{"id":"https://openalex.org/W2071749787","doi":"https://doi.org/10.1137/s1064827503424013","title":"An ADI-Like Preconditioner for Boltzmann Transport","display_name":"An ADI-Like Preconditioner for Boltzmann Transport","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2071749787","doi":"https://doi.org/10.1137/s1064827503424013","mag":"2071749787"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827503424013","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503424013","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/A5067338164","display_name":"E. D\u2019Azevedo","orcid":"https://orcid.org/0000-0002-6945-3206"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"E. F. D'Azevedo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004575978","display_name":"Bronson Messer","orcid":"https://orcid.org/0000-0002-5358-5415"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Messer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027691460","display_name":"Anthony Mezzacappa","orcid":"https://orcid.org/0000-0001-9816-9741"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Mezzacappa","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5083648204","display_name":"M. Liebend\u00f6rfer","orcid":"https://orcid.org/0000-0001-8523-9528"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Liebend\u00f6rfer","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5067338164"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.775,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.85985104,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"26","issue":"3","first_page":"810","last_page":"820"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11367","display_name":"Particle accelerators and beam dynamics","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T11367","display_name":"Particle accelerators and beam dynamics","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10597","display_name":"Nuclear reactor physics and engineering","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11416","display_name":"Numerical methods for differential equations","score":0.988099992275238,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.8002336621284485},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.5948148965835571},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5530784130096436},{"id":"https://openalex.org/keywords/biconjugate-gradient-stabilized-method","display_name":"Biconjugate gradient stabilized method","score":0.48167693614959717},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4751952886581421},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.4687730669975281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46568289399147034},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.45336300134658813},{"id":"https://openalex.org/keywords/neutron-transport","display_name":"Neutron transport","score":0.4452970325946808},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.43462488055229187},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.43200981616973877},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4295980930328369},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4135900139808655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3425081968307495},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3229222595691681},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2449013590812683},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21219757199287415},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.13488975167274475},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10600519180297852}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8002336621284485},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5948148965835571},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5530784130096436},{"id":"https://openalex.org/C120553275","wikidata":"https://www.wikidata.org/wiki/Q4903720","display_name":"Biconjugate gradient stabilized method","level":3,"score":0.48167693614959717},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4751952886581421},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.4687730669975281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46568289399147034},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.45336300134658813},{"id":"https://openalex.org/C66963500","wikidata":"https://www.wikidata.org/wiki/Q3338735","display_name":"Neutron transport","level":3,"score":0.4452970325946808},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.43462488055229187},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.43200981616973877},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4295980930328369},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4135900139808655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3425081968307495},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3229222595691681},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2449013590812683},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21219757199287415},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.13488975167274475},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10600519180297852},{"id":"https://openalex.org/C152568617","wikidata":"https://www.wikidata.org/wiki/Q2348","display_name":"Neutron","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827503424013","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503424013","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":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1491365776","https://openalex.org/W1989752010","https://openalex.org/W1999086185","https://openalex.org/W1999620225","https://openalex.org/W2002989381","https://openalex.org/W2009497596","https://openalex.org/W2023047869","https://openalex.org/W2078311192","https://openalex.org/W2079361963","https://openalex.org/W2089099677","https://openalex.org/W2095036901","https://openalex.org/W2127466194","https://openalex.org/W2140153041","https://openalex.org/W2155216327","https://openalex.org/W2158407804","https://openalex.org/W2995130828"],"related_works":["https://openalex.org/W1567048268","https://openalex.org/W4251450884","https://openalex.org/W2802895139","https://openalex.org/W3190226290","https://openalex.org/W2078681144","https://openalex.org/W2129343865","https://openalex.org/W1974017319","https://openalex.org/W2024011045","https://openalex.org/W2593694184","https://openalex.org/W2345127431"],"abstract_inverted_index":{"Numerical":[0,196],"modeling":[1,48],"of":[2,13,20,39,49,82,107,112,142],"radiation":[3,29,61],"transport":[4,52,68,84,106,162],"and":[5,28,101,109,137,146,182,205,227],"fluid":[6],"dynamics":[7],"are":[8,98,198],"central":[9],"to":[10,24,70,103,117,200],"many":[11],"fields":[12],"science.":[14],"This":[15,57],"paper":[16],"studies":[17],"the":[18,37,47,83,86,104,110,125,130,133,149,160,178,185,202],"application":[19],"preconditioned":[21],"iterative":[22],"methods":[23],"time-dependent":[25,66],"coupled":[26,69],"hydrodynamics":[27,62,71],"(Boltzmann)":[30],"transport.":[31,75,119],"In":[32],"particular,":[33],"we":[34,174],"focus":[35],"on":[36,124],"solution":[38],"Jacobian":[40,87],"matrices":[41,88],"in":[42,46,53,148],"full":[43],"Newton":[44],"iterations":[45],"neutrino":[50,67,134,143],"(radiation)":[51],"core":[54],"collapse":[55],"supernovae.":[56],"is":[58],"a":[59,77,90,140,220],"demanding":[60],"application,":[63],"requiring":[64],"accurate":[65],"driven":[72],"by":[73],"this":[74,118],"Given":[76],"fully":[78],"implicit":[79,170],"finite":[80],"differencing":[81],"equations,":[85],"have":[89],"special":[91],"block":[92],"tridiagonal":[93],"structure.":[94],"The":[95,120,209],"off-diagonal":[96],"blocks":[97],"exactly":[99],"diagonal":[100,122],"correspond":[102],"spatial":[105,114,180,193],"neutrinos":[108],"coupling":[111,131,186],"adjacent":[113],"zones":[115],"owing":[116],"dense":[121],"blocks,":[123],"other":[126],"hand,":[127],"arise":[128],"from":[129],"between":[132],"direction":[135,181],"cosines":[136],"energy,":[138],"as":[139,224],"result":[141],"emission,":[144],"absorption,":[145],"scattering,":[147],"multiple":[150,152],"species":[151],"energy":[153],"group":[154],"discrete":[155],"ordinates":[156],"formulation":[157],"for":[158],"solving":[159],"Boltzmann":[161],"equations.":[163],"We":[164],"consider":[165],"an":[166],"effective":[167],"alternating":[168],"direct":[169],"(ADI)-like":[171],"preconditioner":[172],"where":[173],"alternately":[175],"sweep":[176],"along":[177],"one-dimensional":[179],"separately":[183],"handle":[184],"among":[187],"multidirection":[188],"multigroup":[189],"variables":[190],"within":[191],"each":[192],"discretization":[194],"cell.":[195],"examples":[197],"given":[199],"illustrate":[201],"fast":[203],"convergence":[204,222],"efficient":[206],"parallel":[207],"implementation.":[208],"results":[210],"suggest":[211],"that":[212],"even":[213],"simple":[214],"fixed":[215],"point":[216],"iteration":[217],"can":[218],"achieve":[219],"similar":[221],"rate":[223],"{\\tt":[225,228],"GMRES}":[226],"BICGSTAB}.":[229]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}