{"id":"https://openalex.org/W2073178762","doi":"https://doi.org/10.1109/tvcg.2014.2312012","title":"The Natural Helmholtz-Hodge Decomposition for Open-Boundary Flow Analysis","display_name":"The Natural Helmholtz-Hodge Decomposition for Open-Boundary Flow Analysis","publication_year":2014,"publication_date":"2014-03-17","ids":{"openalex":"https://openalex.org/W2073178762","doi":"https://doi.org/10.1109/tvcg.2014.2312012","mag":"2073178762","pmid":"https://pubmed.ncbi.nlm.nih.gov/26355335"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2014.2312012","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2014.2312012","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5069061531","display_name":"Harsh Bhatia","orcid":"https://orcid.org/0000-0001-8712-7773"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]},{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Harsh Bhatia","raw_affiliation_strings":["Scientific Computing and Imaging Institute, University of Utah, Salt Lake City","Lawrence Livermore National Laboratory, Livermore, CA","Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT"],"affiliations":[{"raw_affiliation_string":"Scientific Computing and Imaging Institute, University of Utah, Salt Lake City","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"Lawrence Livermore National Laboratory, Livermore, CA","institution_ids":["https://openalex.org/I1282311441"]},{"raw_affiliation_string":"Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009460413","display_name":"Valerio Pascucci","orcid":"https://orcid.org/0000-0002-8877-2042"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Valerio Pascucci","raw_affiliation_strings":["Scientific Computing and Imaging Institute, University of Utah, Salt Lake City","Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT"],"affiliations":[{"raw_affiliation_string":"Scientific Computing and Imaging Institute, University of Utah, Salt Lake City","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019902487","display_name":"Peer\u2010Timo Bremer","orcid":"https://orcid.org/0000-0003-4107-3831"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]},{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peer-Timo Bremer","raw_affiliation_strings":["Scientific Computing and Imaging Institute, University of Utah, Salt Lake City","Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT","Lawrence Livermore National Laboratory, Livermore, CA"],"affiliations":[{"raw_affiliation_string":"Scientific Computing and Imaging Institute, University of Utah, Salt Lake City","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"Lawrence Livermore National Laboratory, Livermore, CA","institution_ids":["https://openalex.org/I1282311441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069061531"],"corresponding_institution_ids":["https://openalex.org/I1282311441","https://openalex.org/I223532165"],"apc_list":null,"apc_paid":null,"fwci":4.6647,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.94397199,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"20","issue":"11","first_page":"1566","last_page":"1578"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9976999759674072,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/boundary","display_name":"Boundary (topology)","score":0.591069221496582},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.544860303401947},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5261157155036926},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.5047131776809692},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.5017223358154297},{"id":"https://openalex.org/keywords/boundary-conditions-in-cfd","display_name":"Boundary conditions in CFD","score":0.4800237715244293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45503732562065125},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44189009070396423},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43099331855773926},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39357325434684753},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.2904823422431946},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23403719067573547},{"id":"https://openalex.org/keywords/robin-boundary-condition","display_name":"Robin boundary condition","score":0.17457735538482666},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.12985917925834656},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09302523732185364}],"concepts":[{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.591069221496582},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.544860303401947},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5261157155036926},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.5047131776809692},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5017223358154297},{"id":"https://openalex.org/C79042034","wikidata":"https://www.wikidata.org/wiki/Q4949963","display_name":"Boundary conditions in