{"id":"https://openalex.org/W7220930801","doi":"https://doi.org/10.48550/arxiv.2610.07653","title":"Low-rank SI-DSA and GMRES-DSA for Radiative Transfer Equation with Adaptive Accuracy Control","display_name":"Low-rank SI-DSA and GMRES-DSA for Radiative Transfer Equation with Adaptive Accuracy Control","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220930801","doi":"https://doi.org/10.48550/arxiv.2610.07653"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07653","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07653","pdf_url":"https://arxiv.org/pdf/2610.07653","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.07653","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157962376","display_name":"Chenxi Han","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Han, Chenxi","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , THE HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY , CLEAR WATER BAY , KOWLOON , HONG KONG , CHINA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , THE HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY , CLEAR WATER BAY , KOWLOON , HONG KONG , CHINA","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019445901","display_name":"Lukas  Daniel Einkemmer","orcid":"https://orcid.org/0000-0002-8798-2304","observed_orcids":["https://orcid.org/0000-0002-8798-2304"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Einkemmer, Lukas","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , UNIVERSITY OF INNSBRUCK , TECHNIKERSTRASSE 13 , INNSBRUCK , A-6020 , AUSTRIA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , UNIVERSITY OF INNSBRUCK , TECHNIKERSTRASSE 13 , INNSBRUCK , A-6020 , AUSTRIA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157985589","display_name":"Wei Guo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guo, Wei","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS AND STATISTICS , TEXAS TECH UNIVERSITY , LUBBOCK , TX , 70409 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS AND STATISTICS , TEXAS TECH UNIVERSITY , LUBBOCK , TX , 70409 , USA","institution_ids":["https://openalex.org/I12315562"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102764392","display_name":"Zhichao Peng","orcid":"https://orcid.org/0000-0002-2815-4242","observed_orcids":["https://orcid.org/0000-0002-2815-4242"]},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Peng, Zhichao","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , THE HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY , CLEAR WATER BAY , KOWLOON , HONG KONG , CHINA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , THE HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY , CLEAR WATER BAY , KOWLOON , HONG KONG , CHINA","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12304","display_name":"Radiative Heat Transfer Studies","score":0.9771000146865845,"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"}},"topics":[{"id":"https://openalex.org/T12304","display_name":"Radiative Heat Transfer Studies","score":0.9771000146865845,"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":0.010300000198185444,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.002099999925121665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/radiative-transfer-equation","display_name":"radiative transfer equation","score":0.9990000128746033},{"id":"https://openalex.org/keywords/diffusion-synthetic-acceleration","display_name":"diffusion synthetic acceleration","score":0.8119999766349792},{"id":"https://openalex.org/keywords/source-iteration","display_name":"source iteration","score":0.9070000052452087},{"id":"https://openalex.org/keywords/discrete-empirical-interpolation-method","display_name":"discrete empirical interpolation method","score":0.871999979019165},{"id":"https://openalex.org/keywords/angular-sampling","display_name":"angular sampling","score":0.5870000123977661},{"id":"https://openalex.org/keywords/material-discontinuities","display_name":"material discontinuities","score":0.75},{"id":"https://openalex.org/keywords/krylov-subspace-acceleration","display_name":"Krylov subspace acceleration","score":0.7509999871253967}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.769599974155426},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5895000100135803},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5884000062942505},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5532000064849854},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.552299976348877},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.5508999824523926},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5411999821662903},{"id":"https://openalex.org/C2781395549","wikidata":"https://www.wikidata.org/wiki/Q4680762","display_name":"Adaptive