{"id":"https://openalex.org/W3137662429","doi":"https://doi.org/10.1007/s00211-021-01195-7","title":"Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods","display_name":"Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods","publication_year":2021,"publication_date":"2021-03-25","ids":{"openalex":"https://openalex.org/W3137662429","doi":"https://doi.org/10.1007/s00211-021-01195-7","mag":"3137662429"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-021-01195-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-021-01195-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5101843452","display_name":"Liwei Xu","orcid":"https://orcid.org/0000-0001-5381-337X"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Liwei Xu","raw_affiliation_strings":["School of Mathematical Sciences, University of Electronic Science and Technology of China, Sichuan, 611731, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Electronic Science and Technology of China, Sichuan, 611731, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101883490","display_name":"Tao Yin","orcid":null},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tao Yin","raw_affiliation_strings":["Department of Computing and Mathematical Sciences, California Institute of Technology, 1200 East California Blvd., Pasadena, CA, 91125, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computing and Mathematical Sciences, California Institute of Technology, 1200 East California Blvd., Pasadena, CA, 91125, USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101843452"],"corresponding_institution_ids":["https://openalex.org/I150229711"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.0354,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.70576075,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"147","issue":"4","first_page":"967","last_page":"996"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.8420721292495728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7719711065292358},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6698943376541138},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5726950168609619},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.5574889183044434},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.5453739166259766},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4743213355541229},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.46141254901885986},{"id":"https://openalex.org/keywords/boundary-knot-method","display_name":"Boundary knot method","score":0.45740583539009094},{"id":"https://openalex.org/keywords/method-of-fundamental-solutions","display_name":"Method of fundamental solutions","score":0.45381635427474976},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.43630629777908325},{"id":"https://openalex.org/keywords/mixed-boundary-condition","display_name":"Mixed boundary condition","score":0.42680564522743225},{"id":"https://openalex.org/keywords/robin-boundary-condition","display_name":"Robin boundary condition","score":0.4238704442977905},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4159581661224365}],"concepts":[{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.8420721292495728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7719711065292358},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6698943376541138},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5726950168609619},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.5574889183044434},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.5453739166259766},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4743213355541229},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.46141254901885986},{"id":"https://openalex.org/C52890695","wikidata":"https://www.wikidata.org/wiki/Q4949966","display_name":"Boundary knot method","level":4,"score":0.45740583539009094},{"id":"https://openalex.org/C48395688","wikidata":"https://www.wikidata.org/wiki/Q6823714","display_name":"Method of fundamental solutions","level":5,"score":0.45381635427474976},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.43630629777908325},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.42680564522743225},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.4238704442977905},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4159581661224365},{"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:10.1007/s00211-021-01195-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-021-01195-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:108564","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/108564/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W45217561","https://openalex.org/W399252311","https://openalex.org/W597907832","https://openalex.org/W778457390","https://openalex.org/W1513593694","https://openalex.org/W1523113578","https://openalex.org/W1972960548","https://openalex.org/W1973808722","https://openalex.org/W1979646907","https://openalex.org/W1981266813","https://openalex.org/W1986293636","https://openalex.org/W1995732749","https://openalex.org/W1997352464","https://openalex.org/W2001288210","https://openalex.org/W2003803951","https://openalex.org/W2004475615","https://openalex.org/W2010002946","https://openalex.org/W2029966922","https://openalex.org/W2033742022","https://openalex.org/W2041523977","https://openalex.org/W2058454412","https://openalex.org/W2066812079","https://openalex.org/W2071928229","https://openalex.org/W2072564371","https://openalex.org/W2079051406","https://openalex.org/W2080830659","https://openalex.org/W2085067463","https://openalex.org/W2085192653","https://openalex.org/W2090526616","https://openalex.org/W2102591969","https://openalex.org/W2104709100","https://openalex.org/W2111086304","https://openalex.org/W2113173623","https://openalex.org/W2120062331","https://openalex.org/W2136195225","https://openalex.org/W2139723858","https://openalex.org/W2148262800","https://openalex.org/W2151350667","https://openalex.org/W2152440746","https://openalex.org/W2162138974","https://openalex.org/W2166485094","https://openalex.org/W2226535545","https://openalex.org/W2230104944","https://openalex.org/W2395044955","https://openalex.org/W2519537744","https://openalex.org/W2577596286","https://openalex.org/W2766597181","https://openalex.org/W2903166189","https://openalex.org/W2964255762","https://openalex.org/W3021722416","https://openalex.org/W3107392462","https://openalex.org/W4214519613","https://openalex.org/W4285719527","https://openalex.org/W4292027041"],"related_works":["https://openalex.org/W2092505998","https://openalex.org/W4322770021","https://openalex.org/W1514481392","https://openalex.org/W2950745545","https://openalex.org/W4246256881","https://openalex.org/W2164242665","https://openalex.org/W1974382392","https://openalex.org/W1499757726","https://openalex.org/W2372279110","https://openalex.org/W2976250660"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-30T08:08:38.191290","created_date":"2025-10-10T00:00:00"}