{"id":"https://openalex.org/W2028573964","doi":"https://doi.org/10.1137/110856812","title":"A High Frequency $hp$ Boundary Element Method for Scattering by Convex Polygons","display_name":"A High Frequency $hp$ Boundary Element Method for Scattering by Convex Polygons","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2028573964","doi":"https://doi.org/10.1137/110856812","mag":"2028573964"},"language":"en","primary_location":{"id":"doi:10.1137/110856812","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110856812","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5089364296","display_name":"David P. Hewett","orcid":"https://orcid.org/0000-0003-3302-2567"},"institutions":[{"id":"https://openalex.org/I71052956","display_name":"University of Reading","ror":"https://ror.org/05v62cm79","country_code":"GB","type":"education","lineage":["https://openalex.org/I71052956"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"D. P. Hewett","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, UK","institution_ids":["https://openalex.org/I71052956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072509243","display_name":"S. Langdon","orcid":"https://orcid.org/0000-0002-0572-5137"},"institutions":[{"id":"https://openalex.org/I71052956","display_name":"University of Reading","ror":"https://ror.org/05v62cm79","country_code":"GB","type":"education","lineage":["https://openalex.org/I71052956"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"S. Langdon","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, UK","institution_ids":["https://openalex.org/I71052956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058356670","display_name":"Jens Markus Melenk","orcid":"https://orcid.org/0000-0001-9024-6028"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"J. M. Melenk","raw_affiliation_strings":["Institut f\u00fcr Analysis und Scientific Computing, TU Wien, A-1040 Wien, Austria"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis und Scientific Computing, TU Wien, A-1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089364296"],"corresponding_institution_ids":["https://openalex.org/I71052956"],"apc_list":null,"apc_paid":null,"fwci":2.8674,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.90746753,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"51","issue":"1","first_page":"629","last_page":"653"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998999834060669,"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/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/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"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/mathematics","display_name":"Mathematics","score":0.800224781036377},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5847001075744629},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5768157243728638},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.505406379699707},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.498058557510376},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43525558710098267},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4239519238471985},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.41581177711486816},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.41502711176872253},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33864420652389526},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25270143151283264},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21500834822654724},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07910576462745667}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.800224781036377},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5847001075744629},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5768157243728638},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.505406379699707},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.498058557510376},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43525558710098267},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4239519238471985},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.41581177711486816},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.41502711176872253},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33864420652389526},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25270143151283264},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21500834822654724},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07910576462745667},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/110856812","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110856812","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:centaur.reading.ac.uk:33321","is_oa":false,"landing_page_url":"https://centaur.reading.ac.uk/view/creators/90002802.html>,","pdf_url":null,"source":{"id":"https://openalex.org/S4306402273","display_name":"CentAUR (University of Reading)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71052956","host_organization_name":"University of Reading","host_organization_lineage":["https://openalex.org/I71052956"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.224.8023","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.224.8023","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.reading.ac.uk/web/FILES/maths/preprint_11_18_Langdon.pdf","raw_type":"text"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1523366","is_oa":false,"landing_page_url":"http://discovery.ucl.ac.uk/1523366/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   SIAM JOURNAL ON NUMERICAL ANALYSIS , 51  (1)   pp. 629-653.   (2013)      ","raw_type":"Article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:ac9589e7-759f-46c7-b947-82051896c245","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:ac9589e7-759f-46c7-b947-82051896c245","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5099999904632568,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G3269906927","display_name":null,"funder_award_id":"EP/F067798/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W8052360","https://openalex.org/W91897623","https://openalex.org/W118955685","https://openalex.org/W200443100","https://openalex.org/W571822206","https://openalex.org/W1517670975","https://openalex.org/W1523113578","https://openalex.org/W1538169654","https://openalex.org/W1539256251","https://openalex.org/W1602383637","https://openalex.org/W1965980050","https://openalex.org/W1966368254","https://openalex.org/W1966793029","https://openalex.org/W1967665598","https://openalex.org/W1985048099","https://openalex.org/W1985526385","https://openalex.org/W1994288267","https://openalex.org/W1995356931","https://openalex.org/W2002849390","https://openalex.org/W2009674606","https://openalex.org/W2010501155","https://openalex.org/W2012813672","https://openalex.org/W2015692096","https://openalex.org/W2020818415","https://openalex.org/W2026718533","https://openalex.org/W2026894598","https://openalex.org/W2027727727","https://openalex.org/W2035409961","https://openalex.org/W2038870672","https://openalex.org/W2056171461","https://openalex.org/W2060819023","https://openalex.org/W2071166325","https://openalex.org/W2075662042","https://openalex.org/W2081338783","https://openalex.org/W2084768760","https://openalex.org/W2087828859","https://openalex.org/W2115850109","https://openalex.org/W2121173943","https://openalex.org/W2124387207","https://openalex.org/W2135380580","https://openalex.org/W2137358078","https://openalex.org/W2596290099","https://openalex.org/W2792013640","https://openalex.org/W3130571686"],"related_works":["https://openalex.org/W1995243476","https://openalex.org/W4300013288","https://openalex.org/W2951020105","https://openalex.org/W2952185452","https://openalex.org/W2798106756","https://openalex.org/W2046736294","https://openalex.org/W2980815195","https://openalex.org/W4286857063","https://openalex.org/W2111215486","https://openalex.org/W3040895870"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"propose":[4],"and":[5,52,77],"analyze":[6],"a":[7],"hybrid":[8],"$hp$":[9],"boundary":[10],"element":[11],"method":[12],"for":[13,71],"the":[14,29,41,46,61,64,75,79,85,88,106,116,125,128,131,137],"solution":[15,76],"of":[16,18,45,63,90,108,118,120,127],"problems":[17],"high":[19,42],"frequency":[20,43,89,129,132],"acoustic":[21],"scattering":[22],"by":[23,143],"sound-soft":[24],"convex":[25],"polygons,":[26],"in":[27,83,105,122,134],"which":[28,38,84],"approximation":[30],"space":[31],"is":[32,93,112],"enriched":[33],"with":[34,58],"oscillatory":[35],"basis":[36],"functions":[37],"efficiently":[39],"capture":[40],"asymptotics":[44],"solution.":[47],"We":[48],"demonstrate,":[49],"both":[50],"theoretically":[51],"via":[53],"numerical":[54],"examples,":[55],"exponential":[56],"convergence":[57],"respect":[59],"to":[60,74,78,100,114,124,136],"order":[62],"polynomials,":[65],"moreover":[66],"providing":[67],"rigorous":[68],"error":[69],"estimates":[70,97],"our":[72],"approximations":[73],"far":[80],"field":[81],"pattern,":[82],"dependence":[86],"on":[87],"all":[91],"constants":[92],"explicit.":[94],"Importantly,":[95],"these":[96,109],"prove":[98],"that,":[99],"achieve":[101],"any":[102],"desired":[103],"accuracy":[104],"computation":[107],"quantities,":[110],"it":[111],"sufficient":[113],"increase":[115],"number":[117],"degrees":[119],"freedom":[121],"proportion":[123],"logarithm":[126],"as":[130],"increases,":[133],"contrast":[135],"at":[138],"least":[139],"linear":[140],"growth":[141],"required":[142],"conventional":[144],"methods.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"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":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
