{"id":"https://openalex.org/W1993382696","doi":"https://doi.org/10.1137/120902689","title":"A High-Order Numerical Method for the Helmholtz Equation with Nonstandard Boundary Conditions","display_name":"A High-Order Numerical Method for the Helmholtz Equation with Nonstandard Boundary Conditions","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1993382696","doi":"https://doi.org/10.1137/120902689","mag":"1993382696"},"language":"en","primary_location":{"id":"doi:10.1137/120902689","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120902689","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/A5004427841","display_name":"Darrell Steven Britt","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. S. Britt","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064610183","display_name":"Semyon Tsynkov","orcid":"https://orcid.org/0000-0003-1069-9612"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. V. Tsynkov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011112251","display_name":"Eli Turkel","orcid":"https://orcid.org/0000-0003-4273-0303"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. Turkel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6006,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.931659,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"35","issue":"5","first_page":"A2255","last_page":"A2292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":1.0,"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":1.0,"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":0.9990000128746033,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8123986124992371},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.7170457243919373},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.689419150352478},{"id":"https://openalex.org/keywords/robin-boundary-condition","display_name":"Robin boundary condition","score":0.5962040424346924},{"id":"https://openalex.org/keywords/poincar\u00e9\u2013steklov-operator","display_name":"Poincar\u00e9\u2013Steklov operator","score":0.5681696534156799},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5401759147644043},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5316171050071716},{"id":"https://openalex.org/keywords/compact-finite-difference","display_name":"Compact finite difference","score":0.5301281809806824},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.5281296372413635},{"id":"https://openalex.org/keywords/mixed-boundary-condition","display_name":"Mixed boundary condition","score":0.5146533250808716},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.49418023228645325},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4668249487876892},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.45998141169548035},{"id":"https://openalex.org/keywords/boundary-conditions-in-cfd","display_name":"Boundary conditions in CFD","score":0.4392624497413635},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4267757833003998}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8123986124992371},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.7170457243919373},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.689419150352478},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.5962040424346924},{"id":"https://openalex.org/C65826597","wikidata":"https://www.wikidata.org/wiki/Q17099589","display_name":"Poincar\u00e9\u2013Steklov operator","level":5,"score":0.5681696534156799},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5401759147644043},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5316171050071716},{"id":"https://openalex.org/C2780829570","wikidata":"https://www.wikidata.org/wiki/Q25113057","display_name":"Compact finite difference","level":3,"score":0.5301281809806824},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.5281296372413635},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.5146533250808716},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.49418023228645325},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4668249487876892},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.45998141169548035},{"id":"https://openalex.org/C79042034","wikidata":"https://www.wikidata.org/wiki/Q4949963","display_name":"Boundary conditions in