{"id":"https://openalex.org/W1996736855","doi":"https://doi.org/10.1137/120881956","title":"A Fast Iterative Method for Solving the Eikonal Equation on Tetrahedral Domains","display_name":"A Fast Iterative Method for Solving the Eikonal Equation on Tetrahedral Domains","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1996736855","doi":"https://doi.org/10.1137/120881956","mag":"1996736855","pmid":"https://pubmed.ncbi.nlm.nih.gov/25221418"},"language":"en","primary_location":{"id":"doi:10.1137/120881956","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120881956","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4162315","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110206073","display_name":"Zhisong Fu","orcid":null},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhisong Fu","raw_affiliation_strings":["The Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083523340","display_name":"Robert M. Kirby","orcid":"https://orcid.org/0000-0001-5712-4141"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert M. Kirby","raw_affiliation_strings":["The Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109840277","display_name":"Ross Whitaker","orcid":null},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ross T. Whitaker","raw_affiliation_strings":["The Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112","institution_ids":["https://openalex.org/I223532165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110206073"],"corresponding_institution_ids":["https://openalex.org/I223532165"],"apc_list":null,"apc_paid":null,"fwci":8.4083,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.96712371,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"35","issue":"5","first_page":"C473","last_page":"C494"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9980000257492065,"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":0.9980000257492065,"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":0.996399998664856,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9860000014305115,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.7629902362823486},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.751572847366333},{"id":"https://openalex.org/keywords/simd","display_name":"SIMD","score":0.6845595836639404},{"id":"https://openalex.org/keywords/eikonal-equation","display_name":"Eikonal equation","score":0.6473311185836792},{"id":"https://openalex.org/keywords/massively-parallel","display_name":"Massively parallel","score":0.5224289298057556},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.47928112745285034},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.46846526861190796},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.44760367274284363},{"id":"https://openalex.org/keywords/locality","display_name":"Locality","score":0.44126245379447937},{"id":"https://openalex.org/keywords/multi-core-processor","display_name":"Multi-core processor","score":0.4317063093185425},{"id":"https://openalex.org/keywords/distributed-memory","display_name":"Distributed memory","score":0.4204327464103699},{"id":"https://openalex.org/keywords/shared-memory","display_name":"Shared memory","score":0.31809014081954956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21491146087646484}],"concepts":[{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.7629902362823486},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.751572847366333},{"id":"https://openalex.org/C150552126","wikidata":"https://www.wikidata.org/wiki/Q339387","display_name":"SIMD","level":2,"score":0.6845595836639404},{"id":"https://openalex.org/C40375134","wikidata":"https://www.wikidata.org/wiki/Q1303846","display_name":"Eikonal equation","level":2,"score":0.6473311185836792},{"id":"https://openalex.org/C190475519","wikidata":"https://www.wikidata.org/wiki/Q544384","display_name":"Massively parallel","level":2,"score":0.5224289298057556},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.47928112745285034},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.46846526861190796},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.44760367274284363},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.44126245379447937},{"id":"https://openalex.org/C78766204","wikidata":"https://www.wikidata.org/wiki/Q555032","display_name":"Multi-core processor","level":2,"score":0.4317063093185425},{"id":"https://openalex.org/C91481028","wikidata":"https://www.wikidata.org/wiki/Q1054686","display_name":"Distributed memory","level":3,"score":0.4204327464103699},{"id":"https://openalex.org/C133875982","wikidata":"https://www.wikidata.org/wiki/Q764810","display_name":"Shared memory","level":2,"score":0.31809014081954956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21491146087646484},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/120881956","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120881956","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmid:25221418","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25221418","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM