{"id":"https://openalex.org/W4360999734","doi":"https://doi.org/10.1137/22m1490338","title":"MGM: A Meshfree Geometric Multilevel Method for Systems Arising from Elliptic Equations on Point Cloud Surfaces","display_name":"MGM: A Meshfree Geometric Multilevel Method for Systems Arising from Elliptic Equations on Point Cloud Surfaces","publication_year":2023,"publication_date":"2023-03-27","ids":{"openalex":"https://openalex.org/W4360999734","doi":"https://doi.org/10.1137/22m1490338"},"language":"en","primary_location":{"id":"doi:10.1137/22m1490338","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1490338","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/A5053802738","display_name":"Grady B. Wright","orcid":"https://orcid.org/0000-0001-7441-1791"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Grady B. Wright","raw_affiliation_strings":["Department of Mathematics, Boise State University, Boise, ID 83725 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Boise State University, Boise, ID 83725 USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043638391","display_name":"Andrew M. Jones","orcid":"https://orcid.org/0000-0003-4114-1785"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrew Jones","raw_affiliation_strings":["Department of Mathematics, Boise State University, Boise, ID 83725 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Boise State University, Boise, ID 83725 USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055844388","display_name":"Varun Shankar","orcid":"https://orcid.org/0000-0002-4987-2972"},"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":"Varun Shankar","raw_affiliation_strings":["School of Computing, University of Utah, Salt Lake City, UT 84112 USA"],"affiliations":[{"raw_affiliation_string":"School of Computing, University of Utah, Salt Lake City, UT 84112 USA","institution_ids":["https://openalex.org/I223532165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053802738"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9029,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.82790222,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"45","issue":"2","first_page":"A312","last_page":"A337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.9993000030517578,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6894453167915344},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.6785491704940796},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5155525207519531},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5130318403244019},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.4797202944755554},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.467949777841568},{"id":"https://openalex.org/keywords/point-cloud","display_name":"Point cloud","score":0.46560055017471313},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.4649324119091034},{"id":"https://openalex.org/keywords/meshfree-methods","display_name":"Meshfree methods","score":0.4304463863372803},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.42440080642700195},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3165343105792999},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.31619954109191895},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3159583806991577},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.2749456763267517},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2570430040359497},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19518479704856873}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6894453167915344},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6785491704940796},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5155525207519531},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5130318403244019},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.4797202944755554},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.467949777841568},{"id":"https://openalex.org/C131979681","wikidata":"https://www.wikidata.org/wiki/Q1899648","display_name":"Point cloud","level":2,"score":0.46560055017471313},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.4649324119091034},{"id":"https://openalex.org/C162835735","wikidata":"https://www.wikidata.org/wiki/Q14866890","display_name":"Meshfree