{"id":"https://openalex.org/W2011155152","doi":"https://doi.org/10.1137/s1064827597327541","title":"Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions","display_name":"Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2011155152","doi":"https://doi.org/10.1137/s1064827597327541","mag":"2011155152"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827597327541","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827597327541","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/A5044179575","display_name":"Aaron L. Fogelson","orcid":"https://orcid.org/0000-0002-8885-9420"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aaron L. Fogelson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071828704","display_name":"James P. Keener","orcid":"https://orcid.org/0000-0001-9216-4157"},"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":"James P. Keener","raw_affiliation_strings":["University of Utah,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Utah,","institution_ids":["https://openalex.org/I223532165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.7137,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.95731366,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"22","issue":"5","first_page":"1630","last_page":"1654"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9991000294685364,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9991000294685364,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987999796867371,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9969000220298767,"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/mathematics","display_name":"Mathematics","score":0.7803282141685486},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.670697808265686},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.583763062953949},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5367966890335083},{"id":"https://openalex.org/keywords/regular-grid","display_name":"Regular grid","score":0.5149326920509338},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47827112674713135},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.46853819489479065},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.46698516607284546},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.46252283453941345},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.461592435836792},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4498330056667328},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.4329533576965332},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41765716671943665},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4106711149215698},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3944626748561859},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27405986189842224},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11946189403533936}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7803282141685486},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.670697808265686},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.583763062953949},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5367966890335083},{"id":"https://openalex.org/C43173174","wikidata":"https://www.wikidata.org/wiki/Q2646942","display_name":"Regular grid","level":3,"score":0.5149326920509338},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47827112674713135},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46853819489479065},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.46698516607284546},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.46252283453941345},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.461592435836792},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4498330056667328},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.4329533576965332},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41765716671943665},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4106711149215698},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3944626748561859},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27405986189842224},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11946189403533936},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827597327541","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827597327541","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1525210132","https://openalex.org/W1542333376","https://openalex.org/W1609358141","https://openalex.org/W1968055746","https://openalex.org/W1982396064","https://openalex.org/W1994052003","https://openalex.org/W2012541063","https://openalex.org/W2028085547","https://openalex.org/W2060170348","https://openalex.org/W2063161710","https://openalex.org/W2067216123","https://openalex.org/W2073237947","https://openalex.org/W2088156497","https://openalex.org/W2102369828","https://openalex.org/W2113731277","https://openalex.org/W2141613219","https://openalex.org/W2142237627","https://openalex.org/W2172093368","https://openalex.org/W3081847346","https://openalex.org/W3086400475"],"related_works":["https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W1971388572","https://openalex.org/W2370926798","https://openalex.org/W2005860221","https://openalex.org/W2474502839","https://openalex.org/W2963729233"],"abstract_inverted_index":{"We":[0],"develop":[1],"and":[2,38,58,75],"apply":[3],"a":[4,21,60],"finite-difference":[5],"method":[6,26,34,53,68],"to":[7],"discretize":[8],"the":[9,31,52],"Laplacian":[10],"operator":[11],"with":[12],"Neumann":[13],"boundary":[14],"conditions":[15],"on":[16,71],"an":[17,28],"irregular":[18],"domain":[19],"using":[20],"regular":[22],"Cartesian":[23],"grid.":[24],"The":[25,67],"is":[27,54,63,69],"extension":[29],"of":[30,50],"immersed":[32],"interface":[33],"developed":[35],"by":[36],"LeVeque":[37],"Li":[39],"[SIAM":[40],"J.":[41],"Numer.":[42],"Anal.,":[43],"31":[44],"(1994)":[45],"1019--1044].":[46],"With":[47],"careful":[48],"selection":[49],"stencils,":[51],"second":[55],"order":[56],"accurate":[57],"produces":[59],"matrix":[61],"that":[62],"stable":[64],"(diagonally":[65],"semidominant).":[66],"illustrated":[70],"several":[72],"two-dimensional":[73],"problems":[74],"one":[76],"three-dimensional":[77],"problem.":[78]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}