{"id":"https://openalex.org/W3200491574","doi":"https://doi.org/10.1137/22m1469602","title":"A Multivariate Spline Based Collocation Method for Numerical Solution of Partial Differential Equations","display_name":"A Multivariate Spline Based Collocation Method for Numerical Solution of Partial Differential Equations","publication_year":2022,"publication_date":"2022-09-06","ids":{"openalex":"https://openalex.org/W3200491574","doi":"https://doi.org/10.1137/22m1469602","mag":"3200491574"},"language":"en","primary_location":{"id":"doi:10.1137/22m1469602","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1469602","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/A5103069205","display_name":"Ming-Jun Lai","orcid":"https://orcid.org/0000-0001-8950-7016"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ming-Jun Lai","raw_affiliation_strings":["*University of Georgia;"],"raw_orcid":"https://orcid.org/0000-0001-8950-7016","affiliations":[{"raw_affiliation_string":"*University of Georgia;","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102026410","display_name":"Jinsil Lee","orcid":"https://orcid.org/0000-0002-9861-8399"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jinsil Lee","raw_affiliation_strings":["*University of Georgia;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"*University of Georgia;","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103069205"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8307,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.63807906,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"60","issue":"5","first_page":"2405","last_page":"2434"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T10514","display_name":"Numerical methods in engineering","score":0.9955000281333923,"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":0.9907000064849854,"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/mathematics","display_name":"Mathematics","score":0.787609338760376},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6898510456085205},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.641282856464386},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.6115097403526306},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5673147439956665},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.5295256972312927},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4881787896156311},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.48535433411598206},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.4675162434577942},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.45076262950897217},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43411898612976074},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.42930692434310913},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3810839354991913},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3175539970397949},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.10068053007125854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08913812041282654}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.787609338760376},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6898510456085205},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.641282856464386},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.6115097403526306},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5673147439956665},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.5295256972312927},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4881787896156311},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.48535433411598206},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.4675162434577942},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.45076262950897217},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43411898612976074},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.42930692434310913},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3810839354991913},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3175539970397949},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.10068053007125854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08913812041282654},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1469602","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1469602","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":[],"awards":[{"id":"https://openalex.org/G154604433","display_name":null,"funder_award_id":"864439","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W629836974","https://openalex.org/W1545761024","https://openalex.org/W1967338261","https://openalex.org/W1971589961","https://openalex.org/W1972877576","https://openalex.org/W1974920483","https://openalex.org/W1995448628","https://openalex.org/W2032941427","https://openalex.org/W2169554246","https://openalex.org/W2253392016","https://openalex.org/W2536116556","https://openalex.org/W2739011639","https://openalex.org/W2946656677","https://openalex.org/W2963671148","https://openalex.org/W2999157960","https://openalex.org/W3150454712","https://openalex.org/W3175779768","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W2078318892","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W2889856026","https://openalex.org/W1987365920","https://openalex.org/W1989122168","https://openalex.org/W2000247808","https://openalex.org/W2384941625","https://openalex.org/W2060099884"],"abstract_inverted_index":{"We":[0,21,48],"propose":[1],"a":[2,24,66,90,109,117],"collocation":[3],"method":[4,29,79,107],"based":[5],"on":[6],"multivariate":[7,95],"polynomial":[8],"splines":[9],"over":[10,80],"triangulation":[11],"or":[12],"tetrahedralization":[13],"for":[14,30],"numerical":[15,53,70],"solution":[16,54,60],"of":[17,27,69,77],"partial":[18],"differential":[19],"equations.":[20],"start":[22],"with":[23,92],"detailed":[25],"explanation":[26],"the":[28,31,37,40,52,57,75,78,81,93,105],"Poisson":[32],"equation":[33],"and":[34,83,100,111],"then":[35],"extend":[36],"study":[38],"to":[39,73,102],"second":[41],"order":[42],"elliptic":[43],"PDE":[44,59],"in":[45,98,116],"nondivergence":[46],"form.":[47],"shall":[49],"show":[50,103],"that":[51,104],"can":[55],"approximate":[56],"exact":[58],"very":[61],"well.":[62],"Then":[63],"we":[64,88],"present":[65,89],"large":[67],"amount":[68],"experimental":[71],"results":[72],"demonstrate":[74],"performance":[76],"two-":[82],"three-dimensional":[84],"settings.":[85],"In":[86],"addition,":[87],"comparison":[91],"existing":[94],"spline":[96],"methods":[97],"[2]":[99],"[12]":[101],"new":[106],"produces":[108],"similar":[110],"sometimes":[112],"more":[113,118],"accurate":[114],"approximation":[115],"efficient":[119],"fashion.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}