methods","level":3,"score":0.4304463863372803},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.42440080642700195},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3165343105792999},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.31619954109191895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3159583806991577},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2749456763267517},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2570430040359497},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19518479704856873},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1490338","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1490338","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5121703517","display_name":null,"funder_award_id":"CCF-1714844","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W50490584","https://openalex.org/W112187595","https://openalex.org/W240948612","https://openalex.org/W1486164486","https://openalex.org/W1506342804","https://openalex.org/W1506690472","https://openalex.org/W1572639095","https://openalex.org/W1969299137","https://openalex.org/W1985263109","https://openalex.org/W1997340817","https://openalex.org/W2009262561","https://openalex.org/W2012255853","https://openalex.org/W2017142556","https://openalex.org/W2033559265","https://openalex.org/W2036547869","https://openalex.org/W2036800642","https://openalex.org/W2042842784","https://openalex.org/W2054696734","https://openalex.org/W2059176502","https://openalex.org/W2061987443","https://openalex.org/W2069887143","https://openalex.org/W2070960656","https://openalex.org/W2088046391","https://openalex.org/W2089840306","https://openalex.org/W2120398992","https://openalex.org/W2123732640","https://openalex.org/W2123996636","https://openalex.org/W2130859329","https://openalex.org/W2141870784","https://openalex.org/W2155307607","https://openalex.org/W2157670588","https://openalex.org/W2169437869","https://openalex.org/W2174848899","https://openalex.org/W2338421663","https://openalex.org/W2410432900","https://openalex.org/W2534261149","https://openalex.org/W2559617141","https://openalex.org/W2560552443","https://openalex.org/W2756899824","https://openalex.org/W2808952962","https://openalex.org/W2868924824","https://openalex.org/W2944021381","https://openalex.org/W2945535478","https://openalex.org/W2949596746","https://openalex.org/W2982474290","https://openalex.org/W2998496342","https://openalex.org/W3000448799","https://openalex.org/W3042744354","https://openalex.org/W3121673310","https://openalex.org/W3125178117"],"related_works":["https://openalex.org/W4389317411","https://openalex.org/W1492522302","https://openalex.org/W2096454229","https://openalex.org/W2042199958","https://openalex.org/W3046775784","https://openalex.org/W2103149966","https://openalex.org/W2382988560","https://openalex.org/W2177482563","https://openalex.org/W2120298265","https://openalex.org/W2464766188"],"abstract_inverted_index":{".We":[0],"develop":[1],"a":[2,28,67,99,132],"new":[3,39],"meshfree":[4,40,82],"geometric":[5],"multilevel":[6],"(MGM)":[7],"method":[8,26],"for":[9,33,47,104,139],"solving":[10,140],"linear":[11],"systems":[12],"that":[13],"arise":[14],"from":[15],"discretizing":[16],"elliptic":[17,76],"PDEs":[18,77],"on":[19,44,79,108,159,169],"surfaces":[20],"represented":[21],"by":[22,152],"point":[23,36,53,126],"clouds.":[24,54],"The":[25],"uses":[27],"Poisson":[29],"disk":[30],"sampling-type":[31],"technique":[32],"coarsening":[34,64],"the":[35,51,141,148],"clouds":[37],"and":[38,62,89,102,114,116,122,166],"restriction/interpolation":[41],"operators":[42],"based":[43,78],"polyharmonic":[45],"splines":[46],"transferring":[48],"information":[49],"between":[50],"coarsened":[52],"These":[55],"are":[56],"then":[57],"combined":[58],"with":[59,124],"standard":[60],"smoothing":[61],"operator":[63],"methods":[65,107,138],"in":[66],"V-cycle":[68],"iteration.":[69],"MGM":[70,96,151],"is":[71],"applicable":[72],"to":[73,135,155],"discretizations":[74],"of":[75,150],"various":[80],"localized":[81],"methods,":[83],"including":[84],"RBF":[85],"finite":[86,91],"differences":[87,92],"(RBF-FD)":[88],"generalized":[90],"(GFD).":[93],"We":[94,129],"test":[95,110],"both":[97],"as":[98],"standalone":[100],"solver":[101],"preconditioner":[103],"Krylov":[105],"subspace":[106],"several":[109],"problems":[111],"using":[112],"RBF-FD":[113],"GFD":[115],"numerically":[117],"analyze":[118],"convergence":[119],"rates,":[120],"efficiency,":[121],"scaling":[123],"increasing":[125],"cloud":[127],"sizes.":[128],"also":[130],"perform":[131],"side-by-side":[133],"comparison":[134],"algebraic":[136],"multigrid":[137],"same":[142],"systems.":[143],"Finally,":[144],"we":[145],"further":[146],"demonstrate":[147],"effectiveness":[149],"applying":[153],"it":[154],"three":[156],"challenging":[157],"applications":[158],"complicated":[160],"surfaces:":[161],"pattern":[162],"formation,":[163],"surface":[164],"harmonics,":[165],"geodesic":[167],"distance.KeywordsPDEs":[168],"surfacesRBF-FDGFDmeshfreemeshlessmultilevelpreconditionersMSC":[170],"codes65F0865F1065N5565M5565N2265M22":[171]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}