{"id":"https://openalex.org/W4405492796","doi":"https://doi.org/10.1137/23m1621265","title":"A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces","display_name":"A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces","publication_year":2024,"publication_date":"2024-12-17","ids":{"openalex":"https://openalex.org/W4405492796","doi":"https://doi.org/10.1137/23m1621265"},"language":"en","primary_location":{"id":"doi:10.1137/23m1621265","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1621265","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2412.14761","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065265731","display_name":"V\u00edctor Bayona","orcid":"https://orcid.org/0000-0002-9626-0450"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"V\u00edctor Bayona","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Legan\u00e9s, 28911, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9626-0450","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Legan\u00e9s, 28911, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070802434","display_name":"Argyrios Petras","orcid":"https://orcid.org/0000-0002-3278-620X"},"institutions":[{"id":"https://openalex.org/I4210158379","display_name":"Johann Radon Institute for Computational and Applied Mathematics","ror":"https://ror.org/05a94k872","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I4210158379"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Argyrios Petras","raw_affiliation_strings":["RICAM - Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz 4040, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RICAM - Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz 4040, Austria","institution_ids":["https://openalex.org/I4210158379"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040587059","display_name":"C\u00e9cile Piret","orcid":"https://orcid.org/0000-0002-2857-7173"},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C\u00e9cile Piret","raw_affiliation_strings":["Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931 USA"],"raw_orcid":"https://orcid.org/0000-0002-2857-7173","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931 USA","institution_ids":["https://openalex.org/I11957088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071624369","display_name":"Steven J. Ruuth","orcid":"https://orcid.org/0000-0002-9557-3375"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Steven J. Ruuth","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University, Burnaby V5A 1S6, BC, Canada"],"raw_orcid":"https://orcid.org/0000-0002-9557-3375","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, Burnaby V5A 1S6, BC, Canada","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5065265731"],"corresponding_institution_ids":["https://openalex.org/I50357001"],"apc_list":null,"apc_paid":null,"fwci":1.025,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73191743,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"46","issue":"6","first_page":"A3897","last_page":"A3921"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"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":0.9998000264167786,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9965000152587891,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/mathematics","display_name":"Mathematics","score":0.82705157995224},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6990927457809448},{"id":"https://openalex.org/keywords/meshfree-methods","display_name":"Meshfree methods","score":0.6692160367965698},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47241201996803284},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45194366574287415},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4143914580345154},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.30816811323165894},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1152961254119873}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.82705157995224},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6990927457809448},{"id":"https://openalex.org/C162835735","wikidata":"https://www.wikidata.org/wiki/Q14866890","display_name":"Meshfree methods","level":3,"score":0.6692160367965698},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47241201996803284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45194366574287415},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4143914580345154},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.30816811323165894},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1152961254119873},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":2,"locations":[{"id":"doi:10.1137/23m1621265","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1621265","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:arXiv.org:2412.14761","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.14761","pdf_url":"https://arxiv.org/pdf/2412.14761","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2412.14761","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2412.14761","pdf_url":"https://arxiv.org/pdf/2412.14761","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[{"id":"https://openalex.org/G4386460471","display_name":null,"funder_award_id":"RGPIN 