{"id":"https://openalex.org/W2054756248","doi":"https://doi.org/10.1137/s0036142902400767","title":"Asynchronous Fast Adaptive Composite-Grid Methods for Elliptic Problems: Theoretical Foundations","display_name":"Asynchronous Fast Adaptive Composite-Grid Methods for Elliptic Problems: Theoretical Foundations","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2054756248","doi":"https://doi.org/10.1137/s0036142902400767","mag":"2054756248"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902400767","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902400767","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5044277064","display_name":"Barry Lee","orcid":"https://orcid.org/0000-0003-1948-7384"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Barry Lee","raw_affiliation_strings":["Lawrence Livermore National Laboratory"],"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Laboratory","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046048300","display_name":"Stephen F. McCormick","orcid":"https://orcid.org/0000-0002-6327-790X"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen F. McCormick","raw_affiliation_strings":["Lawrence Livermore National Laboratory"],"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Laboratory","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009690290","display_name":"Bobby Philip","orcid":"https://orcid.org/0000-0001-6716-3515"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bobby Philip","raw_affiliation_strings":["University of Colorado \u2010 Boulder"],"affiliations":[{"raw_affiliation_string":"University of Colorado \u2010 Boulder","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051201607","display_name":"Daniel J. Quinlan","orcid":"https://orcid.org/0000-0001-7467-9173"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel J. Quinlan","raw_affiliation_strings":["University of Colorado \u2010 Boulder"],"affiliations":[{"raw_affiliation_string":"University of Colorado \u2010 Boulder","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5044277064"],"corresponding_institution_ids":["https://openalex.org/I1282311441"],"apc_list":null,"apc_paid":null,"fwci":1.3142,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.79167817,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"1","first_page":"130","last_page":"152"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9991999864578247,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.7151831388473511},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.6589862704277039},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5868095755577087},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5725666284561157},{"id":"https://openalex.org/keywords/asynchronous-communication","display_name":"Asynchronous communication","score":0.5689152479171753},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5306453108787537},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4955192804336548},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4720512330532074},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4557473659515381},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4404168426990509},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.41184574365615845},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39452987909317017},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38268721103668213},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.18292757868766785},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14453601837158203}],"concepts":[{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.7151831388473511},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6589862704277039},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5868095755577087},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5725666284561157},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.5689152479171753},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5306453108787537},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4955192804336548},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4720512330532074},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4557473659515381},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4404168426990509},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.41184574365615845},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39452987909317017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38268721103668213},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.18292757868766785},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14453601837158203},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142902400767","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902400767","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W101816209","https://openalex.org/W118285134","https://openalex.org/W232515440","https://openalex.org/W640709609","https://openalex.org/W1524015806","https://openalex.org/W1530872699","https://openalex.org/W1565479511","https://openalex.org/W1853037326","https://openalex.org/W1866311589","https://openalex.org/W1875067974","https://openalex.org/W1971657081","https://openalex.org/W1975059575","https://openalex.org/W1990671420","https://openalex.org/W1994747981","https://openalex.org/W1997542937","https://openalex.org/W1997831216","https://openalex.org/W2003183416","https://openalex.org/W2010668310","https://openalex.org/W2012492661","https://openalex.org/W2017085690","https://openalex.org/W2018685527","https://openalex.org/W2027095938","https://openalex.org/W2028357997","https://openalex.org/W2042732056","https://openalex.org/W2055962135","https://openalex.org/W2058638623","https://openalex.org/W2059679865","https://openalex.org/W2062246266","https://openalex.org/W2072463419","https://openalex.org/W2072865167","https://openalex.org/W2093538658","https://openalex.org/W2151317657","https://openalex.org/W2153127767","https://openalex.org/W2163732690","https://openalex.org/W2398111268","https://openalex.org/W2626452020","https://openalex.org/W3141654715","https://openalex.org/W4240495313","https://openalex.org/W4246130405","https://openalex.org/W4292169137","https://openalex.org/W4292360407","https://openalex.org/W4300509647","https://openalex.org/W4382891143"],"related_works":["https://openalex.org/W2086110034","https://openalex.org/W334897171","https://openalex.org/W4309223525","https://openalex.org/W1501473830","https://openalex.org/W1691051400","https://openalex.org/W2976039273","https://openalex.org/W104982047","https://openalex.org/W2045152743","https://openalex.org/W2074513997","https://openalex.org/W2387742153"],"abstract_inverted_index":{"Accurate":[0],"numerical":[1,11,40],"modeling":[2],"of":[3,18,71,78,109,119],"complex":[4],"physical,":[5],"chemical,":[6],"and":[7],"biological":[8],"systems":[9],"requires":[10],"simulation":[12],"capability":[13],"over":[14],"a":[15,39,61,69,89],"large":[16],"range":[17],"length":[19],"scales,":[20],"with":[21],"the":[22,52,75,106,110,117,123],"ability":[23],"to":[24,57,81],"capture":[25],"rapidly":[26],"varying":[27],"phenomena":[28],"localized":[29],"in":[30,55,60,122],"space":[31],"and/or":[32],"time.":[33],"Adaptive":[34],"mesh":[35],"refinement":[36,120],"(AMR)":[37],"is":[38],"process":[41],"for":[42,92],"dynamically":[43],"introducing":[44],"local":[45],"fine":[46],"resolution":[47],"on":[48],"computational":[49],"grids":[50,80],"during":[51],"solution":[53],"process,":[54],"response":[56],"unresolved":[58],"error":[59],"computation.":[62],"Fast":[63],"adaptive":[64],"composite-grid":[65],"(FAC)":[66],"methods":[67],"are":[68],"class":[70],"algorithms":[72],"that":[73,105],"exploit":[74],"multilevel":[76,100],"structure":[77],"AMR":[79,124],"solve":[82],"elliptic":[83],"problems":[84],"efficiently.":[85],"This":[86],"paper":[87],"develops":[88],"theoretical":[90],"foundation":[91],"AFACx,":[93],"an":[94],"asynchronous":[95],"FAC":[96],"method.":[97],"A":[98],"new":[99],"condition":[101],"number":[102,118],"estimate":[103],"establishes":[104],"convergence":[107],"rate":[108],"AFACx":[111],"algorithm":[112],"does":[113],"not":[114],"degrade":[115],"as":[116],"levels":[121],"hierarchy":[125],"increases.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}