{"id":"https://openalex.org/W2013265047","doi":"https://doi.org/10.1137/060676192","title":"Computation of Interface Reflection and Regular or Diffuse Transmission of the Planar Symmetric Radiative Transfer Equation with Isotropic Scattering and Its Diffusion Limit","display_name":"Computation of Interface Reflection and Regular or Diffuse Transmission of the Planar Symmetric Radiative Transfer Equation with Isotropic Scattering and Its Diffusion Limit","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2013265047","doi":"https://doi.org/10.1137/060676192","mag":"2013265047"},"language":"en","primary_location":{"id":"doi:10.1137/060676192","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060676192","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017812804","display_name":"Shi Jin","orcid":"https://orcid.org/0000-0002-8635-7435"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shi Jin","raw_affiliation_strings":["jin@math.wisc.edu and xyang@math.wisc.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"jin@math.wisc.edu and xyang@math.wisc.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059251688","display_name":"Xiaomei Liao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaomei Liao","raw_affiliation_strings":["xliao@hsph.harvard.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"xliao@hsph.harvard.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004956299","display_name":"Xu Yang","orcid":"https://orcid.org/0000-0001-6239-1922"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xu Yang","raw_affiliation_strings":["University of Wisconsin, Madison"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin, Madison","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017812804"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5082,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.91786467,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"30","issue":"4","first_page":"1992","last_page":"2017"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9994000196456909,"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":0.9991999864578247,"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/reflection","display_name":"Reflection (computer programming)","score":0.6935939788818359},{"id":"https://openalex.org/keywords/radiative-transfer","display_name":"Radiative transfer","score":0.6512653827667236},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.6406397819519043},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.5891770124435425},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.56684410572052},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5453126430511475},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5402052402496338},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.5026559829711914},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4917755424976349},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.48982617259025574},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4699575901031494},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4465409219264984},{"id":"https://openalex.org/keywords/computational-physics","display_name":"Computational physics","score":0.4023476243019104},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35920873284339905},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.29218804836273193},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1301649808883667},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12235894799232483},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10169956088066101},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.07435479760169983}],"concepts":[{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.6935939788818359},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.6512653827667236},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.6406397819519043},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.5891770124435425},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.56684410572052},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5453126430511475},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5402052402496338},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.5026559829711914},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4917755424976349},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.48982617259025574},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4699575901031494},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4465409219264984},{"id":"https://openalex.org/C30475298","wikidata":"https://www.wikidata.org/wiki/Q909554","display_name":"Computational physics","level":1,"score":0.4023476243019104},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35920873284339905},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.29218804836273193},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1301649808883667},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12235894799232483},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10169956088066101},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.07435479760169983},{"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060676192","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060676192","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.9200000166893005,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1037328034","https://openalex.org/W1555627060","https://openalex.org/W1573293896","https://openalex.org/W1967562270","https://openalex.org/W1968055746","https://openalex.org/W1984627781","https://openalex.org/W1995266347","https://openalex.org/W2005316292","https://openalex.org/W2005733131","https://openalex.org/W2013315479","https://openalex.org/W2022088322","https://openalex.org/W2049993329","https://openalex.org/W2050873954","https://openalex.org/W2054031825","https://openalex.org/W2054210282","https://openalex.org/W2059739202","https://openalex.org/W2067216123","https://openalex.org/W2072397434","https://openalex.org/W2073649388","https://openalex.org/W2076764497","https://openalex.org/W2105705213","https://openalex.org/W2111427335","https://openalex.org/W2141613219","https://openalex.org/W2159737370","https://openalex.org/W2163030116","https://openalex.org/W2592479139","https://openalex.org/W2610542513","https://openalex.org/W3042562017","https://openalex.org/W3135227555"],"related_works":["https://openalex.org/W2794789911","https://openalex.org/W4298134547","https://openalex.org/W2122976425","https://openalex.org/W2088773039","https://openalex.org/W4382753160","https://openalex.org/W2284229495","https://openalex.org/W2028697747","https://openalex.org/W4320084277","https://openalex.org/W2383822543","https://openalex.org/W2039891891"],"abstract_inverted_index":{"In":[0],"this":[1,83,109],"paper,":[2],"we":[3,103],"develop":[4],"a":[5],"numerical":[6,77,106],"scheme":[7,99,111],"for":[8,34,58],"the":[9,13,26,29,44,51,66,71,76,89,93,98,116,125,129,137,141],"interface":[10,67,143],"problem":[11],"in":[12,25,36,43],"planar":[14],"symmetric":[15],"radiative":[16],"transfer":[17],"equation":[18],"with":[19,39,88,140],"isotropic":[20],"scattering.":[21],"Such":[22],"problems":[23],"arise":[24],"modeling":[27],"of":[28,31,54,82,97],"propagation":[30],"energy":[32],"density":[33],"waves":[35],"heterogeneous":[37],"media":[38],"weak":[40],"random":[41],"fluctuation":[42],"high":[45],"frequency":[46],"regime.":[47],"The":[48,79,95],"idea,":[49],"following":[50],"earlier":[52],"work":[53],"Jin":[55],"and":[56,61,73,122],"Wen":[57],"regular":[59],"transmission":[60,91,121],"reflection,":[62],"is":[63,85,100,112],"to":[64,86,114,134],"build":[65],"condition,":[68],"which":[69],"characterizes":[70],"reflection":[72,123],"transmission,":[74],"into":[75],"flux.":[78],"new":[80,110],"contribution":[81],"article":[84],"deal":[87],"diffuse":[90],"at":[92],"interface.":[94],"positivity":[96],"proven.":[101],"Moreover,":[102],"show,":[104],"via":[105],"examples,":[107],"that":[108],"able":[113],"capture":[115,136],"correct":[117,142],"(regular":[118],"or":[119],"diffuse)":[120],"through":[124],"interface,":[126],"and,":[127],"as":[128],"mean":[130],"free":[131],"path":[132],"goes":[133],"zero,":[135],"diffusion":[138],"limit":[139],"conditions.":[144]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}