{"id":"https://openalex.org/W3018058054","doi":"https://doi.org/10.1137/20m1326209","title":"Computing Multiple Solutions of Topology Optimization Problems","display_name":"Computing Multiple Solutions of Topology Optimization Problems","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3018058054","doi":"https://doi.org/10.1137/20m1326209","mag":"3018058054"},"language":"en","primary_location":{"id":"doi:10.1137/20m1326209","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1326209","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2004.11797","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045247038","display_name":"Ioannis P. A. Papadopoulos","orcid":"https://orcid.org/0000-0003-3522-8761"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ioannis P. A. Papadopoulos","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102855060","display_name":"Patrick E. Farrell","orcid":"https://orcid.org/0000-0002-1241-7060"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Patrick E. Farrell","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040157819","display_name":"Thomas M. Surowiec","orcid":"https://orcid.org/0000-0003-2473-4984"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas M. Surowiec","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045247038"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00509803,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"43","issue":"3","first_page":"A1555","last_page":"A1582"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T11115","display_name":"Topology Optimization in Engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.996399998664856,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9828000068664551,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/maxima-and-minima","display_name":"Maxima and minima","score":0.8869501352310181},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6697074770927429},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.6536189317703247},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.618390679359436},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.598352313041687},{"id":"https://openalex.org/keywords/topology-optimization","display_name":"Topology optimization","score":0.5503902435302734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5463743805885315},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.487901896238327},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4626632034778595},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4433269202709198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3439289629459381}],"concepts":[{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.8869501352310181},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6697074770927429},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6536189317703247},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.618390679359436},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.598352313041687},{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.5503902435302734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5463743805885315},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.487901896238327},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4626632034778595},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4433269202709198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3439289629459381},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/20m1326209","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1326209","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"},{"id":"pmh:oai:arXiv.org:2004.11797","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.11797","pdf_url":"https://arxiv.org/pdf/2004.11797","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":"","raw_type":"text"},{"id":"mag:3018058054","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2004.11797","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":"pmh:oai:ora.ox.ac.uk:uuid:455f5465-af68-49c7-8e11-96909cdb82a1","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:455f5465-af68-49c7-8e11-96909cdb82a1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Hyrax Deposit","raw_type":"Thesis"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:d190ce94-2aba-4113-b612-4849cffa5d73","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:d190ce94-2aba-4113-b612-4849cffa5d73","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},{"id":"doi:10.48550/arxiv.2004.11797","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2004.11797","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"},{"id":"doi:10.5287/ora-8npjngzkb","is_oa":true,"landing_page_url":"https://doi.org/10.5287/ora-8npjngzkb","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"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":"thesis"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2004.11797","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.11797","pdf_url":"https://arxiv.org/pdf/2004.11797","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1327798365","display_name":"EPSRC Centre for Doctoral Training in Partial Differential Equations: Analysis and Applications","funder_award_id":"EP/L015811/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1934935867","display_name":null,"funder_award_id":"Engineering and Physical Sciences R","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3957501995","display_name":null,"funder_award_id":"EP/R029423/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4162891482","display_name":null,"funder_award_id":"R029423/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6447561440","display_name":null,"funder_award_id":"EP/L015811/","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6609029749","display_name":null,"funder_award_id":"SU 963/1-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7295259756","display_name":"PRISM: Platform for Research In Simulation Methods","funder_award_id":"EP/R029423/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320315144","display_name":"MathWorks","ror":"https://ror.org/01n8qtk87"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3018058054.pdf","grobid_xml":"https://content.openalex.org/works/W3018058054.