{"id":"https://openalex.org/W2995622182","doi":"https://doi.org/10.1137/19m130861x","title":"Analysis of a Sinclair-Type Domain Decomposition Solver for Atomistic/Continuum Coupling","display_name":"Analysis of a Sinclair-Type Domain Decomposition Solver for Atomistic/Continuum Coupling","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2995622182","doi":"https://doi.org/10.1137/19m130861x","mag":"2995622182"},"language":"en","primary_location":{"id":"doi:10.1137/19m130861x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m130861x","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://export.arxiv.org/pdf/1912.10530","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064082194","display_name":"Max Hodapp","orcid":"https://orcid.org/0000-0002-6220-0417"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Max Hodapp","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064082194"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00196476,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"4","first_page":"1499","last_page":"1537"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.7006874084472656},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6236509084701538},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5772682428359985},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5233568549156189},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4961746633052826},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46996352076530457},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.4637698829174042},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4616270363330841},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.44195619225502014},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4409412741661072},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43779414892196655},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4192863702774048},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3279978334903717},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.32417505979537964},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3077520430088043},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29872947931289673},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2319299280643463}],"concepts":[{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.7006874084472656},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6236509084701538},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5772682428359985},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5233568549156189},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4961746633052826},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46996352076530457},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.4637698829174042},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4616270363330841},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.44195619225502014},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4409412741661072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43779414892196655},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4192863702774048},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3279978334903717},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.32417505979537964},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3077520430088043},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29872947931289673},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2319299280643463},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m130861x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m130861x","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"mag:2995622182","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1912.10530","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1912.10530","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1912.10530","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"mag:2995622182","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1912.10530","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1037483004","display_name":null,"funder_award_id":"2016-7","funder_id":"https://openalex.org/F4320324442","funder_display_name":"Skolkovo Institute of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320324442","display_name":"Skolkovo Institute of Science and Technology","ror":"https://ror.org/03f9nc143"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1517019223","https://openalex.org/W1544636804","https://openalex.org/W1548589512","https://openalex.org/W1755818662","https://openalex.org/W1899836022","https://openalex.org/W1966223778","https://openalex.org/W1969593540","https://openalex.org/W1970100137","https://openalex.org/W1973986951","https://openalex.org/W1980684997","https://openalex.org/W1984273566","https://openalex.org/W1985400493","https://openalex.org/W1997397055","https://openalex.org/W1998459768","https://openalex.org/W1999959044","https://openalex.org/W2003301106","https://openalex.org/W2005745935","https://openalex.org/W2005904620","https://openalex.org/W2008808718","https://openalex.org/W2017430744","https://openalex.org/W2018419001","https://openalex.org/W2019976783","https://openalex.org/W2026374723","https://openalex.org/W2030430698","https://openalex.org/W2032634061","https://openalex.org/W2053087016","https://openalex.org/W2058367641","https://openalex.org/W2073575966","https://openalex.org/W2083206954","https://openalex.org/W2084277380","https://openalex.org/W2088422413","https://openalex.org/W2147059966","https://openalex.org/W2161684051","https://openalex.org/W2161980787","https://openalex.org/W2289891550","https://openalex.org/W2398055650","https://openalex.org/W2800685917","https://openalex.org/W2889261193","https://openalex.org/W2915251043","https://openalex.org/W3098399558","https://openalex.org/W3103516595"],"related_works":["https://openalex.org/W2915251043","https://openalex.org/W2294441545","https://openalex.org/W1867526242","https://openalex.org/W2050038442","https://openalex.org/W648137771","https://openalex.org/W1701499610","https://openalex.org/W2805177917","https://openalex.org/W2767049640","https://openalex.org/W1964232941","https://openalex.org/W2078359384","https://openalex.org/W2003292056","https://openalex.org/W1719871498","https://openalex.org/W2951715448","https://openalex.org/W2990974632","https://openalex.org/W2336649755","https://openalex.org/W2142697083","https://openalex.org/W3011436154","https://openalex.org/W2255986885","https://openalex.org/W1759360200","https://openalex.org/W3091618037"],"abstract_inverted_index":{"The":[0],"\"flexible":[1],"boundary":[2,150],"condition\"":[3],"method,":[4],"introduced":[5],"by":[6,60],"Sinclair":[7,138],"and":[8,50,143,187,230],"coworkers":[9],"in":[10,26,96],"the":[11,15,34,56,63,68,125,129,137,155,167,170,194,206,219,223,237],"1970s,":[12],"remains":[13],"among":[14],"most":[16],"popular":[17],"methods":[18],"for":[19,189,228],"simulating":[20],"isolated":[21],"two-dimensional":[22],"crystalline":[23],"defects,":[24],"embedded":[25],"an":[27,145,211],"effectively":[28],"infinite":[29,156],"atomistic":[30],"domain.":[31],"In":[32,86],"essence,":[33],"method":[35,43,106,139,152,172,195],"can":[36],"be":[37],"characterized":[38],"as":[39],"a":[40,47,51,87,148,161,176,183,190,216],"domain":[41],"decomposition":[42],"which":[44],"iterates":[45],"between":[46,222],"local":[48],"anharmonic":[49],"global":[52,177],"harmonic":[53],"problem,":[54],"where":[55],"latter":[57],"is":[58,196],"solved":[59],"means":[61],"of":[62,67,116,118,128,169,173,218],"lattice":[64,131],"Green":[65,132],"function":[66],"ideal":[69],"crystal.":[70],"This":[71],"local/global":[72],"splitting":[73],"gives":[74],"rise":[75],"to":[76,109,140,153,160,235],"tremendously":[77],"improved":[78],"convergence":[79,185,207],"rates":[80],"over":[81],"related":[82],"alternating":[83],"Schwarz":[84],"methods.":[85],"previous":[88],"publication":[89],"(Hodapp":[90],"et":[91],"al.,":[92],"2019,":[93],"Comput.":[94],"Methods":[95],"Appl.":[97],"Mech.":[98],"Eng.":[99],"348),":[100],"we":[101,135,181,209],"have":[102],"shown":[103],"that":[104,193],"this":[105],"also":[107],"applies":[108],"large-scale":[110],"three-dimensional":[111],"problems,":[112],"possibly":[113],"involving":[114],"hundreds":[115],"thousands":[117],"atoms,":[119],"using":[120,147],"fast":[121],"summation":[122],"techniques":[123],"exploiting":[124],"low-rank":[126],"nature":[127],"asymptotic":[130],"function.":[133],"Here,":[134],"generalize":[136],"bounded":[141],"domains":[142],"develop":[144,210],"implementation":[146],"discrete":[149],"element":[151],"correct":[154],"solution":[157],"with":[158],"respect":[159],"prescribed":[162],"far-field":[163],"condition,":[164],"thus":[165],"preserving":[166],"advantage":[168],"original":[171],"not":[174],"requiring":[175],"spatial":[178],"discretization.":[179],"Moreover,":[180],"present":[182],"detailed":[184],"analysis":[186],"show":[188],"one-dimensional":[191],"problem":[192],"unconditionally":[197],"stable":[198],"under":[199],"physically":[200],"motivated":[201],"assumptions.":[202],"To":[203],"further":[204],"improve":[205],"behavior,":[208],"acceleration":[212],"technique":[213],"based":[214],"on":[215],"relaxation":[217],"transmission":[220],"conditions":[221],"two":[224],"subproblems.":[225],"Numerical":[226],"examples":[227],"linear":[229],"nonlinear":[231],"problems":[232],"are":[233],"presented":[234],"validate":[236],"proposed":[238],"methodology.":[239]},"counts_by_year":[],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}
