{"id":"https://openalex.org/W2063036688","doi":"https://doi.org/10.1137/070680357","title":"Fast Marching Methods for Stationary Hamilton\u2013Jacobi Equations with Axis-Aligned Anisotropy","display_name":"Fast Marching Methods for Stationary Hamilton\u2013Jacobi Equations with Axis-Aligned Anisotropy","publication_year":2008,"publication_date":"2008-11-26","ids":{"openalex":"https://openalex.org/W2063036688","doi":"https://doi.org/10.1137/070680357","mag":"2063036688"},"language":"en","primary_location":{"id":"doi:10.1137/070680357","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070680357","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/A5111934623","display_name":"Ken Alton","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Ken Alton","raw_affiliation_strings":["Department of Computer Science, University of British Columbia, Vancouver, BC V6T 1Z4, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, BC V6T 1Z4, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086488324","display_name":"Ian M. Mitchell","orcid":"https://orcid.org/0000-0001-7053-441X"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ian M. Mitchell","raw_affiliation_strings":["Department of Computer Science, University of British Columbia, Vancouver, BC V6T 1Z4, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, BC V6T 1Z4, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111934623"],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":null,"apc_paid":null,"fwci":4.1072,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.93700787,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"47","issue":"1","first_page":"363","last_page":"385"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.996999979019165,"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":0.996999979019165,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.9437999725341797,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eikonal-equation","display_name":"Eikonal equation","score":0.8741239309310913},{"id":"https://openalex.org/keywords/fast-marching-method","display_name":"Fast marching method","score":0.8483961224555969},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.7351143956184387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6914314031600952},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4581107795238495},{"id":"https://openalex.org/keywords/dijkstras-algorithm","display_name":"Dijkstra's algorithm","score":0.43970951437950134},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.3953416347503662},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39268043637275696},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3259250223636627},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3100040555000305},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.25968408584594727},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.14646151661872864}],"concepts":[{"id":"https://openalex.org/C40375134","wikidata":"https://www.wikidata.org/wiki/Q1303846","display_name":"Eikonal equation","level":2,"score":0.8741239309310913},{"id":"https://openalex.org/C17866373","wikidata":"https://www.wikidata.org/wiki/Q5437042","display_name":"Fast marching method","level":2,"score":0.8483961224555969},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.7351143956184387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6914314031600952},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4581107795238495},{"id":"https://openalex.org/C173870130","wikidata":"https://www.wikidata.org/wiki/Q8548","display_name":"Dijkstra's algorithm","level":4,"score":0.43970951437950134},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.3953416347503662},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39268043637275696},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3259250223636627},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3100040555000305},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.25968408584594727},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.14646151661872864}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/070680357","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070680357","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.8638","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.8638","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ubc.ca/~mitchell/Papers/publishedSINUM08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.205.1542","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.205.1542","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ubc.ca/%7Ekalton/papers/ubctechrep2008a.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1535896976","https://openalex.org/W1973965874","https://openalex.org/W1989131020","https://openalex.org/W1990466879","https://openalex.org/W1994875376","https://openalex.org/W1999244633","https://openalex.org/W1999690352","https://openalex.org/W2003009438","https://openalex.org/W2025550225","https://openalex.org/W2027978220","https://openalex.org/W2032316144","https://openalex.org/W2049391017","https://openalex.org/W2054113582","https://openalex.org/W2055341194","https://openalex.org/W2094668823","https://openalex.org/W2113222527","https://openalex.org/W2113566579","https://openalex.org/W2118268140","https://openalex.org/W2126757501","https://openalex.org/W2132202988","https://openalex.org/W2154018969","https://openalex.org/W2168463767","https://openalex.org/W2169528473","https://openalex.org/W2177195156","https://openalex.org/W2561843528","https://openalex.org/W2998023265"],"related_works":["https://openalex.org/W2474675250","https://openalex.org/W2200845428","https://openalex.org/W1970732967","https://openalex.org/W176770976","https://openalex.org/W2415867404","https://openalex.org/W2050394778","https://openalex.org/W2052629386","https://openalex.org/W3083851338","https://openalex.org/W2348332226","https://openalex.org/W2168915761"],"abstract_inverted_index":{"The":[0],"fast":[1],"marching":[2],"method":[3],"(FMM)":[4],"has":[5,99],"proved":[6],"to":[7,41,82],"be":[8,73],"a":[9,22,34,48,60,92],"very":[10],"efficient":[11],"algorithm":[12,27,84],"for":[13,28,63,91,151],"solving":[14],"the":[15,30,76,78,83,87,131,134,154,159],"isotropic":[16],"Eikonal":[17,155],"equation.":[18],"Because":[19],"it":[20],"is":[21,38,85],"minor":[23],"modification":[24,80],"of":[25,51,96,117,129,133,153,168],"Dijkstra's":[26],"finding":[29],"shortest":[31],"path":[32,107],"through":[33],"discrete":[35],"graph,":[36],"FMM":[37],"also":[39,125],"easy":[40],"implement.":[42],"In":[43],"this":[44],"paper":[45],"we":[46,124,146],"describe":[47],"new":[49],"class":[50,95,116],"Hamilton\u2013Jacobi":[52],"(HJ)":[53],"PDEs":[54,98,119],"with":[55,172],"axis-aligned":[56],"anisotropy":[57],"which":[58],"satisfy":[59],"causality":[61],"condition":[62],"standard":[64],"finite-difference":[65],"schemes":[66],"on":[67,165],"orthogonal":[68,166],"grids":[69,121,142,167],"and":[70,105,109,120,143,162,171],"can":[71],"hence":[72],"solved":[74],"using":[75],"FMM;":[77],"only":[79],"required":[81],"in":[86,101],"local":[88,135],"update":[89,136,149],"equation":[90,156],"node.":[93],"This":[94],"HJ":[97,118],"applications":[100],"anelliptic":[102],"wave":[103],"propagation":[104],"robotic":[106],"planning,":[108],"brief":[110],"examples":[111],"are":[112],"included.":[113],"Since":[114],"our":[115],"permit":[122],"asymmetries,":[123],"examine":[126],"some":[127],"methods":[128],"improving":[130],"efficiency":[132],"that":[137,157],"do":[138],"not":[139],"require":[140],"symmetric":[141],"PDEs.":[144],"Finally,":[145],"include":[147],"explicit":[148],"formulas":[150],"variations":[152],"use":[158],"Manhattan,":[160],"Euclidean,":[161],"infinity":[163],"norms":[164],"arbitrary":[169],"dimension":[170],"variable":[173],"node":[174],"spacing.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
