{"id":"https://openalex.org/W2088046391","doi":"https://doi.org/10.1137/130929497","title":"The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces","display_name":"The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2088046391","doi":"https://doi.org/10.1137/130929497","mag":"2088046391"},"language":"en","primary_location":{"id":"doi:10.1137/130929497","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130929497","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/A5100736990","display_name":"Yujia Chen","orcid":"https://orcid.org/0000-0002-9794-7131"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yujia Chen","raw_affiliation_strings":["Mathematical Institute, University of Oxford, OX1 3LB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, OX1 3LB, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068343828","display_name":"Colin B. Macdonald","orcid":"https://orcid.org/0000-0002-4557-8637"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Colin B. Macdonald","raw_affiliation_strings":["Mathematical Institute, University of Oxford, OX1 3LB, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, OX1 3LB, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068343828"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":3.187,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.9083816,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"37","issue":"1","first_page":"A134","last_page":"A155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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":0.9993000030517578,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9976999759674072,"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/multigrid-method","display_name":"Multigrid method","score":0.9079923033714294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.813367486000061},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.6456195116043091},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6057248115539551},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5884543061256409},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.554624080657959},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.5327076315879822},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5245506763458252},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.4500841498374939},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42656630277633667},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.42053312063217163},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4204503893852234},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21565920114517212},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13588851690292358}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.9079923033714294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.813367486000061},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.6456195116043091},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6057248115539551},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5884543061256409},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.554624080657959},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.5327076315879822},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5245506763458252},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.4500841498374939},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42656630277633667},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.42053312063217163},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4204503893852234},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21565920114517212},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13588851690292358},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130929497","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130929497","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:CiteSeerX.psu:10.1.1.744.653","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.744.653","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1307.4354.pdf","raw_type":"text"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/599886","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/599886","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah 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/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"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/G7255873218","display_name":null,"funder_award_id":"KUK-C1-013-04","funder_id":"https://openalex.org/F4320322320","funder_display_name":"King Abdullah University of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W50490584","https://openalex.org/W1504765007","https://openalex.org/W1508165980","https://openalex.org/W1530872699","https://openalex.org/W1621614599","https://openalex.org/W1981115560","https://openalex.org/W1990431791","https://openalex.org/W2004880766","https://openalex.org/W2009262561","https://openalex.org/W2012255853","https://openalex.org/W2022819931","https://openalex.org/W2024394198","https://openalex.org/W2033994983","https://openalex.org/W2043546299","https://openalex.org/W2051018698","https://openalex.org/W2054557638","https://openalex.org/W2064240269","https://openalex.org/W2065729312","https://openalex.org/W2066880755","https://openalex.org/W2083691506","https://openalex.org/W2094108357","https://openalex.org/W2094963146","https://openalex.org/W2121048128","https://openalex.org/W2123996636","https://openalex.org/W2127981460","https://openalex.org/W2144614420","https://openalex.org/W2162703509","https://openalex.org/W2167606637","https://openalex.org/W2296319761","https://openalex.org/W2998496342","https://openalex.org/W3100925412","https://openalex.org/W3200227310"],"related_works":["https://openalex.org/W2356816331","https://openalex.org/W2307054062","https://openalex.org/W322277319","https://openalex.org/W2344267562","https://openalex.org/W1632720046","https://openalex.org/W1984227015","https://openalex.org/W2042128780","https://openalex.org/W1566351512","https://openalex.org/W364294403","https://openalex.org/W2054004413"],"abstract_inverted_index":{"Elliptic":[0],"partial":[1],"differential":[2],"equations":[3,26],"are":[4,130],"important":[5],"from":[6],"both":[7,112],"application":[8],"and":[9,58,119],"analysis":[10],"points":[11],"of":[12,37,71,104,115,122],"view.":[13],"In":[14,84],"this":[15],"paper":[16],"we":[17,41,94],"apply":[18],"the":[19,33,38,47,69,72,76,88,102,105,113,116,120,123],"closest":[20,34,106],"point":[21,35,107],"method":[22,100],"to":[23,86],"solve":[24,87],"elliptic":[25,49],"on":[27,32,61,79],"general":[28],"curved":[29],"surfaces.":[30],"Based":[31],"representation":[36],"underlying":[39],"surface,":[40],"formulate":[42],"an":[43],"embedding":[44],"equation":[45,78],"for":[46,75],"surface":[48],"problem,":[50],"then":[51],"discretize":[52],"it":[53],"using":[54],"standard":[55],"finite":[56],"differences":[57],"interpolation":[59],"schemes":[60],"banded":[62],"but":[63],"uniform":[64],"Cartesian":[65],"grids.":[66],"We":[67],"prove":[68],"convergence":[70],"difference":[73,117],"scheme":[74,118],"Poisson's":[77],"a":[80,96],"smooth":[81],"closed":[82],"curve.":[83],"order":[85],"resulting":[89],"large":[90],"sparse":[91],"linear":[92],"systems,":[93],"propose":[95],"specific":[97],"geometric":[98],"multigrid":[99,124],"in":[101,111],"setting":[103],"method.":[108],"Convergence":[109],"studies":[110],"accuracy":[114],"speed":[121],"algorithm":[125],"show":[126],"that":[127],"our":[128],"approaches":[129],"effective.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