2022-03302","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G7556596340","display_name":null,"funder_award_id":"H2SAFE-CM-UC3M","funder_id":"https://openalex.org/F4320313831","funder_display_name":"Comunidad de Madrid"}],"funders":[{"id":"https://openalex.org/F4320313831","display_name":"Comunidad de Madrid","ror":null},{"id":"https://openalex.org/F4320323770","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405492796.pdf"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W334580453","https://openalex.org/W1991566405","https://openalex.org/W2005720059","https://openalex.org/W2020462115","https://openalex.org/W2048269209","https://openalex.org/W2059176502","https://openalex.org/W2065729312","https://openalex.org/W2066880755","https://openalex.org/W2083691506","https://openalex.org/W2094108357","https://openalex.org/W2123996636","https://openalex.org/W2157670588","https://openalex.org/W2169437869","https://openalex.org/W2180038452","https://openalex.org/W2254823475","https://openalex.org/W2268201048","https://openalex.org/W2289542516","https://openalex.org/W2403418182","https://openalex.org/W2481312347","https://openalex.org/W2560552443","https://openalex.org/W2756899824","https://openalex.org/W2770920520","https://openalex.org/W2785887210","https://openalex.org/W2801282740","https://openalex.org/W2808952962","https://openalex.org/W2868924824","https://openalex.org/W2907465467","https://openalex.org/W2907526013","https://openalex.org/W2951361707","https://openalex.org/W2969497701","https://openalex.org/W2993215726","https://openalex.org/W3000448799","https://openalex.org/W3010912522","https://openalex.org/W3075502700","https://openalex.org/W3100925412","https://openalex.org/W3184879880","https://openalex.org/W4292651623","https://openalex.org/W4372266441","https://openalex.org/W4385323473"],"related_works":["https://openalex.org/W2055836843","https://openalex.org/W2726835731","https://openalex.org/W2755775996","https://openalex.org/W3131818128","https://openalex.org/W2095941963","https://openalex.org/W2366062865","https://openalex.org/W2069701013","https://openalex.org/W2043466553","https://openalex.org/W574172409","https://openalex.org/W2169158840"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,48,51,91,100,153,158],"novel":[4],"meshfree":[5],"methodology":[6],"based":[7],"on":[8,24,130,143,172],"Radial":[9],"Basis":[10],"Function-Finite":[11],"Difference":[12],"(RBF-FD)":[13],"approximations":[14],"for":[15],"the":[16,37,40,45,58,95,105,109,120,123,163,166,176,183,191],"numerical":[17,180],"solution":[18],"of":[19,26,39,47,60,108,122,165,190],"partial":[20],"differential":[21],"equations":[22],"(PDEs)":[23],"surfaces":[25,144,174],"codimension":[27],"1":[28],"embedded":[29,62],"in":[30,169,175],"$\\mathbb{R}^3$.":[31],"The":[32],"method":[33,161,168],"is":[34,87,116],"built":[35],"upon":[36],"principles":[38,66],"closest":[41,52],"point":[42,53,150],"method,":[43],"without":[44],"use":[46],"grid":[49],"or":[50,148],"mapping.":[54],"We":[55,125],"show":[56,84],"that":[57,85],"combination":[59],"local":[61],"stencils":[63],"with":[64,157],"these":[65],"can":[67],"be":[68],"employed":[69],"to":[70,89,103,118],"approximate":[71],"surface":[72,133,136],"derivatives":[73],"using":[74],"polyharmonic":[75],"spline":[76],"kernels":[77],"and":[78,135,138,186],"polynomials":[79],"(PHS+Poly)":[80],"RBF-FD.":[81],"Specifically,":[82],"we":[83],"it":[86],"enough":[88],"consider":[90],"constant":[92],"extension":[93],"along":[94],"normal":[96,177],"direction":[97],"only":[98],"at":[99],"single":[101],"node":[102],"overcome":[104],"rank":[106],"deficiency":[107],"polynomial":[110],"basis.":[111],"An":[112],"extensive":[113],"parameter":[114],"analysis":[115],"presented":[117],"test":[119],"dependence":[121],"approach.":[124,192],"demonstrate":[126],"high-order":[127,187],"convergence":[128,189],"rates":[129],"problems":[131],"involving":[132],"advection":[134],"diffusion,":[137],"solve":[139],"Turing":[140],"pattern":[141],"formations":[142],"defined":[145],"either":[146],"implicitly":[147],"by":[149],"clouds.":[151],"Moreover,":[152],"simple":[154],"coupling":[155],"approach":[156],"particle":[159],"tracking":[160],"demonstrates":[162],"potential":[164],"proposed":[167],"solving":[170],"PDEs":[171],"evolving":[173],"direction.":[178],"Our":[179],"results":[181],"confirm":[182],"stability,":[184],"flexibility,":[185],"algebraic":[188]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2}],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2024-12-18T00:00:00"}
