{"id":"https://openalex.org/W2015699640","doi":"https://doi.org/10.1137/s0036139993269266","title":"Exact Nonreflecting Boundary Conditions for the Time Dependent Wave Equation","display_name":"Exact Nonreflecting Boundary Conditions for the Time Dependent Wave Equation","publication_year":1995,"publication_date":"1995-04-01","ids":{"openalex":"https://openalex.org/W2015699640","doi":"https://doi.org/10.1137/s0036139993269266","mag":"2015699640"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139993269266","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139993269266","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5040323736","display_name":"Marcus J. Grote","orcid":"https://orcid.org/0000-0001-8129-0799"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Marcus J. Grote","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108775680","display_name":"Joseph B. Keller","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joseph B. Keller","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040323736"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.4845,"has_fulltext":false,"cited_by_count":234,"citation_normalized_percentile":{"value":0.97939104,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"55","issue":"2","first_page":"280","last_page":"297"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11609","display_name":"Geophysical Methods and Applications","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"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/mathematical-analysis","display_name":"Mathematical analysis","score":0.7299998998641968},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.702257513999939},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6639178991317749},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.659480094909668},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.6550923585891724},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6381825804710388},{"id":"https://openalex.org/keywords/mixed-boundary-condition","display_name":"Mixed boundary condition","score":0.626417875289917},{"id":"https://openalex.org/keywords/robin-boundary-condition","display_name":"Robin boundary condition","score":0.595106303691864},{"id":"https://openalex.org/keywords/poincar\u00e9\u2013steklov-operator","display_name":"Poincar\u00e9\u2013Steklov operator","score":0.5875271558761597},{"id":"https://openalex.org/keywords/cauchy-boundary-condition","display_name":"Cauchy boundary condition","score":0.5566332936286926},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5257452726364136},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5111411213874817},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4892887771129608},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"Free boundary problem","score":0.4162582457065582}],"concepts":[{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.7299998998641968},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.702257513999939},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6639178991317749},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.659480094909668},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.6550923585891724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6381825804710388},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.626417875289917},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.595106303691864},{"id":"https://openalex.org/C65826597","wikidata":"https://www.wikidata.org/wiki/Q17099589","display_name":"Poincar\u00e9\u2013Steklov operator","level":5,"score":0.5875271558761597},{"id":"https://openalex.org/C106947605","wikidata":"https://www.wikidata.org/wiki/Q3278575","display_name":"Cauchy boundary condition","level":4,"score":0.5566332936286926},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5257452726364136},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5111411213874817},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4892887771129608},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.4162582457065582}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139993269266","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139993269266","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1485393633","https://openalex.org/W1966339154","https://openalex.org/W2068799998","https://openalex.org/W2095016845","https://openalex.org/W2994660742"],"related_works":["https://openalex.org/W1586418441","https://openalex.org/W2393913967","https://openalex.org/W2378263446","https://openalex.org/W1548901099","https://openalex.org/W1991436309","https://openalex.org/W2092652774","https://openalex.org/W2606825881","https://openalex.org/W2950745545","https://openalex.org/W3136311820","https://openalex.org/W4382763327"],"abstract_inverted_index":{"An":[0],"exact":[1],"nonreflecting":[2],"boundary":[3,25,41,59,66],"condition":[4,42,60,67],"is":[5,27,61],"derived":[6],"for":[7,48,68],"solutions":[8,49],"of":[9,51,55,90],"the":[10,64,69],"time":[11,47],"dependent":[12],"wave":[13],"equation":[14],"in":[15,29,33,44,76,82,86],"three":[16],"space":[17,45],"dimensions.":[18],"It":[19,35,72],"holds":[20],"on":[21],"a":[22,40,52,87],"spherical":[23,56],"artificial":[24],"and":[26,46],"local":[28,43],"time,":[30],"but":[31],"nonlocal":[32],"space.":[34,91],"can":[36,73],"be":[37,74],"reduced":[38],"to":[39,63],"consisting":[50],"finite":[53],"number":[54],"harmonics.":[57],"The":[58],"related":[62],"Dirichlet-to-Neumann":[65],"Helmholtz":[70],"equation.":[71],"used":[75],"scattering":[77],"problems":[78,83],"as":[79,81],"well":[80],"involving":[84],"nonlinearity":[85],"bounded":[88],"region":[89]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":9}],"updated_date":"2026-05-09T13:55:54.758798","created_date":"2025-10-10T00:00:00"}