sampling","level":3,"score":0.47119998931884766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46459999680519104},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4562000036239624},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.42579999566078186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39579999446868896},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3677000105381012},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3479999899864197},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.32249999046325684},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.2849000096321106},{"id":"https://openalex.org/C146168522","wikidata":"https://www.wikidata.org/wiki/Q1068239","display_name":"Radiosity (computer graphics)","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C206588197","wikidata":"https://www.wikidata.org/wiki/Q846574","display_name":"Reuse","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07653","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07653","pdf_url":"https://arxiv.org/pdf/2610.07653","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},{"id":"doi:10.48550/arxiv.2610.07653","doi":"https://doi.org/10.48550/arxiv.2610.07653","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07653","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.07653","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07653","pdf_url":"https://arxiv.org/pdf/2610.07653","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220930801.pdf","grobid_xml":"https://content.openalex.org/works/W7220930801.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W3211600616","https://openalex.org/W4416065711","https://openalex.org/W4416111970","https://openalex.org/W4416247126","https://openalex.org/W7125786425","https://openalex.org/W7171998462"],"related_works":["https://openalex.org/W7141630855","https://openalex.org/W4416685802","https://openalex.org/W7140111407","https://openalex.org/W4388421313","https://openalex.org/W2948057265","https://openalex.org/W4401074475","https://openalex.org/W3159227499","https://openalex.org/W7130316211","https://openalex.org/W3207877496","https://openalex.org/W4213165123"],"abstract_inverted_index":{"Recently,":[0],"efficient":[1],"sweep-based":[2,177],"low-rank":[3,56,123,178,218],"iterative":[4],"solvers":[5],"have":[6],"been":[7],"developed":[8],"to":[9,149,182,212],"reduce":[10],"the":[11,22,33,75,133,155,171,183,186,190,229,232],"computational":[12,129],"costs":[13],"of":[14,21,49,185,217,231],"steady-state":[15],"solves":[16],"and":[17,78,128,189,207],"implicit":[18],"time":[19],"integration":[20],"radiative":[23],"transfer":[24],"equation":[25],"(RTE).":[26],"In":[27],"particular,":[28],"angular":[29,84,157],"sampling":[30,141,151],"based":[31],"on":[32,40,224],"discrete":[34],"empirical":[35],"interpolation":[36],"method":[37],"(DEIM)":[38],"or":[39],"error-indicated":[41],"randomized":[42],"greedy":[43],"selection":[44],"enables":[45],"efficient,":[46],"non-intrusive":[47],"reuse":[48,83],"existing":[50],"transport":[51],"sweep":[52],"implementations.":[53],"However,":[54],"randomized-greedy":[55,122],"source":[57,71],"iteration":[58],"with":[59,103],"diffusion":[60],"synthetic":[61],"acceleration":[62,146],"(SI--DSA)":[63],"enforces":[64],"uniformly":[65],"tight":[66],"accuracy":[67,119,134,215],"tolerances":[68],"across":[69],"all":[70],"iterations,":[72,77],"thereby":[73,200],"oversolving":[74],"early":[76],"it":[79],"does":[80],"not":[81,198],"explicitly":[82],"bases":[85],"from":[86],"preceding":[87,156],"iterations.":[88],"More":[89],"critically,":[90],"like":[91],"its":[92],"full-rank":[93],"counterpart,":[94],"this":[95],"approach":[96],"may":[97],"lose":[98],"effectiveness":[99,230],"in":[100,175,204],"multiscale":[101],"problems":[102,226],"strong":[104],"material":[105],"discontinuities.":[106],"We":[107,220],"address":[108],"these":[109],"limitations":[110],"through":[111],"two":[112],"complementary":[113],"developments.":[114],"First,":[115],"we":[116,163],"introduce":[117],"adaptive":[118,214],"control":[120,216],"into":[121],"SI--DSA,":[124],"reducing":[125],"intermediate":[126],"ranks":[127],"cost":[130],"while":[131],"maintaining":[132],"required":[135],"for":[136,170],"convergence.":[137],"A":[138],"two-stage":[139],"hybrid":[140],"strategy":[142],"can":[143],"provide":[144],"further":[145],"by":[147],"switching":[148],"DEIM-based":[150],"near":[152],"convergence,":[153],"once":[154],"basis":[158,196],"becomes":[159],"sufficiently":[160],"representative.":[161],"Second,":[162],"develop":[164],"an":[165],"inexact":[166],"flexible":[167],"GMRES--DSA":[168],"solver":[169],"integral":[172],"scalar-flux":[173,194],"reformulation,":[174],"which":[176],"approximations":[179],"are":[180],"confined":[181],"construction":[184],"right-hand":[187],"side":[188],"matrix--vector":[191],"products.":[192],"The":[193],"Krylov":[195],"is":[197],"compressed,":[199],"preserving":[201],"Arnoldi":[202],"orthogonality":[203],"exact":[205],"arithmetic":[206],"allowing":[208],"established":[209],"inexact-GMRES":[210],"analysis":[211],"guide":[213],"operations.":[219],"present":[221],"numerical":[222],"results":[223],"benchmark":[225],"that":[227],"demonstrate":[228],"proposed":[233],"methods.":[234]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}