{"id":"https://openalex.org/W3022521945","doi":"https://doi.org/10.1007/s11075-020-00926-5","title":"An optimal 13-point finite difference scheme for a 2D Helmholtz equation with a perfectly matched layer boundary condition","display_name":"An optimal 13-point finite difference scheme for a 2D Helmholtz equation with a perfectly matched layer boundary condition","publication_year":2020,"publication_date":"2020-05-02","ids":{"openalex":"https://openalex.org/W3022521945","doi":"https://doi.org/10.1007/s11075-020-00926-5","mag":"3022521945"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-020-00926-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-020-00926-5","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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/A5012751750","display_name":"Hatef Dastour","orcid":"https://orcid.org/0000-0002-2119-9077"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Hatef Dastour","raw_affiliation_strings":["Department of Mathematics & Statistics, University of Calgary, AB, T2N 1N4, Calgary, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, University of Calgary, AB, T2N 1N4, Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027271308","display_name":"Wenyuan Liao","orcid":"https://orcid.org/0000-0002-6566-9341"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Wenyuan Liao","raw_affiliation_strings":["Department of Mathematics & Statistics, University of Calgary, AB, T2N 1N4, Calgary, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, University of Calgary, AB, T2N 1N4, Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5012751750"],"corresponding_institution_ids":["https://openalex.org/I168635309"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.2442,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.49123847,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"86","issue":"3","first_page":"1109","last_page":"1141"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9987999796867371,"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":0.7987606525421143},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.7927666902542114},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6318938136100769},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6293200254440308},{"id":"https://openalex.org/keywords/perfectly-matched-layer","display_name":"Perfectly matched layer","score":0.6020154356956482},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5684857368469238},{"id":"https://openalex.org/keywords/boundary-layer","display_name":"Boundary layer","score":0.5668370723724365},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4618801772594452},{"id":"https://openalex.org/keywords/layer","display_name":"Layer (electronics)","score":0.4609859883785248},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.45964622497558594},{"id":"https://openalex.org/keywords/blasius-boundary-layer","display_name":"Blasius boundary layer","score":0.4494952857494354},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.44942522048950195},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4348210096359253},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4271204173564911},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4198765158653259},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3469124436378479},{"id":"https://openalex.org/keywords/boundary-layer-thickness","display_name":"Boundary layer thickness","score":0.31341487169265747},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1167404055595398},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11108222603797913},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10125356912612915}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7987606525421143},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.7927666902542114},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6318938136100769},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6293200254440308},{"id":"https://openalex.org/C16895185","wikidata":"https://www.wikidata.org/wiki/Q15101726","display_name":"Perfectly matched layer","level":3,"score":0.6020154356956482},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5684857368469238},{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.5668370723724365},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4618801772594452},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.4609859883785248},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.45964622497558594},{"id":"https://openalex.org/C23221634","wikidata":"https://www.wikidata.org/wiki/Q4925317","display_name":"Blasius boundary layer","level":4,"score":0.4494952857494354},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.44942522048950195},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4348210096359253},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4271204173564911},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4198765158653259},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3469124436378479},{"id":"https://openalex.org/C151890184","wikidata":"https://www.wikidata.org/wiki/Q1660471","display_name":"Boundary layer thickness","level":3,"score":0.31341487169265747},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1167404055595398},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11108222603797913},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10125356912612915},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-020-00926-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-020-00926-5","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8991251288","display_name":"Mathematical theory and computational methods  for seismic full waveform inversion problems","funder_award_id":"rgpin-2019-04830","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1966763308","https://openalex.org/W1969041915","https://openalex.org/W1976538983","https://openalex.org/W1987066751","https://openalex.org/W1991290104","https://openalex.org/W2002363316","https://openalex.org/W2003017040","https://openalex.org/W2005733061","https://openalex.org/W2011936333","https://openalex.org/W2019840928","https://openalex.org/W2024381649","https://openalex.org/W2030729182","https://openalex.org/W2032794959","https://openalex.org/W2042015995","https://openalex.org/W2042199958","https://openalex.org/W2051917325","https://openalex.org/W2057948975","https://openalex.org/W2060690636","https://openalex.org/W2064660626","https://openalex.org/W2070875961","https://openalex.org/W2082971559","https://openalex.org/W2088160222","https://openalex.org/W2100245965","https://openalex.org/W2101615520","https://openalex.org/W2102369828","https://openalex.org/W2108332067","https://openalex.org/W2108822617","https://openalex.org/W2115272362","https://openalex.org/W2118843696","https://openalex.org/W2125977519","https://openalex.org/W2150300407","https://openalex.org/W2150333845","https://openalex.org/W2164639651","https://openalex.org/W2168110839","https://openalex.org/W2509466404","https://openalex.org/W2609596110","https://openalex.org/W2617415243","https://openalex.org/W2783325651","https://openalex.org/W2969463226","https://openalex.org/W3104165448"],"related_works":["https://openalex.org/W2032794959","https://openalex.org/W2149804981","https://openalex.org/W4367296780","https://openalex.org/W2131186711","https://openalex.org/W2162587964","https://openalex.org/W277277552","https://openalex.org/W4254005143","https://openalex.org/W210631101","https://openalex.org/W2539603238","https://openalex.org/W4206395706"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
