"require":[4],"high-intensity":[5],"numerical":[6],"simulation.":[7],"We":[8,33],"show":[9],"that":[10],"such":[11],"computations":[12],"can":[13,68],"be":[14],"performed":[15],"efficiently":[16],"on":[17,84],"the":[18],"GPU,":[19],"which":[20],"we":[21],"regard":[22],"as":[23],"a":[24,41,48],"full":[25],"function":[26],"streaming":[27],"processor":[28],"with":[29],"high":[30],"floating-point":[31],"performance.":[32],"implemented":[34],"two":[35],"basic,":[36],"broadly":[37],"useful,":[38],"computational":[39],"kernels:":[40],"sparse":[42],"matrix":[43],"conjugate":[44],"gradient":[45],"solver":[46,51],"and":[47,60,65,80],"regular-grid":[49],"multigrid":[50],".":[52],"Real":[53],"time":[54],"ranging":[56],"from":[57,71],"mesh":[58],"smoothing":[59],"parameterization":[61],"to":[62],"fluid":[63,81],"solvers":[64],"solid":[66],"mechanics":[67],"greatly":[69],"benefit":[70],"these,":[72],"evidence":[73],"our":[74],"example":[75],"of":[77],"geometric":[78],"flow":[79],"simulation":[82],"running":[83],"NVIDIA's":[85],"GeForce":[86],"FX.":[87]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":33},{"year":2015,"cited_by_count":34},{"year":2014,"cited_by_count":37},{"year":2013,"cited_by_count":39},{"year":2012,"cited_by_count":38}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2020-01-10T00:00:00"}