{"id":"https://openalex.org/W2055548619","doi":"https://doi.org/10.1137/050632920","title":"A Stable High\u2010Order Method for Two\u2010Dimensional Bounded\u2010Obstacle Scattering","display_name":"A Stable High\u2010Order Method for Two\u2010Dimensional Bounded\u2010Obstacle Scattering","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2055548619","doi":"https://doi.org/10.1137/050632920","mag":"2055548619"},"language":"en","primary_location":{"id":"doi:10.1137/050632920","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050632920","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/A5034314035","display_name":"David P. Nicholls","orcid":"https://orcid.org/0000-0002-7424-9832"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David P. Nicholls","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028981574","display_name":"Jie Shen","orcid":"https://orcid.org/0000-0002-4885-5732"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jie Shen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7305,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.84516994,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"28","issue":"4","first_page":"1398","last_page":"1419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9997000098228455,"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":0.9997000098228455,"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/T10514","display_name":"Numerical methods in engineering","score":0.9993000030517578,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8142145872116089},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.7328419089317322},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.650810182094574},{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.5839361548423767},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.572652280330658},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5697165727615356},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5238656401634216},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.517630398273468},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.46237891912460327},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4585111141204834},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.4477958381175995},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4410381317138672},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4384627938270569},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38385263085365295},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.35372334718704224},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19950178265571594},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.14464688301086426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09335437417030334}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8142145872116089},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.7328419089317322},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.650810182094574},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.5839361548423767},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.572652280330658},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5697165727615356},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5238656401634216},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.517630398273468},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.46237891912460327},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4585111141204834},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.4477958381175995},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4410381317138672},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4384627938270569},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38385263085365295},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.35372334718704224},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19950178265571594},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.14464688301086426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09335437417030334},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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:10.1137/050632920","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050632920","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.86.7575","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.7575","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uic.edu/~nicholls/papers/Final/bo2d.sisc.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W61626614","https://openalex.org/W187705252","https://openalex.org/W1523113578","https://openalex.org/W1966348553","https://openalex.org/W1966475972","https://openalex.org/W1969990706","https://openalex.org/W1971885174","https://openalex.org/W1977336080","https://openalex.org/W1981266813","https://openalex.org/W1984650156","https://openalex.org/W1986872269","https://openalex.org/W2000065163","https://openalex.org/W2003909841","https://openalex.org/W2005059268","https://openalex.org/W2010051028","https://openalex.org/W2012813672","https://openalex.org/W2028644499","https://openalex.org/W2054565622","https://openalex.org/W2055738068","https://openalex.org/W2056658486","https://openalex.org/W2058038018","https://openalex.org/W2072564371","https://openalex.org/W2082427843","https://openalex.org/W2082849992","https://openalex.org/W2092328081","https://openalex.org/W2100461433","https://openalex.org/W2106526278","https://openalex.org/W2114057352","https://openalex.org/W2136535472","https://openalex.org/W2140107886","https://openalex.org/W2150954010","https://openalex.org/W2169481569","https://openalex.org/W2410898212"],"related_works":["https://openalex.org/W2003238696","https://openalex.org/W2108572708","https://openalex.org/W2843106559","https://openalex.org/W4309131391","https://openalex.org/W1964914287","https://openalex.org/W2338063770","https://openalex.org/W1983679522","https://openalex.org/W3143288670","https://openalex.org/W2022522399","https://openalex.org/W3047676097"],"abstract_inverted_index":{"A":[0],"stable":[1],"and":[2,66],"high\u2010order":[3,40],"method":[4,25,44],"for":[5],"solving":[6],"the":[7,63,69],"Helmholtz":[8],"equation":[9],"on":[10,28],"a":[11,16,29,38],"two\u2010dimensional":[12],"domain":[13],"exterior":[14],"to":[15,61],"bounded":[17],"obstacle":[18],"is":[19,26,45],"developed":[20],"in":[21],"this":[22],"paper.":[23],"The":[24,43],"based":[27],"boundary":[30],"perturbation":[31],"technique":[32],"(\u201ctransformed":[33],"field":[34],"expansions\u201d)":[35],"coupled":[36],"with":[37,48],"well\u2010conditioned":[39],"spectral\u2010Galerkin":[41],"solver.":[42],"further":[46],"enhanced":[47],"numerical":[49,57],"analytic":[50],"continuation,":[51],"implemented":[52],"via":[53],"Pad\u00e9":[54],"approximation.":[55],"Ample":[56],"results":[58],"are":[59],"presented":[60],"show":[62],"accuracy,":[64],"stability,":[65],"versatility":[67],"of":[68],"proposed":[70],"method.":[71]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
