{"id":"https://openalex.org/W7214185488","doi":"https://doi.org/10.48550/arxiv.2609.28135","title":"A Lloyd-stabilized Voronoi particle method","display_name":"A Lloyd-stabilized Voronoi particle method","publication_year":2026,"publication_date":"2026-09-23","ids":{"openalex":"https://openalex.org/W7214185488","doi":"https://doi.org/10.48550/arxiv.2609.28135"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.28135","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28135","pdf_url":"https://arxiv.org/pdf/2609.28135","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.28135","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113826510","display_name":"Bruno Despr\u00e9s","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Despr\u00e9s, Bruno","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions AND"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions AND","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049531040","display_name":"Borjan Geshkovski","orcid":"https://orcid.org/0000-0002-7890-3352","observed_orcids":["https://orcid.org/0000-0002-7890-3352"]},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Geshkovski, Borjan","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions","institution_ids":["https://openalex.org/I4210158291"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210158291"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.5313000082969666,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.5313000082969666,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.3662000000476837,"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/T11694","display_name":"Fluid Dynamics Simulations and Interactions","score":0.008500000461935997,"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/lloyd-s-algorithm","display_name":"Lloyd's algorithm","score":0.8930000066757202},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi tessellation","score":0.984000027179718},{"id":"https://openalex.org/keywords/particle-methods","display_name":"particle methods","score":0.7250000238418579},{"id":"https://openalex.org/keywords/lagrangian-transport","display_name":"Lagrangian transport","score":0.8569999933242798},{"id":"https://openalex.org/keywords/stability-analysis","display_name":"stability analysis","score":0.5640000104904175},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.5920000076293945},{"id":"https://openalex.org/keywords/wasserstein-distance","display_name":"Wasserstein distance","score":0.9589999914169312},{"id":"https://openalex.org/keywords/mesh-regularity","display_name":"mesh regularity","score":0.8159999847412109},{"id":"https://openalex.org/keywords/compressible-euler-equations","display_name":"compressible Euler equations","score":0.8529999852180481},{"id":"https://openalex.org/keywords/meshless-methods","display_name":"meshless methods","score":0.34599998593330383}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6887000203132629},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.6071000099182129},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.532800018787384},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5318999886512756},{"id":"https://openalex.org/C2987747430","wikidata":"https://www.wikidata.org/wiki/Q24898874","display_name":"Particle method","level":3,"score":0.5235000252723694},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5055000185966492},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.476500004529953},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.4596000015735626},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.459199994802475},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4268999993801117},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.4115999937057495},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4036000072956085},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.3903999924659729},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.31189998984336853},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3018999993801117},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C89901390","wikidata":"https://www.wikidata.org/wiki/Q6418927","display_name":"Lagrangian and Eulerian specification of the flow field","level":4,"score":0.2896000146865845},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2865999937057495},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C5192115","wikidata":"https://www.wikidata.org/wiki/Q2705141","display_name":"Compressible flow","level":3,"score":0.26919999718666077},{"id":"https://openalex.org/C135649769","wikidata":"https://www.wikidata.org/wiki/Q27794802","display_name":"Particle density","level":3,"score":0.25839999318122864},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2542000114917755},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2535000145435333},{"id":"https://openalex.org/C2776392105","wikidata":"https://www.wikidata.org/wiki/Q875744","display_name":"Euler\u2013Lagrange equation","level":3,"score":0.2533999979496002},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.28135","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28135","pdf_url":"https://arxiv.org/pdf/2609.28135","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05762240v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05762240v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.28135","doi":"https://doi.org/10.48550/arxiv.2609.28135","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.28135","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.28135","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28135","pdf_url":"https://arxiv.org/pdf/2609.28135","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214185488.pdf","grobid_xml":"https://content.openalex.org/works/W7214185488.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4415329210"],"related_works":["https://openalex.org/W1865155990","https://openalex.org/W4387353373","https://openalex.org/W4385270339","https://openalex.org/W4402577696","https://openalex.org/W2767940698","https://openalex.org/W1636504988","https://openalex.org/W4405185413","https://openalex.org/W2974785804","https://openalex.org/W7096376592","https://openalex.org/W1985975417"],"abstract_inverted_index":{"We":[0,23],"study":[1],"the":[2,13,35,41,48,52,59,63,75],"stability":[3],"and":[4],"consistency":[5],"of":[6,16],"Lloyd's":[7],"algorithm":[8],"used":[9],"in":[10,44],"combination":[11],"with":[12],"Lagrangian":[14,66],"transport":[15],"a":[17,20],"density":[18],"on":[19],"Vorono\u00ef":[21],"tessellation.":[22],"show":[24],"that":[25,65],"relaxation":[26],"rates":[27],"as":[28,30],"strong":[29],"$O(h^{-1/2})$,":[31],"where":[32],"$h$":[33],"is":[34,72],"mesh":[36,53],"size,":[37],"give":[38],"convergence":[39],"to":[40],"continuity":[42],"equation":[43],"Wasserstein":[45],"distance":[46],"at":[47],"rate":[49],"$O(h^{1/4})$.":[50],"Thus":[51],"can":[54],"be":[55],"kept":[56],"regular":[57],"by":[58],"correction":[60],"alone,":[61],"without":[62],"remeshing":[64],"methods":[67],"usually":[68],"require.":[69],"An":[70],"application":[71],"proposed":[73],"for":[74],"compressible":[76],"Euler":[77],"equations.":[78]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-25T00:00:00"}
