{"id":"https://openalex.org/W7117972199","doi":"https://doi.org/10.1137/24m1694379","title":"A Gradient-Flow Approach for Combined Layout-Control Design of Wave Energy Parks","display_name":"A Gradient-Flow Approach for Combined Layout-Control Design of Wave Energy Parks","publication_year":2026,"publication_date":"2026-01-02","ids":{"openalex":"https://openalex.org/W7117972199","doi":"https://doi.org/10.1137/24m1694379"},"language":"en","primary_location":{"id":"doi:10.1137/24m1694379","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1694379","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/A5092345120","display_name":"Marco Gambarini","orcid":"https://orcid.org/0000-0001-9562-1456"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Gambarini","raw_affiliation_strings":["MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9562-1456","affiliations":[{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000105184","display_name":"Gabriele Ciaramella","orcid":"https://orcid.org/0000-0002-5877-4426"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gabriele Ciaramella","raw_affiliation_strings":["MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081542982","display_name":"Edie Miglio","orcid":"https://orcid.org/0000-0002-2165-0083"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Edie Miglio","raw_affiliation_strings":["MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0002-2165-0083","affiliations":[{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00871938,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"1","first_page":"B59","last_page":"B82"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11250","display_name":"Wave and Wind Energy Systems","score":0.9556999802589417,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T11250","display_name":"Wave and Wind Energy Systems","score":0.9556999802589417,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T10223","display_name":"Microgrid Control and Optimization","score":0.002300000051036477,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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":0.0020000000949949026,"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/energy","display_name":"Energy (signal processing)","score":0.4999000132083893},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.31459999084472656},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.2815999984741211},{"id":"https://openalex.org/keywords/energy-method","display_name":"Energy method","score":0.2815000116825104},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.2623000144958496},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.26089999079704285}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5640000104904175},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4999000132083893},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39169999957084656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3167000114917755},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2808000147342682},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/24m1694379","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1694379","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:re.public.polimi.it:11311/1309344","is_oa":false,"landing_page_url":"https://hdl.handle.net/11311/1309344","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8188319802284241,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1545761024","https://openalex.org/W1965063966","https://openalex.org/W1967957237","https://openalex.org/W1978501146","https://openalex.org/W1986602910","https://openalex.org/W2011256979","https://openalex.org/W2020706127","https://openalex.org/W2049410726","https://openalex.org/W2059313737","https://openalex.org/W2059652663","https://openalex.org/W2066954330","https://openalex.org/W2078675418","https://openalex.org/W2094187331","https://openalex.org/W2111221652","https://openalex.org/W2134645620","https://openalex.org/W2156420298","https://openalex.org/W2161530984","https://openalex.org/W2909663994","https://openalex.org/W2967618336","https://openalex.org/W3009714924","https://openalex.org/W3024767046","https://openalex.org/W3038462393","https://openalex.org/W3063913079","https://openalex.org/W3181590451","https://openalex.org/W3202735425","https://openalex.org/W4229053010","https://openalex.org/W4249820770","https://openalex.org/W4283206985","https://openalex.org/W4285674648","https://openalex.org/W4285794468","https://openalex.org/W4309809692","https://openalex.org/W4366751322","https://openalex.org/W4386608408","https://openalex.org/W4391651868","https://openalex.org/W4396835232","https://openalex.org/W4402243770"],"related_works":[],"abstract_inverted_index":{"Wave":[0],"energy":[1],"converters":[2],"(WECs)":[3],"represent":[4],"an":[5,121],"innovative":[6],"technology":[7],"for":[8,47,54,102,133],"power":[9,32,178],"generation":[10],"from":[11],"renewable":[12],"sources":[13],"(marine":[14],"energy).":[15],"Although":[16],"there":[17],"has":[18,38],"been":[19],"a":[20,35,83,89,109,181],"great":[21],"deal":[22],"of":[23,34,56,66,96,128,140,163,194,215,226,245],"research":[24],"into":[25],"such":[26],"devices":[27],"in":[28,43],"recent":[29],"decades,":[30],"the":[31,63,72,98,116,126,129,136,141,152,160,167,171,176,192,207,216,224,227,238],"output":[33],"single":[36],"device":[37],"remained":[39],"low.":[40],"Therefore,":[41],"installation":[42],"parks":[44,55],"is":[45,58,94,173,241],"required":[46],"economic":[48],"reasons.":[49],"The":[50],"optimal":[51,99],"design":[52,100],"problem":[53,76,101],"WECs":[57],"challenging":[59],"since":[60],"it":[61],"requires":[62,154],"simultaneous":[64],"optimization":[65],"positions":[67],"and":[68,119,139,186,190,202,243],"control":[69],"parameters.":[70],"While":[71],"literature":[73],"on":[74,88,135],"this":[75],"usually":[77],"considers":[78],"metaheuristic":[79],"algorithms,":[80],"we":[81,107],"present":[82],"novel":[84],"numerical":[85],"framework":[86,93],"based":[87],"gradient-flow":[90,117],"formulation.":[91],"This":[92],"capable":[95],"solving":[97],"WEC":[103,169],"parks.":[104],"In":[105],"particular,":[106],"use":[108],"low-order":[110],"adaptive":[111],"Runge-Kutta":[112],"scheme":[113,143],"to":[114,147,166,174,184,191,221],"integrate":[115],"equation":[118],"introduce":[120],"inexact":[122],"solution":[123],"procedure.":[124],"Here,":[125],"tolerances":[127],"linear":[130],"solver":[131],"used":[132],"projection":[134],"constraint":[137],"nullspace":[138],"time-advancing":[142],"are":[144,248],"automatically":[145],"adapted":[146],"avoid":[148],"oversolving":[149],"so":[150],"that":[151,237],"method":[153],"minimal":[155],"tuning.":[156],"We":[157],"then":[158],"provide":[159],"specific":[161],"details":[162],"its":[164],"application":[165],"considered":[168],"problem:":[170],"goal":[172],"maximize":[175],"average":[177],"produced":[179],"by":[180],"park,":[182],"subject":[183],"hydrodynamic":[185],"dynamic":[187],"governing":[188],"equations":[189],"constraints":[193],"available":[195],"sea":[196],"area,":[197],"minimum":[198],"distance":[199],"between":[200],"devices,":[201],"limited":[203],"oscillation":[204],"amplitude":[205],"around":[206],"undisturbed":[208],"free":[209],"surface":[210],"elevation.":[211],"A":[212],"suitable":[213],"choice":[214],"discrete":[217],"models":[218],"allows":[219],"us":[220],"compute":[222],"analytically":[223],"Jacobian":[225],"state":[228],"problem\u2019s":[229],"residual.":[230],"Numerical":[231],"tests":[232],"with":[233],"realistic":[234],"parameters":[235],"show":[236],"proposed":[239],"algorithm":[240],"efficient,":[242],"results":[244],"physical":[246],"interest":[247],"obtained.":[249]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-01-02T00:00:00"}