CFD","level":5,"score":0.4392624497413635},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4267757833003998},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120902689","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120902689","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.4099999964237213,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W80404800","https://openalex.org/W1572071726","https://openalex.org/W1965847476","https://openalex.org/W1967227764","https://openalex.org/W1969041915","https://openalex.org/W1988884264","https://openalex.org/W1992124711","https://openalex.org/W2005316292","https://openalex.org/W2006902835","https://openalex.org/W2018317633","https://openalex.org/W2021615646","https://openalex.org/W2022385500","https://openalex.org/W2025124289","https://openalex.org/W2030729182","https://openalex.org/W2036156779","https://openalex.org/W2037512470","https://openalex.org/W2042033521","https://openalex.org/W2045962706","https://openalex.org/W2047463395","https://openalex.org/W2049451120","https://openalex.org/W2052033178","https://openalex.org/W2052801759","https://openalex.org/W2052871565","https://openalex.org/W2064842485","https://openalex.org/W2066283113","https://openalex.org/W2069595221","https://openalex.org/W2070875961","https://openalex.org/W2084131634","https://openalex.org/W2086409661","https://openalex.org/W2092567413","https://openalex.org/W2102694816","https://openalex.org/W2104955184","https://openalex.org/W2120660542","https://openalex.org/W2126950425","https://openalex.org/W2127499504","https://openalex.org/W2135990121","https://openalex.org/W2137551014","https://openalex.org/W2139279183","https://openalex.org/W2142094322","https://openalex.org/W2147347249","https://openalex.org/W2160910187","https://openalex.org/W2164639651","https://openalex.org/W4231203926"],"related_works":["https://openalex.org/W2378263446","https://openalex.org/W1514481392","https://openalex.org/W2393913967","https://openalex.org/W3136311820","https://openalex.org/W1586418441","https://openalex.org/W1548901099","https://openalex.org/W3104842942","https://openalex.org/W4322770021","https://openalex.org/W4246256881","https://openalex.org/W2100405323"],"abstract_inverted_index":{"We":[0,144,234],"describe":[1],"a":[2,48,88,111,152,188,192],"high-order":[3,31],"accurate":[4],"methodology":[5,207],"for":[6,91,159],"the":[7,15,34,53,59,107,122,139,146,160,201,211,220,223,228],"numerical":[8,148],"simulation":[9],"of":[10,36,52,55,61,67,81,95,101,135,141,154,215,222],"time-harmonic":[11],"waves":[12],"governed":[13],"by":[14,40,150],"Helmholtz":[16,161],"equation.":[17,162],"Our":[18],"approach":[19],"combines":[20],"compact":[21],"finite":[22],"difference":[23,37,68,142],"schemes":[24],"that":[25,105,237],"provide":[26],"an":[27,244],"inexpensive":[28],"venue":[29],"toward":[30],"accuracy":[32,82],"with":[33,78,166,177],"method":[35,54,66,103,140],"potentials":[38,69],"developed":[39],"Ryaben'kii.":[41],"The":[42,65],"latter":[43],"can":[44,70],"be":[45],"interpreted":[46],"as":[47,232],"generalized":[49],"discrete":[50],"version":[51],"Calderon's":[56],"operators":[57],"in":[58],"theory":[60],"partial":[62],"differential":[63],"equations.":[64],"accommodate":[71],"nonconforming":[72],"boundaries":[73],"on":[74],"regular":[75],"structured":[76],"grids":[77],"no":[79],"loss":[80],"due":[83],"to":[84,121],"staircasing.":[85],"It":[86],"introduces":[87],"universal":[89],"framework":[90],"treating":[92],"boundary":[93,108,136,156,170,180,194,240],"conditions":[94,137,171],"any":[96,118],"type.":[97],"A":[98],"significant":[99],"advantage":[100],"this":[102,129],"is":[104,125],"changing":[106],"condition":[109,241],"within":[110],"fairly":[112],"broad":[113],"variety":[114],"does":[115],"not":[116,226],"require":[117],"major":[119],"changes":[120],"algorithm":[123],"and":[124,175,191],"computationally":[126],"inexpensive.":[127],"In":[128,182],"paper,":[130],"we":[131,186],"address":[132],"various":[133],"types":[134],"using":[138],"potentials.":[143],"demonstrate":[145],"resulting":[147],"capabilities":[149],"solving":[151],"range":[153],"nonstandard":[155],"value":[157],"problems":[158,165,176],"These":[163],"include":[164],"variable":[167],"coefficient":[168],"Robin":[169],"(including":[172],"discontinuous":[173],"coefficients)":[174],"mixed":[178],"(Dirichlet/Neumann)":[179],"conditions.":[181],"all":[183],"our":[184,206],"simulations,":[185],"use":[187],"Cartesian":[189],"grid":[190,216],"circular":[193],"curve.":[195],"For":[196],"those":[197],"test":[198],"cases":[199],"where":[200],"overall":[202],"solution":[203,224],"was":[204,225],"smooth,":[205],"has":[208],"consistently":[209],"demonstrated":[210],"design":[212],"fourth-order":[213],"rate":[214],"convergence,":[217],"whereas":[218],"when":[219],"regularity":[221],"sufficient,":[227],"convergence":[229],"slowed":[230],"down,":[231],"expected.":[233],"also":[235],"show":[236],"every":[238],"additional":[239,246],"requires":[242],"only":[243],"incremental":[245],"expense.":[247]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}