{"id":"https://openalex.org/W2964299189","doi":"https://doi.org/10.1137/16m1065690","title":"Modified Virtual Grid Difference for Discretizing the Laplace--Beltrami Operator on Point Clouds","display_name":"Modified Virtual Grid Difference for Discretizing the Laplace--Beltrami Operator on Point Clouds","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2964299189","doi":"https://doi.org/10.1137/16m1065690","mag":"2964299189"},"language":"en","primary_location":{"id":"doi:10.1137/16m1065690","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1065690","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/A5100377147","display_name":"Meng Wang","orcid":"https://orcid.org/0000-0002-3094-7735"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meng Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059208158","display_name":"Shingyu Leung","orcid":"https://orcid.org/0000-0002-4549-2761"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shingyu Leung","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5069922005","display_name":"Hongkai Zhao","orcid":"https://orcid.org/0000-0002-2358-9028"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hongkai Zhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8327,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.72274863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"40","issue":"1","first_page":"A1","last_page":"A21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9994000196456909,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9994000196456909,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9957000017166138,"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":0.9955999851226807,"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/discretization","display_name":"Discretization","score":0.7338960766792297},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6754688620567322},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5578907132148743},{"id":"https://openalex.org/keywords/regular-grid","display_name":"Regular grid","score":0.4989199638366699},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.48755186796188354},{"id":"https://openalex.org/keywords/point-cloud","display_name":"Point cloud","score":0.4757625460624695},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4687972664833069},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.41421374678611755},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40956738591194153},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3613537549972534},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34212279319763184},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2645520269870758},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24241575598716736},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09645357728004456}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7338960766792297},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6754688620567322},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5578907132148743},{"id":"https://openalex.org/C43173174","wikidata":"https://www.wikidata.org/wiki/Q2646942","display_name":"Regular grid","level":3,"score":0.4989199638366699},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.48755186796188354},{"id":"https://openalex.org/C131979681","wikidata":"https://www.wikidata.org/wiki/Q1899648","display_name":"Point cloud","level":2,"score":0.4757625460624695},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4687972664833069},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.41421374678611755},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40956738591194153},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3613537549972534},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34212279319763184},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2645520269870758},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24241575598716736},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09645357728004456}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1065690","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1065690","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:repository.ust.hk:1783.1-89719","is_oa":false,"landing_page_url":"http://lbdiscover.ust.hk/uresolver?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rfr_id=info:sid/HKUST:SPI&rft.genre=article&rft.issn=1064-8275&rft.volume=v. 40&rft.issue=(1)&rft.date=2018&rft.spage=A1&rft.aulast=Wang&rft.aufirst=Meng&rft.atitle=MODIFIED+VIRTUAL+GRID+DIFFERENCE+FOR+DISCRETIZING+THE+LAPLACE-BELTRAMI+OPERATOR+ON+POINT+CLOUDS&rft.title=SIAM+JOURNAL+ON+SCIENTIFIC+COMPUTING","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5259929423","display_name":null,"funder_award_id":"DMS-1418422","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7902557464","display_name":null,"funder_award_id":"16309316","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G82155845","display_name":null,"funder_award_id":"16303114","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1964311064","https://openalex.org/W2010000065","https://openalex.org/W2010106767","https://openalex.org/W2012255853","https://openalex.org/W2017132804","https://openalex.org/W2031367292","https://openalex.org/W2038988575","https://openalex.org/W2048269209","https://openalex.org/W2058524213","https://openalex.org/W2069016826","https://openalex.org/W2107059366","https://openalex.org/W2129134793","https://openalex.org/W2137531922","https://openalex.org/W2150712551","https://openalex.org/W2324902717","https://openalex.org/W2330285877","https://openalex.org/W2617010780","https://openalex.org/W3106352682","https://openalex.org/W4213367101","https://openalex.org/W4214886506"],"related_works":["https://openalex.org/W3114093281","https://openalex.org/W4295736060","https://openalex.org/W4220931593","https://openalex.org/W2989780569","https://openalex.org/W2466288331","https://openalex.org/W2145321474","https://openalex.org/W2474502839","https://openalex.org/W1999290823","https://openalex.org/W2513224081","https://openalex.org/W2056334836"],"abstract_inverted_index":{"We":[0,151,175],"propose":[1,83],"a":[2,37,47,65,70,84],"new":[3,136],"and":[4,36,52,147,161,180,190],"simple":[5],"discretization,":[6],"named":[7],"the":[8,18,34,59,74,90,95,101,112,119,124,128,132,143,154,170,188,191,194],"modified":[9,85],"virtual":[10,67,91,108],"grid":[11,68,92,109,125],"difference":[12,87,115],"(MVGD),":[13],"for":[14],"numerical":[15,178],"approximation":[16],"of":[17,99,193],"Laplace--Beltrami":[19],"(LB)":[20],"operator":[21],"on":[22,40,58,89,106],"manifolds":[23],"sampled":[24],"by":[25,164],"point":[26],"clouds.":[27],"The":[28,135],"key":[29],"observation":[30],"is":[31],"that":[32,153],"both":[33,43],"manifold":[35],"function":[38,120],"defined":[39],"it":[41],"can":[42,157],"be":[44,158],"parametrized":[45],"in":[46],"local":[48,66,102],"Cartesian":[49],"coordinate":[50],"system":[51,146,156],"approximated":[53],"using":[54,100],"least":[55,103],"squares.":[56],"Based":[57],"above":[60],"observation,":[61],"we":[62,82,117],"first":[63],"introduce":[64],"with":[69,131,182],"scale":[71],"adapted":[72],"to":[73,93,142,186],"sampling":[75],"density":[76],"centered":[77],"at":[78,123,127],"each":[79],"point.":[80],"Then":[81],"finite":[86,114],"scheme":[88],"discretize":[94],"LB":[96],"operator.":[97],"Instead":[98],"squares":[104],"values":[105],"all":[107],"points":[110],"like":[111],"typical":[113],"method,":[116],"use":[118],"value":[121],"explicitly":[122],"located":[126],"center":[129],"(coinciding":[130],"data":[133],"point).":[134],"discretization":[137],"provides":[138],"more":[139],"diagonal":[140],"dominance":[141],"resulting":[144],"linear":[145,155],"improves":[148],"its":[149],"conditioning.":[150],"show":[152],"robustly,":[159],"efficiently":[160],"accurately":[162],"solved":[163],"existing":[165,184],"fast":[166],"solver":[167],"such":[168],"as":[169],"algebraic":[171],"multigrid":[172],"(AMG)":[173],"method.":[174],"will":[176],"present":[177],"tests":[179],"comparison":[181],"other":[183],"methods":[185],"demonstrate":[187],"effectiveness":[189],"performance":[192],"proposed":[195],"approach.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
