{"id":"https://openalex.org/W2034244672","doi":"https://doi.org/10.1137/0915013","title":"Fast Adaptive Methods for the Free-Space Heat Equation","display_name":"Fast Adaptive Methods for the Free-Space Heat Equation","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W2034244672","doi":"https://doi.org/10.1137/0915013","mag":"2034244672"},"language":"en","primary_location":{"id":"doi:10.1137/0915013","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915013","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"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://escholarship.org/content/qt9kc0v0rs/qt9kc0v0rs.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086443955","display_name":"John Strain","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"John Strain","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5086443955"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.506,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.59291369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"15","issue":"1","first_page":"185","last_page":"206"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/heat-equation","display_name":"Heat equation","score":0.7010133266448975},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.648643970489502},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5955775380134583},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5101121068000793},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4949571490287781},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46959200501441956},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43785661458969116},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.4162953197956085},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.41368162631988525},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41065287590026855},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.41044679284095764},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3902813494205475},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30602532625198364},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3013783097267151},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.135370671749115}],"concepts":[{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.7010133266448975},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.648643970489502},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5955775380134583},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5101121068000793},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4949571490287781},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46959200501441956},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43785661458969116},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.4162953197956085},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.41368162631988525},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41065287590026855},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.41044679284095764},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3902813494205475},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30602532625198364},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3013783097267151},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.135370671749115},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/0915013","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915013","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":"pmh:oai:escholarship.org/ark:/13030/qt9kc0v0rs","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/9kc0v0rs","pdf_url":"https://escholarship.org/content/qt9kc0v0rs/qt9kc0v0rs.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, vol 15, iss 1","raw_type":"article"},{"id":"pmh:qt9kc0v0rs","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/9kc0v0rs","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Strain, J. (1994). Fast Adaptive Methods for the Free-Space Heat Equation. SIAM Journal on Scientific Computing, 15(1), 185 - 206. doi: 10.1137/0915013. UC Berkeley: Retrieved from: http://www.escholarship.org/uc/item/9kc0v0rs","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:escholarship.org/ark:/13030/qt9kc0v0rs","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/9kc0v0rs","pdf_url":"https://escholarship.org/content/qt9kc0v0rs/qt9kc0v0rs.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, vol 15, iss 1","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2034244672.pdf","grobid_xml":"https://content.openalex.org/works/W2034244672.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1551073729","https://openalex.org/W1582171922","https://openalex.org/W1966773805","https://openalex.org/W2075085615","https://openalex.org/W2077852080","https://openalex.org/W2095044295","https://openalex.org/W2138478089","https://openalex.org/W2160431995","https://openalex.org/W3038165843","https://openalex.org/W4295022726","https://openalex.org/W4300793121"],"related_works":["https://openalex.org/W2263119459","https://openalex.org/W1970616601","https://openalex.org/W3131993578","https://openalex.org/W4234588361","https://openalex.org/W2374567876","https://openalex.org/W2288394291","https://openalex.org/W2005876858","https://openalex.org/W2293645281","https://openalex.org/W3036140763","https://openalex.org/W2913782054"],"abstract_inverted_index":{"Standard":[0],"numerical":[1],"methods":[2,38,49,126],"for":[3,133],"the":[4,21,41,51,62,87,101],"heat":[5,43,88],"equation":[6,44,89],"in":[7,23,90,120],"two":[8,121],"or":[9,113,136,140],"more":[10],"space":[11,122],"dimensions":[12,123],"are":[13],"excellent":[14],"if":[15],"it":[16,99],"is":[17,78,144],"necessary":[18],"to":[19,69,80,85,127],"follow":[20],"evolution":[22],"great":[24],"detail":[25],"through":[26],"many":[27],"small":[28],"timesteps.":[29,47],"This":[30],"paper":[31],"presents":[32],"efficient":[33],"and":[34,84,130],"accurate":[35,104,129],"new":[36],"adaptive":[37,57],"that":[39,60],"solve":[40,81,86],"free-space":[42],"with":[45,55,93,97],"large":[46],"These":[48],"combine":[50],"fast":[52,115],"Gauss":[53],"transform":[54],"an":[56],"refinement":[58],"scheme":[59],"represents":[61],"solution":[63],"as":[64],"a":[65,70],"continuous":[66],"piecewise":[67],"polynomial,":[68],"user-specified":[71],"degree":[72],"of":[73,103],"accuracy.":[74],"The":[75],"same":[76],"approach":[77],"extended":[79],"inhomogeneous":[82],"problems":[83,96],"moving":[91],"domains":[92],"boundaries.":[94],"In":[95],"boundaries,":[98],"allows":[100],"use":[102],"boundary":[105],"representations":[106],"without":[107],"requiring":[108],"difficult":[109],"product":[110],"integration":[111],"formulas":[112],"precluding":[114],"evaluation":[116],"schemes.":[117],"Numerical":[118],"experiments":[119],"show":[124],"these":[125],"be":[128],"efficient,":[131],"especially":[132],"highly":[134],"nonuniform":[135],"discontinuous":[137],"initial":[138],"data":[139],"when":[141],"substantial":[142],"accuracy":[143],"required.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}