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W7155719","https://openalex.org/W73123583","https://openalex.org/W90568776","https://openalex.org/W262449150","https://openalex.org/W1498887287","https://openalex.org/W1508326339","https://openalex.org/W1966287322","https://openalex.org/W1967688281","https://openalex.org/W1975383645","https://openalex.org/W1977282511","https://openalex.org/W1984303764","https://openalex.org/W1984396065","https://openalex.org/W1990541396","https://openalex.org/W1992688650","https://openalex.org/W1995067704","https://openalex.org/W2016413885","https://openalex.org/W2017655467","https://openalex.org/W2026365342","https://openalex.org/W2026463274","https://openalex.org/W2039513266","https://openalex.org/W2048797084","https://openalex.org/W2055183575","https://openalex.org/W2062334428","https://openalex.org/W2062523101","https://openalex.org/W2063784058","https://openalex.org/W2069671092","https://openalex.org/W2070299075","https://openalex.org/W2070584352","https://openalex.org/W2079482881","https://openalex.org/W2080633310","https://openalex.org/W2086674516","https://openalex.org/W2088880127","https://openalex.org/W2092490304","https://openalex.org/W2092801729","https://openalex.org/W2093274919","https://openalex.org/W2093742335","https://openalex.org/W2095630168","https://openalex.org/W2107837483","https://openalex.org/W2110696842","https://openalex.org/W2112311198","https://openalex.org/W2113734366","https://openalex.org/W2120494006","https://openalex.org/W2132034927","https://openalex.org/W2140142240","https://openalex.org/W2143163345","https://openalex.org/W2563402977","https://openalex.org/W2591133976","https://openalex.org/W2626795344","https://openalex.org/W2756807742","https://openalex.org/W2798766386","https://openalex.org/W2800239682","https://openalex.org/W2898903842","https://openalex.org/W2911461151","https://openalex.org/W2949182381","https://openalex.org/W2962828807","https://openalex.org/W3005264741","https://openalex.org/W3008232643"],"related_works":["https://openalex.org/W2586440992","https://openalex.org/W3012293442","https://openalex.org/W2910982790","https://openalex.org/W2995651674","https://openalex.org/W2186270969","https://openalex.org/W3209838302","https://openalex.org/W3106163595","https://openalex.org/W60686164","https://openalex.org/W2106365662","https://openalex.org/W3005487825","https://openalex.org/W436679424","https://openalex.org/W2597612688","https://openalex.org/W235694958","https://openalex.org/W1497252293","https://openalex.org/W2713287247","https://openalex.org/W2804302623","https://openalex.org/W3095252918","https://openalex.org/W3036250584","https://openalex.org/W2967699988","https://openalex.org/W3007406095"],"abstract_inverted_index":{"Topology":[0],"optimization":[1,32,77,104,198,215,229,242],"finds":[2],"the":[3,48,59,73,79,82,85,88,93,127,203,222,228,236],"optimal":[4],"material":[5],"distribution":[6],"of":[7,61,75,81,87,95,100,116,126,150,193,206,210],"a":[8,11,24,96,101,114,124,148,185,194,211],"continuum":[9],"in":[10,23,58,108,246],"domain,":[12],"subject":[13],"to":[14,46,72,123,157,202,234,238],"PDE":[15],"and":[16,27,84,171],"volume":[17,26],"constraints.":[18],"Density-based":[19],"models":[20],"often":[21],"result":[22],"PDE,":[25],"inequality":[28],"constrained,":[29],"nonconvex,":[30],"infinite-dimensional":[31,128],"problem.":[33,105,129,199,216],"These":[34],"problems":[35],"can":[36,55,188],"exhibit":[37],"many":[38],"local":[39],"minima.":[40],"In":[41,63,136],"practice,":[42],"heuristics":[43],"are":[44,232],"used":[45],"aid":[47],"search":[49],"for":[50,164,221],"better":[51],"minima,":[52],"but":[53],"these":[54,133,161],"fail":[56],"even":[57],"simplest":[60],"cases.":[62],"this":[64],"thesis":[65],"we":[66,91,143,231,250],"address":[67],"two":[68],"core":[69],"issues":[70],"related":[71],"nonconvexity":[74],"topology":[76,103,197,214,241],"problems:":[78],"convergence":[80,94],"discretization":[83,99],"computation":[86,205],"solutions.":[89,255],"First,":[90],"consider":[92],"finite":[97,117,151,168,177],"element":[98,118,152,169,178],"fluid":[102,213,240],"Results":[106],"available":[107],"literature":[109],"show":[110,144],"that":[111,120,145,154,158,187,225],"there":[112,146],"exists":[113,147],"sequence":[115,149],"solutions":[119,153,209],"weakly(-*)":[121],"converges":[122,156],"solution":[125],"We":[130,180],"improve":[131],"on":[132,183],"classical":[134],"results.":[135],"particular,":[137],"by":[138,218],"fixing":[139],"any":[140],"isolated":[141],"minimizer,":[142],"\\emph{strongly}":[155],"minimizer.":[159],"Moreover,":[160],"results":[162],"hold":[163],"both":[165],"traditional":[166],"conforming":[167],"methods":[170],"more":[172],"sophisticated":[173],"divergence-free":[174],"discontinuous":[175],"Galerkin":[176],"methods.":[179],"then":[181],"focus":[182],"developing":[184,219],"solver":[186,237],"systematically":[189],"compute":[190,251],"multiple":[191],"minimizers":[192],"general":[195],"density-based":[196],"This":[200,244],"leads":[201],"successful":[204],"42":[207],"distinct":[208,253],"two-dimensional":[212],"Finally,":[217],"preconditioners":[220],"linear":[223],"systems":[224],"arise":[226],"during":[227],"process,":[230],"able":[233],"apply":[235],"three-dimensional":[239,254],"problems.":[243],"culminates":[245],"an":[247],"example":[248],"where":[249],"11":[252]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