CFD","level":5,"score":0.4800237715244293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45503732562065125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44189009070396423},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43099331855773926},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39357325434684753},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.2904823422431946},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23403719067573547},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.17457735538482666},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.12985917925834656},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09302523732185364},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tvcg.2014.2312012","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2014.2312012","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},{"id":"pmid:26355335","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26355335","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on visualization and computer graphics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W8289804","https://openalex.org/W46507908","https://openalex.org/W105195103","https://openalex.org/W155896169","https://openalex.org/W1489309590","https://openalex.org/W1651879600","https://openalex.org/W1910188845","https://openalex.org/W1967421663","https://openalex.org/W1972490838","https://openalex.org/W1977150043","https://openalex.org/W1999616998","https://openalex.org/W2001272551","https://openalex.org/W2005780385","https://openalex.org/W2009997314","https://openalex.org/W2017258831","https://openalex.org/W2044385827","https://openalex.org/W2046407491","https://openalex.org/W2051661029","https://openalex.org/W2053465967","https://openalex.org/W2060182705","https://openalex.org/W2064438863","https://openalex.org/W2069600275","https://openalex.org/W2073470731","https://openalex.org/W2077332343","https://openalex.org/W2087920602","https://openalex.org/W2092929058","https://openalex.org/W2099200620","https://openalex.org/W2101335227","https://openalex.org/W2101731201","https://openalex.org/W2101915079","https://openalex.org/W2105986440","https://openalex.org/W2107536609","https://openalex.org/W2117694687","https://openalex.org/W2123315447","https://openalex.org/W2127446985","https://openalex.org/W2137730007","https://openalex.org/W2147493123","https://openalex.org/W2237109911","https://openalex.org/W2295821368","https://openalex.org/W2463867990","https://openalex.org/W2533610325","https://openalex.org/W2794597669","https://openalex.org/W2995136929","https://openalex.org/W3216003845","https://openalex.org/W4232974858","https://openalex.org/W4253944293","https://openalex.org/W4255193216","https://openalex.org/W4285719527","https://openalex.org/W4292023257","https://openalex.org/W6604231136","https://openalex.org/W6749740482"],"related_works":["https://openalex.org/W2111215486","https://openalex.org/W4313256290","https://openalex.org/W2187308915","https://openalex.org/W2378263446","https://openalex.org/W2520827356","https://openalex.org/W2100405323","https://openalex.org/W2359496479","https://openalex.org/W3136311820","https://openalex.org/W2038877176","https://openalex.org/W2133690079"],"abstract_inverted_index":{"The":[0],"Helmholtz-Hodge":[1],"decomposition":[2],"(HHD),":[3],"which":[4,89,111],"describes":[5],"a":[6,17,21,45,124,137,140,144,165,196],"flow":[7,75,117],"as":[8],"the":[9,32,51,56,64,74,86,108,116,128,162,171,186,189],"sum":[10],"of":[11,185,198],"an":[12,14],"incompressible,":[13],"irrotational,":[15],"and":[16,26,95,120,146,175,201,207],"harmonic":[18],"flow,":[19],"is":[20,34,112,191],"fundamental":[22],"tool":[23],"for":[24,29,149,182,195],"simulation":[25,57,65],"analysis.":[27],"Unfortunately,":[28],"bounded":[30],"domains,":[31],"HHD":[33,163],"not":[35,59,82],"uniquely":[36],"defined,":[37],"traditionally,":[38],"boundary":[39,52,69,79,135,156],"conditions":[40,53,80,136],"are":[41],"imposed":[42,76],"to":[43,91,170,193],"obtain":[44],"unique":[46],"solution.":[47],"However,":[48],"in":[49,97,168,204],"general,":[50],"used":[54],"during":[55],"may":[58,66,81],"be":[60,83],"known":[61],"known,":[62],"or":[63,154],"use":[67],"open":[68,152],"conditions.":[70,157],"In":[71],"these":[72],"cases,":[73],"by":[77,114],"traditional":[78],"compatible":[84],"with":[85,151],"given":[87],"data,":[88],"leads":[90],"sometimes":[92],"drastic":[93],"artifacts":[94],"distortions":[96],"all":[98],"three":[99,208],"components,":[100],"hence":[101],"producing":[102],"unphysical":[103],"results.":[104],"This":[105],"paper":[106],"proposes":[107],"natural":[109],"HHD,":[110],"defined":[113],"separating":[115],"into":[118],"internal":[119],"external":[121],"components.":[122],"Using":[123],"completely":[125],"data-driven":[126],"approach,":[127],"proposed":[129],"technique":[130,190],"obtains":[131],"uniqueness":[132],"without":[133],"assuming":[134],"priori.":[138],"As":[139],"result,":[141],"it":[142],"enables":[143],"reliable":[145],"artifact-free":[147],"analysis":[148],"flows":[150],"boundaries":[153],"unknown":[155],"Furthermore,":[158],"our":[159],"approach":[160],"computes":[161],"on":[164],"point-wise":[166],"basis":[167],"contrast":[169],"existing":[172],"global":[173],"techniques,":[174],"thus":[176],"supports":[177],"computing":[178],"inexpensive":[179],"local":[180],"approximations":[181],"any":[183],"subset":[184],"domain.":[187],"Finally,":[188],"easy":[192],"implement":[194],"variety":[197],"spatial":[199],"discretizations":[200],"interpolated":[202],"fields":[203],"both":[205],"two":[206],"dimensions.":[209]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-09T08:58:05.943551","created_date":"2025-10-10T00:00:00"}
