{"id":"https://openalex.org/W1973433413","doi":"https://doi.org/10.1090/s0025-5718-2012-02605-6","title":"Analysis of a numerical solver for radiative transport equation","display_name":"Analysis of a numerical solver for radiative transport equation","publication_year":2012,"publication_date":"2012-04-11","ids":{"openalex":"https://openalex.org/W1973433413","doi":"https://doi.org/10.1090/s0025-5718-2012-02605-6","mag":"1973433413","pmid":"https://pubmed.ncbi.nlm.nih.gov/24771949"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2012-02605-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02605-6","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02605-6/S0025-5718-2012-02605-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02605-6/S0025-5718-2012-02605-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046684345","display_name":"Hao Gao","orcid":"https://orcid.org/0000-0001-6852-9435"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hao Gao","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles, CA 90095-1555, haog@math.ucla.edu","Department of Mathematics, University of California, Los Angeles, CA 90095-1555,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, CA 90095-1555, haog@math.ucla.edu","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, CA 90095-1555,","institution_ids":["https://openalex.org/I161318765"]}]},{"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":"Hongkai Zhao","raw_affiliation_strings":["Department of Mathematics, University of California, Irvine, CA 92697-3875, zhao@math.uci.edu","Department of Mathematics, University of California, Irvine, CA 92697-3875,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Irvine, CA 92697-3875, zhao@math.uci.edu","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, University of California, Irvine, CA 92697-3875,","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046684345"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":1.7553,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.80700513,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"82","issue":"281","first_page":"153","last_page":"172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12304","display_name":"Radiative Heat Transfer Studies","score":0.9987000226974487,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8520749807357788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7733016014099121},{"id":"https://openalex.org/keywords/radiative-transfer","display_name":"Radiative transfer","score":0.6879787445068359},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.671995222568512},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6122514605522156},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5904434323310852},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5477785468101501},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.5121967196464539},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5051506161689758},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5009720325469971},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4750887453556061},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.45296549797058105},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.45074278116226196},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4069538116455078},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2024783194065094},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1411585807800293},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08614692091941833},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.047846466302871704}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8520749807357788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7733016014099121},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.6879787445068359},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.671995222568512},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6122514605522156},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5904434323310852},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5477785468101501},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5121967196464539},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5051506161689758},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5009720325469971},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4750887453556061},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.45296549797058105},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.45074278116226196},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4069538116455078},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2024783194065094},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1411585807800293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08614692091941833},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.047846466302871704},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-2012-02605-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02605-6","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02605-6/S0025-5718-2012-02605-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmid:24771949","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/24771949","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":"Mathematics of computation","raw_type":null},{"id":"pmh:oai:europepmc.org:2977227","is_oa":false,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3999906","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2012-02605-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02605-6","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02605-6/S0025-5718-2012-02605-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2156112071","display_name":null,"funder_award_id":"DMS0811254","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2839419555","display_name":null,"funder_award_id":"EB013387","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G3354284890","display_name":null,"funder_award_id":"NIBIB","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G5357615285","display_name":"The Fast Sweeping Method and Its Applications","funder_award_id":"0811254","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337363","display_name":"National Institute of Biomedical Imaging and Bioengineering","ror":"https://ror.org/00372qc85"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1973433413.pdf","grobid_xml":"https://content.openalex.org/works/W1973433413.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W49087508","https://openalex.org/W202835528","https://openalex.org/W1583686354","https://openalex.org/W1966021993","https://openalex.org/W1998381637","https://openalex.org/W2003438645","https://openalex.org/W2006015046","https://openalex.org/W2038462676","https://openalex.org/W2084944524","https://openalex.org/W2317107851","https://openalex.org/W3208201226","https://openalex.org/W4242957978","https://openalex.org/W4245820193"],"related_works":["https://openalex.org/W2080994790","https://openalex.org/W1997618141","https://openalex.org/W2070144563","https://openalex.org/W1590663584","https://openalex.org/W4367189851","https://openalex.org/W3147068302","https://openalex.org/W2008560581","https://openalex.org/W55019828","https://openalex.org/W4246077076","https://openalex.org/W2089783241"],"abstract_inverted_index":{"We":[0],"analyze":[1],"a":[2],"numerical":[3],"algorithm":[4],"for":[5],"solving":[6],"radiative":[7],"transport":[8],"equation":[9],"with":[10,21],"vacuum":[11],"or":[12,34],"reflection":[13],"boundary":[14],"condition":[15],"that":[16],"was":[17],"proposed":[18],"in":[19],"[4]":[20],"angular":[22],"discretization":[23,30],"by":[24,31],"finite":[25,35],"element":[26],"method":[27],"and":[28],"spatial":[29],"discontinuous":[32],"Galerkin":[33],"difference":[36],"method.":[37]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}