{"id":"https://openalex.org/W2071925186","doi":"https://doi.org/10.1137/s1064827503428540","title":"A Boundary Condition--Capturing Multigrid Approach to Irregular Boundary Problems","display_name":"A Boundary Condition--Capturing Multigrid Approach to Irregular Boundary Problems","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2071925186","doi":"https://doi.org/10.1137/s1064827503428540","mag":"2071925186"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827503428540","doi":"https://doi.org/10.1137/s1064827503428540","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503428540","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,"listed_in":["cwts-core","jufo-3","norway-2"],"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"},"volume":null,"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/A5102887139","display_name":"Justin W. L. Wan","orcid":"https://orcid.org/0000-0001-8367-6337","observed_orcids":["https://orcid.org/0000-0001-8367-6337"]},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Justin W. L. Wan","raw_affiliation_strings":["(University of Waterloo)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(University of Waterloo)","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":null,"display_name":"Xu-Dong Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xu-Dong Liu","raw_affiliation_strings":["Department of Mathematics, University of California at Santa Barbara, Santa Barbara, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California at Santa Barbara, Santa Barbara, CA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4019,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.6481198,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"25","issue":"6","first_page":"1982","last_page":"2003"},"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":0.975600004196167,"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":0.975600004196167,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.013299999758601189,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.0038999998942017555,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geometric-multigrid","display_name":"geometric multigrid","score":0.8960000276565552},{"id":"https://openalex.org/keywords/multiple-interfaces","display_name":"multiple interfaces","score":0.8629999756813049},{"id":"https://openalex.org/keywords/level-set-function","display_name":"level set function","score":0.7260000109672546},{"id":"https://openalex.org/keywords/interpolation","display_name":"interpolation","score":0.6240000128746033},{"id":"https://openalex.org/keywords/boundary-conditions","display_name":"boundary conditions","score":0.6589999794960022},{"id":"https://openalex.org/keywords/linear-systems","display_name":"linear systems","score":0.8220000267028809},{"id":"https://openalex.org/keywords/algebraic-multigrid","display_name":"algebraic multigrid","score":1.0}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.9581953287124634},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6424734592437744},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6100748777389526},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6091745495796204},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5456392168998718},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.530433177947998},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45475780963897705},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4271089732646942},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.417820006608963},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33314040303230286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29140958189964294},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.27834510803222656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2724156975746155},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26795536279678345},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827503428540","doi":"https://doi.org/10.1137/s1064827503428540","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503428540","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,"listed_in":["cwts-core","jufo-3","norway-2"],"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:10.1.1.83.337","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.337","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uwaterloo.ca/~jwlwan/papers/WanLiu04.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Sustainable cities and communities","score":0.5,"id":"https://metadata.un.org/sdg/11"}],"study_designs":[],"awards":[{"id":"https://openalex.org/G8175157710","display_name":"Scalable Multilevel Algorithms in Computational Sciences","funder_award_id":"0072112","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"},{"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":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W202241982","https://openalex.org/W1486400850","https://openalex.org/W1596538833","https://openalex.org/W1607829564","https://openalex.org/W1976115257","https://openalex.org/W1977856502","https://openalex.org/W1984797906","https://openalex.org/W1986746311","https://openalex.org/W1991113069","https://openalex.org/W1992657818","https://openalex.org/W1998461805","https://openalex.org/W2005316292","https://openalex.org/W2016641139","https://openalex.org/W2017085690","https://openalex.org/W2029495360","https://openalex.org/W2031887218","https://openalex.org/W2045545335","https://openalex.org/W2056715474","https://openalex.org/W2065385312","https://openalex.org/W2079308547","https://openalex.org/W2081708354","https://openalex.org/W2083279088","https://openalex.org/W2102369828","https://openalex.org/W2127981460","https://openalex.org/W2142304406","https://openalex.org/W2151317657","https://openalex.org/W2158647718","https://openalex.org/W2172093368","https://openalex.org/W2252040419","https://openalex.org/W2498157954","https://openalex.org/W2728627120"],"related_works":["https://openalex.org/W2077078424","https://openalex.org/W2182328658","https://openalex.org/W1519938374","https://openalex.org/W84272617","https://openalex.org/W613282331","https://openalex.org/W2092341060","https://openalex.org/W66408621","https://openalex.org/W2493281735","https://openalex.org/W2171218546","https://openalex.org/W2543276709"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,28,77],"geometric":[3],"multigrid":[4,55,88,95],"method":[5,89],"for":[6],"solving":[7],"linear":[8],"systems":[9],"arising":[10],"from":[11],"irregular":[12],"boundary":[13,71],"problems":[14],"involving":[15],"multiple":[16],"interfaces":[17,75],"in":[18],"two":[19],"and":[20,41,93],"three":[21],"dimensions.":[22],"In":[23],"this":[24],"method,":[25],"we":[26,32,42],"adopt":[27],"matrix-free":[29],"approach;":[30],"i.e.,":[31],"do":[33],"not":[34],"form":[35,44],"the":[36,47,69,74],"fine":[37],"grid":[38,49],"matrix":[39],"explicitly":[40],"never":[43],"nor":[45],"store":[46],"coarse":[48],"matrices,":[50],"as":[51],"many":[52],"other":[53],"robust":[54],"methods":[56],"do.":[57],"The":[58],"main":[59],"idea":[60],"is":[61],"to":[62,85],"construct":[63],"an":[64],"accurate":[65],"interpolation":[66],"which":[67],"captures":[68],"correct":[70],"conditions":[72],"at":[73],"via":[76],"level":[78],"set":[79],"function.":[80],"Numerical":[81],"results":[82],"are":[83],"given":[84],"compare":[86],"our":[87],"with":[90],"black":[91],"box":[92],"algebraic":[94],"methods.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2025-10-10T00:00:00"}
