{"id":"https://openalex.org/W2593356793","doi":"https://doi.org/10.1090/s0025-5718-08-02164-9","title":"Nonlinear nonoverlapping Schwarz waveform relaxation for semilinear wave propagation","display_name":"Nonlinear nonoverlapping Schwarz waveform relaxation for semilinear wave propagation","publication_year":2008,"publication_date":"2008-07-01","ids":{"openalex":"https://openalex.org/W2593356793","doi":"https://doi.org/10.1090/s0025-5718-08-02164-9","mag":"2593356793"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02164-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02164-9","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02164-9/S0025-5718-08-02164-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02164-9/S0025-5718-08-02164-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113857548","display_name":"Laurence Halpern","orcid":"https://orcid.org/0000-0002-7877-7130"},"institutions":[{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I4210102686","display_name":"Laboratoire Analyse, G\u00e9om\u00e9trie et Applications","ror":"https://ror.org/018nzqy79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210102686","https://openalex.org/I4210141950","https://openalex.org/I48825208"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Laurence Halpern","raw_affiliation_strings":["LAGA, Institut Galil\u00c3\u00a9e, Universit\u00c3\u00a9 Paris XIII, 93430 Villetaneuse, France","LAGA, Institut Galil\u00e9e, Universit\u00e9 Paris XIII, 93430 Villetaneuse, France"],"affiliations":[{"raw_affiliation_string":"LAGA, Institut Galil\u00c3\u00a9e, Universit\u00c3\u00a9 Paris XIII, 93430 Villetaneuse, France","institution_ids":["https://openalex.org/I4210102686","https://openalex.org/I4210091279"]},{"raw_affiliation_string":"LAGA, Institut Galil\u00e9e, Universit\u00e9 Paris XIII, 93430 Villetaneuse, France","institution_ids":["https://openalex.org/I4210102686","https://openalex.org/I4210091279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108725023","display_name":"J\u00e9r\u00e9mie Szeftel","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]},{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00e9mie Szeftel","raw_affiliation_strings":["Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000, and C.N.R.S., Math\u00c3\u00a9matiques Appliqu\u00c3\u00a9es de Bordeaux, Universit\u00c3\u00a9 Bordeaux 1, 351 cours de la Lib\u00c3\u00a9ration, 3 3405 Talence cedex France","Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000, and C.N.R.S., Math\u00e9matiques Appliqu\u00e9es de Bordeaux, Universit\u00e9 Bordeaux 1, 351 cours de la Lib\u00e9ration, 3 3405 Talence cedex France"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000, and C.N.R.S., Math\u00c3\u00a9matiques Appliqu\u00c3\u00a9es de Bordeaux, Universit\u00c3\u00a9 Bordeaux 1, 351 cours de la Lib\u00c3\u00a9ration, 3 3405 Talence cedex France","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000, and C.N.R.S., Math\u00e9matiques Appliqu\u00e9es de Bordeaux, Universit\u00e9 Bordeaux 1, 351 cours de la Lib\u00e9ration, 3 3405 Talence cedex France","institution_ids":["https://openalex.org/I4210166017","https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113857548"],"corresponding_institution_ids":["https://openalex.org/I4210091279","https://openalex.org/I4210102686"],"apc_list":null,"apc_paid":null,"fwci":0.6782,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.76179292,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"78","issue":"266","first_page":"865","last_page":"889"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998000264167786,"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":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"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":0.9984999895095825,"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":0.8188943862915039},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.794806957244873},{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.7193691730499268},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.691872775554657},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.6761763095855713},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6624128818511963},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6431900858879089},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5192208886146545},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5164056420326233},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4438685476779938},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.4405940771102905},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4234505891799927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4064680337905884},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4039181172847748},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.13860154151916504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09226733446121216}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8188943862915039},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.794806957244873},{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.7193691730499268},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.691872775554657},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.6761763095855713},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6624128818511963},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6431900858879089},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5192208886146545},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5164056420326233},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4438685476779938},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.4405940771102905},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4234505891799927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4064680337905884},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4039181172847748},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.13860154151916504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09226733446121216},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","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},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-08-02164-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02164-9","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02164-9/S0025-5718-08-02164-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-08-02164-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02164-9","pdf_url":"https://www.ams.org/mcom/2009-78-266/S0025-5718-08-02164-9/S0025-5718-08-02164-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.5299999713897705,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G6124680253","display_name":"Numerical computation and qualitative properties of nonlinear Partial Differential Equations","funder_award_id":"0504720","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2593356793.pdf","grobid_xml":"https://content.openalex.org/works/W2593356793.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W312948893","https://openalex.org/W598044257","https://openalex.org/W1480366635","https://openalex.org/W1489373617","https://openalex.org/W1986788497","https://openalex.org/W2009575526","https://openalex.org/W2025377524","https://openalex.org/W2028172193","https://openalex.org/W2031027147","https://openalex.org/W2092129801","https://openalex.org/W2318637407","https://openalex.org/W2502764250","https://openalex.org/W4285719527","https://openalex.org/W4297993633"],"related_works":["https://openalex.org/W2902154408","https://openalex.org/W1515964003","https://openalex.org/W2504287632","https://openalex.org/W1994696552","https://openalex.org/W3046643187","https://openalex.org/W2286395548","https://openalex.org/W4241403127","https://openalex.org/W1423765865","https://openalex.org/W2493580937","https://openalex.org/W132556536"],"abstract_inverted_index":{"We":[0,31,50,56,70],"introduce":[1,52],"a":[2,27,47],"nonoverlapping":[3],"variant":[4],"of":[5,21,60],"the":[6,19,34,58,61,68],"Schwarz":[7],"waveform":[8],"relaxation":[9],"algorithm":[10,35,63],"for":[11],"semilinear":[12],"wave":[13],"propagation":[14],"in":[15],"one":[16],"dimension.":[17],"Using":[18],"theory":[20],"absorbing":[22],"boundary":[23],"conditions,":[24],"we":[25,39],"derive":[26],"new":[28],"nonlinear":[29],"algorithm.":[30],"show":[32],"that":[33],"is":[36],"well-posed":[37],"and":[38,46],"prove":[40,57],"its":[41],"convergence":[42,59],"by":[43],"energy":[44],"estimates":[45],"Galerkin":[48],"method.":[49],"then":[51],"an":[53],"explicit":[54],"scheme.":[55],"discrete":[62],"with":[64,75],"suitable":[65],"assumptions":[66],"on":[67],"nonlinearity.":[69],"finally":[71],"illustrate":[72],"our":[73],"analysis":[74],"numerical":[76],"experiments.":[77]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}