journal on scientific computing : a publication of the Society for Industrial and Applied Mathematics","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.656.1835","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.656.1835","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.sci.utah.edu/publications/Fu2013a/Fu_JSC2013.pdf","raw_type":"text"},{"id":"pmh:oai:pubmedcentral.nih.gov:4162315","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4162315","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM J Sci Comput","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:4162315","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4162315","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM J Sci Comput","raw_type":"Text"},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W58978348","https://openalex.org/W384351984","https://openalex.org/W1542243431","https://openalex.org/W1597508330","https://openalex.org/W1599469073","https://openalex.org/W1970390879","https://openalex.org/W1970680757","https://openalex.org/W1977946246","https://openalex.org/W1980251225","https://openalex.org/W1988044952","https://openalex.org/W1999244633","https://openalex.org/W1999690352","https://openalex.org/W2003009438","https://openalex.org/W2021223176","https://openalex.org/W2049391017","https://openalex.org/W2055341194","https://openalex.org/W2066585395","https://openalex.org/W2070232376","https://openalex.org/W2071121523","https://openalex.org/W2094668823","https://openalex.org/W2095830854","https://openalex.org/W2097873952","https://openalex.org/W2127292566","https://openalex.org/W2135694650","https://openalex.org/W2139822104","https://openalex.org/W2143842017","https://openalex.org/W2159786075","https://openalex.org/W2167690872","https://openalex.org/W2172242796","https://openalex.org/W2276898705"],"related_works":["https://openalex.org/W2026512611","https://openalex.org/W1985165680","https://openalex.org/W4245497162","https://openalex.org/W2353146130","https://openalex.org/W1990817968","https://openalex.org/W2150064838","https://openalex.org/W1933089384","https://openalex.org/W2185094550","https://openalex.org/W2088823210","https://openalex.org/W2135766592"],"abstract_inverted_index":{"Generating":[0],"numerical":[1],"solutions":[2,147],"to":[3,43,125,157,170,179,191],"the":[4,19,62,75,93,172,183,207],"eikonal":[5,63,229],"equation":[6,64],"and":[7,21,48,89,96,120,151,182,221],"its":[8],"many":[9],"variations":[10],"has":[11],"a":[12,57,135,155,196,210],"broad":[13],"range":[14],"of":[15,77,98,206],"applications":[16],"in":[17,115,195],"both":[18,149],"natural":[20,173],"computational":[22,200],"sciences.":[23],"Efficient":[24],"solvers":[25],"on":[26,65,81,105,112,148],"cutting-edge,":[27],"parallel":[28,58,152,192],"architectures":[29,84],"require":[30],"new":[31,132,166],"algorithms":[32],"that":[33,40,145,198],"may":[34],"not":[35],"be":[36],"theoretically":[37],"optimal,":[38],"but":[39],"are":[41],"designed":[42],"allow":[44],"asynchronous":[45],"solution":[46],"updates":[47],"have":[49],"limited":[50],"memory":[51,220],"access":[52],"patterns.":[53],"This":[54,102],"paper":[55,117],"presents":[56],"algorithm":[59],"for":[60,74,108,142,187,209],"solving":[61,109],"fully":[66],"unstructured":[67],"tetrahedral":[68,143],"meshes.":[69],"The":[70],"method":[71],"is":[72],"appropriate":[73],"type":[76],"fine-grained":[78],"parallelism":[79],"found":[80],"modern":[82],"massively-SIMD":[83],"such":[85],"as":[86,213,215],"graphics":[87],"processors":[88,194],"takes":[90],"into":[91],"account":[92],"particular":[94],"constraints":[95],"capabilities":[97],"these":[99,110],"computing":[100],"platforms.":[101],"work":[103,107],"builds":[104],"previous":[106,122],"equations":[111],"triangle":[113],"meshes;":[114],"this":[116],"we":[118,203],"adapt":[119],"extend":[121],"two-dimensional":[123],"strategies":[124],"accommodate":[126],"three-dimensional,":[127],"unstructured,":[128],"tetrahedralized":[129],"domains.":[130],"These":[131],"developments":[133],"include":[134],"local":[136],"update":[137,167],"strategy":[138],"with":[139,154,218,224],"data":[140,174,184,190],"compaction":[141],"meshes":[144],"provides":[146],"serial":[150],"architectures,":[153,223],"generalization":[156],"inhomogeneous,":[158],"anisotropic":[159],"speed":[160],"functions.":[161],"We":[162],"also":[163],"propose":[164],"two":[165],"schemes,":[168],"specialized":[169],"mitigate":[171],"increase":[175],"observed":[176],"when":[177],"moving":[178],"three":[180],"dimensions,":[181],"structures":[185],"necessary":[186],"efficiently":[188],"mapping":[189],"SIMD":[193,222],"way":[197],"maintains":[199],"density.":[201],"Finally,":[202],"present":[204],"descriptions":[205],"implementations":[208],"single":[211],"CPU,":[212],"well":[214],"multicore":[216],"CPUs":[217],"shared":[219],"comparative":[225],"results":[226],"against":[227],"state-of-the-art":[228],"solvers.":[230]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":10}],"updated_date":"2026-06-03T09:05:47.796612","created_date":"2025-10-10T00:00:00"}