{"id":"https://openalex.org/W2089454352","doi":"https://doi.org/10.1137/05063800x","title":"A Multigrid-Fourier Method for the Computation of Elastic Fields with Application to Heteroepitaxy","display_name":"A Multigrid-Fourier Method for the Computation of Elastic Fields with Application to Heteroepitaxy","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2089454352","doi":"https://doi.org/10.1137/05063800x","mag":"2089454352"},"language":"en","primary_location":{"id":"doi:10.1137/05063800x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/05063800x","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 & Simulation","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/A5037976295","display_name":"Giovanni Russo","orcid":"https://orcid.org/0000-0003-4215-1926"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giovanni Russo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047070692","display_name":"Peter Smereka","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter Smereka","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5616,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.93886355,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"5","issue":"1","first_page":"130","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11799","display_name":"Adhesion, Friction, and Surface Interactions","score":0.9995999932289124,"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/T11799","display_name":"Adhesion, Friction, and Surface Interactions","score":0.9995999932289124,"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/T10460","display_name":"Electronic Packaging and Soldering Technologies","score":0.9929999709129333,"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9922999739646912,"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/multigrid-method","display_name":"Multigrid method","score":0.9215114712715149},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6920801401138306},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6825780868530273},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.6621285676956177},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.61421799659729},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.49614962935447693},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.4851430356502533},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.420624703168869},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4163115322589874},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3698952794075012},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.3394680619239807},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25875598192214966},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.23609477281570435}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.9215114712715149},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6920801401138306},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6825780868530273},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6621285676956177},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.61421799659729},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.49614962935447693},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.4851430356502533},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.420624703168869},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4163115322589874},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3698952794075012},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3394680619239807},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25875598192214966},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.23609477281570435},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/05063800x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/05063800x","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 & Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W154333462","https://openalex.org/W1530872699","https://openalex.org/W1973915291","https://openalex.org/W1988434428","https://openalex.org/W1991117744","https://openalex.org/W1996612117","https://openalex.org/W1996818261","https://openalex.org/W1997542937","https://openalex.org/W2004284586","https://openalex.org/W2051888772","https://openalex.org/W2073326327","https://openalex.org/W2074470009","https://openalex.org/W2127981460","https://openalex.org/W2137919032","https://openalex.org/W2151317657","https://openalex.org/W4238112325"],"related_works":["https://openalex.org/W2320412982","https://openalex.org/W2017823752","https://openalex.org/W2165559438","https://openalex.org/W4323309137","https://openalex.org/W4312630278","https://openalex.org/W4312337410","https://openalex.org/W2479552906","https://openalex.org/W2065770361","https://openalex.org/W4241180363","https://openalex.org/W1996627772"],"abstract_inverted_index":{"A":[0,15],"multigrid-Fourier":[1,199],"method":[2,63,200],"is":[3,26,40,49,75,169,184,201],"formulated":[4],"for":[5,57,95,128,195],"the":[6,29,34,37,45,58,80,83,87,96,102,111,121,129,132,135,172,188,198],"computation":[7],"of":[8,33,44,99,113,123,174,182,187],"elastic":[9,97],"fields":[10],"with":[11,21],"applications":[12],"to":[13,71,106,177,204],"heteroepitaxy.":[14],"discrete":[16],"ball":[17],"and":[18,68,86,116,140,163],"spring":[19],"model":[20],"an":[22],"underlying":[23],"cubic":[24],"structure":[25],"considered,":[27],"where":[28],"natural":[30],"lattice":[31],"spacing":[32],"atoms":[35,81,89,100,115,133],"comprising":[36],"deposited":[38,84],"film":[39,85,103],"different":[41],"than":[42,208],"those":[43],"substrate.":[46],"This":[47,155],"system":[48,56,74,189],"linearized":[50],"resulting":[51],"in":[52,82,101,134,160],"a":[53,107,117,151,179],"large":[54,196],"linear":[55],"displacement":[59,98],"field.":[60],"An":[61],"efficient":[62],"based":[64],"on":[65],"combining":[66],"Fourier":[67,153],"multigrid":[69,125],"formulations":[70],"solve":[72],"this":[73,78],"presented.":[76],"In":[77],"algorithm,":[79],"substrate":[88,136],"are":[90,104,137],"handled":[91],"differently.":[92],"The":[93],"equations":[94],"extended":[105],"rectangular":[108],"region":[109],"by":[110,142],"use":[112],"fictitious":[114],"connectivity":[118],"matrix,":[119],"allowing":[120],"application":[122],"standard":[124],"ideas.":[126],"Except":[127],"top":[130],"layer,":[131],"completely":[138],"removed":[139],"replaced":[141],"equivalent":[143],"forces":[144],"which":[145],"can":[146],"be":[147],"efficiently":[148],"evaluated":[149],"using":[150,166],"fast":[152],"transform.":[154],"formulation":[156],"has":[157],"been":[158],"implemented":[159],"both":[161],"two":[162],"three":[164],"dimensions":[165],"V-cycles.":[167],"It":[168],"found":[170],"that":[171,194],"number":[173],"V-cycles":[175],"needed":[176],"reach":[178],"certain":[180],"level":[181],"accuracy":[183],"essentially":[185],"independent":[186],"size.":[190],"Numerical":[191],"tests":[192],"show":[193],"domains,":[197],"approximately":[202],"6":[203],"10":[205],"times":[206],"faster":[207],"conjugate-gradient-based":[209],"methods.":[210]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}