{"id":"https://openalex.org/W1980251225","doi":"https://doi.org/10.1137/050627083","title":"Fast Sweeping Methods for Eikonal Equations on Triangular Meshes","display_name":"Fast Sweeping Methods for Eikonal Equations on Triangular Meshes","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1980251225","doi":"https://doi.org/10.1137/050627083","mag":"1980251225"},"language":"en","primary_location":{"id":"doi:10.1137/050627083","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050627083","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","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/A5013248904","display_name":"Jianliang Qian","orcid":"https://orcid.org/0000-0003-3058-0096"},"institutions":[{"id":"https://openalex.org/I39587148","display_name":"Wichita State University","ror":"https://ror.org/00c4e7y75","country_code":"US","type":"education","lineage":["https://openalex.org/I39587148"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianliang Qian","raw_affiliation_strings":["WICHITA STATE UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"WICHITA STATE UNIVERSITY","institution_ids":["https://openalex.org/I39587148"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100703417","display_name":"Yong\u2010Tao Zhang","orcid":"https://orcid.org/0000-0002-0831-6590"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yong\u2010Tao Zhang","raw_affiliation_strings":["University of California, at Irvine#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, at Irvine#TAB#","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107748638","display_name":"Hongkai Zhao","orcid":"https://orcid.org/0000-0003-2148-238X"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hong\u2010Kai Zhao","raw_affiliation_strings":["University of California, at Irvine#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, at Irvine#TAB#","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":13.2299,"has_fulltext":false,"cited_by_count":199,"citation_normalized_percentile":{"value":0.9934671,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"45","issue":"1","first_page":"83","last_page":"107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9929999709129333,"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/mathematics","display_name":"Mathematics","score":0.6578229069709778},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.6033661961555481},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5983330607414246},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.54749596118927},{"id":"https://openalex.org/keywords/flops","display_name":"FLOPS","score":0.48552489280700684},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.47475937008857727},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4578818380832672},{"id":"https://openalex.org/keywords/eikonal-equation","display_name":"Eikonal equation","score":0.4442139267921448},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.377417653799057},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29046839475631714},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1686427891254425},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14589187502861023},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.13152703642845154}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6578229069709778},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.6033661961555481},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5983330607414246},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.54749596118927},{"id":"https://openalex.org/C3826847","wikidata":"https://www.wikidata.org/wiki/Q188768","display_name":"FLOPS","level":2,"score":0.48552489280700684},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.47475937008857727},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4578818380832672},{"id":"https://openalex.org/C40375134","wikidata":"https://www.wikidata.org/wiki/Q1303846","display_name":"Eikonal equation","level":2,"score":0.4442139267921448},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.377417653799057},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29046839475631714},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1686427891254425},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14589187502861023},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.13152703642845154},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050627083","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050627083","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W58978348","https://openalex.org/W153353184","https://openalex.org/W1487586009","https://openalex.org/W1532111732","https://openalex.org/W1549037739","https://openalex.org/W1552159942","https://openalex.org/W1666853924","https://openalex.org/W1680579736","https://openalex.org/W1888294994","https://openalex.org/W1977018860","https://openalex.org/W1989131020","https://openalex.org/W1994875376","https://openalex.org/W1995720627","https://openalex.org/W1997419185","https://openalex.org/W1999690352","https://openalex.org/W2003009438","https://openalex.org/W2012872284","https://openalex.org/W2021513670","https://openalex.org/W2027438381","https://openalex.org/W2041138953","https://openalex.org/W2049391017","https://openalex.org/W2050890325","https://openalex.org/W2058615912","https://openalex.org/W2065666685","https://openalex.org/W2074451231","https://openalex.org/W2085961516","https://openalex.org/W2093834886","https://openalex.org/W2097873952","https://openalex.org/W2103790247","https://openalex.org/W2118268140","https://openalex.org/W2125671914","https://openalex.org/W2126473663","https://openalex.org/W2132003031","https://openalex.org/W2133558469","https://openalex.org/W2138571234","https://openalex.org/W2141603699","https://openalex.org/W2154018969","https://openalex.org/W2157204523","https://openalex.org/W2162693461","https://openalex.org/W2165033235","https://openalex.org/W2169528473","https://openalex.org/W2282349494","https://openalex.org/W2495629635","https://openalex.org/W2558639087","https://openalex.org/W2561843528","https://openalex.org/W2562330627","https://openalex.org/W2749408143","https://openalex.org/W2752885492","https://openalex.org/W2911709767","https://openalex.org/W3038698521","https://openalex.org/W3145128584","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3176564347","https://openalex.org/W3031039437","https://openalex.org/W3204184292","https://openalex.org/W1985458517","https://openalex.org/W2355833770","https://openalex.org/W4382323155","https://openalex.org/W4315697128","https://openalex.org/W3101398262","https://openalex.org/W2911626006","https://openalex.org/W3095877357"],"abstract_inverted_index":{"The":[0,124],"original":[1],"fast":[2,32,79],"sweeping":[3,33,80],"method,":[4,170],"which":[5,159],"is":[6,130,173],"an":[7],"efficient":[8],"iterative":[9],"method":[10,34],"for":[11,145,152],"stationary":[12],"Hamilton\u2013Jacobi":[13],"equations,":[14],"relies":[15],"on":[16],"natural":[17],"ordering":[18,27],"provided":[19],"by":[20,111,164],"a":[21,100,166,190],"rectangular":[22],"mesh.":[23,44],"We":[24,66,116],"propose":[25],"novel":[26],"strategies":[28],"so":[29],"that":[30,46,68,136,184],"the":[31,56,72,78,114,118,121,128,134,137,155,174,185],"can":[35,85,96,108,160],"be":[36,97,109,161],"extended":[37],"efficiently":[38,162],"and":[39,53,105,148],"easily":[40],"to":[41,59,62],"any":[42,94],"unstructured":[43],"To":[45],"end":[47],"we":[48],"introduce":[49],"multiple":[50],"reference":[51,64],"points":[52],"order":[54],"all":[55,87],"nodes":[57],"according":[58],"their":[60],"$l^p$\u2010metrics":[61],"those":[63],"points.":[65,179],"show":[67],"these":[69,83],"orderings":[70,84],"satisfy":[71],"two":[73],"most":[74],"important":[75],"properties":[76],"underlying":[77],"method:":[81],"(1)":[82],"cover":[86],"directions":[88],"of":[89,103,113,120,127,142,177,193,196],"information":[90],"propagating":[91],"efficiently;":[92],"(2)":[93],"characteristic":[95],"decomposed":[98],"into":[99],"finite":[101,191],"number":[102,176,192],"pieces":[104],"each":[106],"piece":[107],"covered":[110],"one":[112],"orderings.":[115],"prove":[117],"convergence":[119],"new":[122,186],"algorithm.":[123],"computational":[125,139],"complexity":[126],"algorithm":[129,187],"nearly":[131],"optimal":[132],"in":[133,189],"sense":[135],"total":[138,175],"cost":[140],"consists":[141],"$O(M)$":[143],"flops":[144,151],"iteration":[146],"steps":[147],"$O(M{\\rm":[149],"log}M)$":[150],"sorting":[153,169],"at":[154],"predetermined":[156],"initialization":[157],"step":[158],"optimized":[163],"adopting":[165],"linear":[167],"time":[168],"where":[171],"M":[172],"mesh":[178,197],"Extensive":[180],"numerical":[181],"examples":[182],"demonstrate":[183],"converges":[188],"iterations":[194],"independent":[195],"size.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":5}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}