{"id":"https://openalex.org/W1972866386","doi":"https://doi.org/10.1137/040620461","title":"Accuracy Properties of the Wave\u2010Ray Multigrid Algorithm for Helmholtz Equations","display_name":"Accuracy Properties of the Wave\u2010Ray Multigrid Algorithm for Helmholtz Equations","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1972866386","doi":"https://doi.org/10.1137/040620461","mag":"1972866386"},"language":"en","primary_location":{"id":"doi:10.1137/040620461","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040620461","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/A5091798887","display_name":"I. M. Livshits","orcid":"https://orcid.org/0000-0002-8390-013X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Irene Livshits","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002716963","display_name":"Achi Brandt","orcid":"https://orcid.org/0000-0001-5957-8550"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Achi Brandt","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":1.1372,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.77986171,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"28","issue":"4","first_page":"1228","last_page":"1251"},"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":0.9994000196456909,"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/T10787","display_name":"Lightning and Electromagnetic Phenomena","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/multigrid-method","display_name":"Multigrid method","score":0.8927827477455139},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.849002480506897},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6543340682983398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6356282830238342},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.5896381139755249},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5584539771080017},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.556348979473114},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.502709150314331},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.49451252818107605},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45964694023132324},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.43547549843788147},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4085090160369873},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4067089557647705},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2803342342376709},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19465109705924988},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11007684469223022}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8927827477455139},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.849002480506897},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6543340682983398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6356282830238342},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5896381139755249},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5584539771080017},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.556348979473114},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.502709150314331},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.49451252818107605},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45964694023132324},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.43547549843788147},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4085090160369873},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4067089557647705},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2803342342376709},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19465109705924988},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11007684469223022},{"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:10.1137/040620461","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040620461","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1965605578","https://openalex.org/W1968873140","https://openalex.org/W1969600280","https://openalex.org/W1976538983","https://openalex.org/W2003017040","https://openalex.org/W2005733061","https://openalex.org/W2008720207","https://openalex.org/W2021615646","https://openalex.org/W2025124289","https://openalex.org/W2034374312","https://openalex.org/W2075241282","https://openalex.org/W2151478420","https://openalex.org/W4233575842"],"related_works":["https://openalex.org/W2573021234","https://openalex.org/W2106610492","https://openalex.org/W4365420316","https://openalex.org/W3193896743","https://openalex.org/W1758121264","https://openalex.org/W2383355899","https://openalex.org/W1501940787","https://openalex.org/W3176862315","https://openalex.org/W1524119935","https://openalex.org/W3120022531"],"abstract_inverted_index":{"Helmholtz":[0,62],"equations":[1,16,63],"with":[2,90,106,124],"their":[3],"highly":[4],"oscillatory":[5],"solutions":[6],"play":[7],"an":[8,100],"important":[9],"role":[10],"in":[11,80],"physics":[12],"and":[13,26,38,64],"engineering.":[14],"These":[15],"present":[17],"the":[18,61,67,75,91,103,110,113,118],"main":[19],"computational":[20],"difficulties":[21],"typical":[22],"to":[23,102],"acoustic,":[24],"electromagnetic,":[25],"other":[27],"wave":[28],"problems.":[29],"They":[30],"are":[31,39,78,131],"often":[32],"accompanied":[33],"by":[34,133],"radiation":[35,68],"boundary":[36,69,119],"conditions":[37,120],"considered":[40],"on":[41],"infinite":[42],"domains.":[43],"Solving":[44],"them":[45],"numerically":[46],"using":[47],"standard":[48],"procedures,":[49],"including":[50],"multigrid,":[51],"is":[52],"too":[53],"expensive.":[54],"The":[55],"wave\u2010ray":[56,76],"multigrid":[57],"algorithm":[58,97],"efficiently":[59],"solves":[60],"naturally":[65],"incorporates":[66],"conditions.":[70],"Important":[71],"accuracy":[72,107,111],"properties":[73],"of":[74,94,112],"solver":[77],"discussed":[79],"this":[81,96],"paper.":[82],"Using":[83],"various":[84],"mode":[85],"analyses,":[86],"we":[87],"show":[88],"that,":[89],"right":[92],"choice":[93],"parameters,":[95],"can":[98,121],"obtain":[99],"approximation":[101],"differential":[104],"solution":[105],"that":[108],"equals":[109],"target":[114],"grid":[115],"discretization.":[116],"Moreover,":[117],"be":[122],"introduced":[123],"any":[125],"desired":[126],"accuracy.":[127],"Our":[128],"theoretical":[129],"conclusions":[130],"confirmed":[132],"numerical":[134],"experiments.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}