{"id":"https://openalex.org/W2051659788","doi":"https://doi.org/10.1137/130914000","title":"Efficient Mesh Optimization Using the Gradient Flow of the Mean Volume","display_name":"Efficient Mesh Optimization Using the Gradient Flow of the Mean Volume","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2051659788","doi":"https://doi.org/10.1137/130914000","mag":"2051659788"},"language":"en","primary_location":{"id":"doi:10.1137/130914000","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130914000","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5036544610","display_name":"Dimitris Vartziotis","orcid":"https://orcid.org/0000-0003-1030-0309"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dimitris Vartziotis","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075338234","display_name":"Benjamin Himpel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Benjamin Himpel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036544610"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.4292,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.94125801,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"52","issue":"2","first_page":"1050","last_page":"1075"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9923999905586243,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/mathematics","display_name":"Mathematics","score":0.7383937835693359},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.7314791083335876},{"id":"https://openalex.org/keywords/hexahedron","display_name":"Hexahedron","score":0.5780671834945679},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5437179803848267},{"id":"https://openalex.org/keywords/volume-mesh","display_name":"Volume mesh","score":0.4943060874938965},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.47802504897117615},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.46629399061203003},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.456757128238678},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44515591859817505},{"id":"https://openalex.org/keywords/volume","display_name":"Volume (thermodynamics)","score":0.42323291301727295},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3766786754131317},{"id":"https://openalex.org/keywords/mesh-generation","display_name":"Mesh generation","score":0.28495341539382935},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07993265986442566}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7383937835693359},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.7314791083335876},{"id":"https://openalex.org/C22411076","wikidata":"https://www.wikidata.org/wiki/Q668113","display_name":"Hexahedron","level":3,"score":0.5780671834945679},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5437179803848267},{"id":"https://openalex.org/C170589453","wikidata":"https://www.wikidata.org/wiki/Q7940896","display_name":"Volume mesh","level":4,"score":0.4943060874938965},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.47802504897117615},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.46629399061203003},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.456757128238678},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44515591859817505},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.42323291301727295},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3766786754131317},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.28495341539382935},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07993265986442566},{"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":1,"locations":[{"id":"doi:10.1137/130914000","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130914000","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6499999761581421,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W12947790","https://openalex.org/W50634792","https://openalex.org/W65479554","https://openalex.org/W84390757","https://openalex.org/W847439287","https://openalex.org/W1486721501","https://openalex.org/W1490688156","https://openalex.org/W1540910825","https://openalex.org/W1568294133","https://openalex.org/W1793332957","https://openalex.org/W1968141870","https://openalex.org/W1971169262","https://openalex.org/W1983419028","https://openalex.org/W1984132759","https://openalex.org/W1988396840","https://openalex.org/W2003158973","https://openalex.org/W2007185418","https://openalex.org/W2008571824","https://openalex.org/W2008617812","https://openalex.org/W2013761912","https://openalex.org/W2044355921","https://openalex.org/W2046549643","https://openalex.org/W2055802612","https://openalex.org/W2078393607","https://openalex.org/W2082528405","https://openalex.org/W2087076015","https://openalex.org/W2094342549","https://openalex.org/W2105735474","https://openalex.org/W2117774341","https://openalex.org/W2117863317","https://openalex.org/W2118818634","https://openalex.org/W2128441984","https://openalex.org/W2133500334","https://openalex.org/W2158742482","https://openalex.org/W2166173515","https://openalex.org/W2166554539","https://openalex.org/W2170054950","https://openalex.org/W2187081055","https://openalex.org/W2239286097","https://openalex.org/W2275544444","https://openalex.org/W2731598242","https://openalex.org/W2950200454","https://openalex.org/W2963279477","https://openalex.org/W3102109908","https://openalex.org/W3106306093"],"related_works":["https://openalex.org/W2037812407","https://openalex.org/W2330661319","https://openalex.org/W2383759168","https://openalex.org/W2109770908","https://openalex.org/W2962853751","https://openalex.org/W2745694944","https://openalex.org/W4239526988","https://openalex.org/W1971404246","https://openalex.org/W2119558010","https://openalex.org/W1968086293"],"abstract_inverted_index":{"The":[0,44],"signed":[1],"volume":[2,12,15,46,57,102],"function":[3,13,47],"for":[4,14,56,110],"polyhedra":[5],"can":[6],"be":[7],"generalized":[8],"to":[9,31,41,49,89],"a":[10,42,53,104],"mean":[11,45,101],"elements":[16],"by":[17],"averaging":[18],"over":[19],"the":[20,23,35,62,69,85,95,100,111,117,128,134],"triangulations":[21],"of":[22,65,72,76,99,130],"underlying":[24],"polyhedron.":[25],"If":[26],"we":[27,123],"consider":[28],"these":[29],"up":[30],"translation":[32],"and":[33,81,106,133,140],"scaling,":[34],"resulting":[36,135],"quotient":[37],"space":[38],"is":[39,52],"diffeomorphic":[40],"sphere.":[43],"restricted":[48],"this":[50,66,131],"sphere":[51],"quality":[54],"measure":[55],"elements.":[58],"We":[59,92],"show":[60,93],"that":[61,83,94],"gradient":[63,97],"ascent":[64],"map":[67],"regularizes":[68],"building":[70],"blocks":[71],"hybrid":[73],"meshes":[74],"consisting":[75],"tetrahedra,":[77],"hexahedra,":[78],"prisms,":[79],"pyramids,":[80],"octahedra,":[82],"is,":[84],"optimization":[86,108],"process":[87],"converges":[88],"regular":[90],"polyhedra.":[91],"(normalized)":[96],"flow":[98],"yields":[103],"fast":[105],"efficient":[107],"scheme":[109],"finite":[112],"element":[113,119],"method":[114,132],"known":[115],"as":[116],"geometric":[118],"transformation":[120],"method.":[121],"Furthermore,":[122],"shed":[124],"some":[125],"light":[126],"on":[127],"dynamics":[129],"smoothing":[136],"procedure":[137],"both":[138],"theoretically":[139],"experimentally.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
