{"id":"https://openalex.org/W2035615628","doi":"https://doi.org/10.1137/s1064827502417039","title":"A Hierarchical 3-D Direct Helmholtz Solver by Domain Decomposition and Modified Fourier Method","display_name":"A Hierarchical 3-D Direct Helmholtz Solver by Domain Decomposition and Modified Fourier Method","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2035615628","doi":"https://doi.org/10.1137/s1064827502417039","mag":"2035615628"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827502417039","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502417039","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/A5030484468","display_name":"Elena Braverman","orcid":"https://orcid.org/0000-0002-6476-585X"},"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":"E. Braverman","raw_affiliation_strings":["University of Calgary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Calgary","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111602084","display_name":"M. Israeli","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Israeli","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080836593","display_name":"Amir Averbuch","orcid":"https://orcid.org/0000-0001-8177-235X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Averbuch","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.15815983,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"26","issue":"5","first_page":"1504","last_page":"1524"},"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/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":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.8255507349967957},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7109968662261963},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.7066370248794556},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6384357810020447},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5716484189033508},{"id":"https://openalex.org/keywords/parallelepiped","display_name":"Parallelepiped","score":0.5362982153892517},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.5167957544326782},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5070133209228516},{"id":"https://openalex.org/keywords/hexahedron","display_name":"Hexahedron","score":0.49707868695259094},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.48664602637290955},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.4741855561733246},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4708283245563507},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4413473308086395},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.4182165265083313},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41217589378356934},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38461846113204956},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3352741301059723},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24433904886245728},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.24086874723434448},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21502813696861267},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1383133828639984},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.07703626155853271}],"concepts":[{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.8255507349967957},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7109968662261963},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.7066370248794556},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6384357810020447},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5716484189033508},{"id":"https://openalex.org/C2779788511","wikidata":"https://www.wikidata.org/wiki/Q181658","display_name":"Parallelepiped","level":2,"score":0.5362982153892517},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5167957544326782},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5070133209228516},{"id":"https://openalex.org/C22411076","wikidata":"https://www.wikidata.org/wiki/Q668113","display_name":"Hexahedron","level":3,"score":0.49707868695259094},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.48664602637290955},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4741855561733246},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4708283245563507},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4413473308086395},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.4182165265083313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41217589378356934},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38461846113204956},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3352741301059723},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24433904886245728},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.24086874723434448},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21502813696861267},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1383133828639984},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.07703626155853271},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s1064827502417039","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502417039","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:10.1.1.409.2994","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.409.2994","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~amir1/PS/sisc041703_21.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.409.3942","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.409.3942","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~amir1/PS/Helmholtz-3D.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1549220217","https://openalex.org/W1621158592","https://openalex.org/W1912930600","https://openalex.org/W1965399207","https://openalex.org/W1993938602","https://openalex.org/W2003408966","https://openalex.org/W2005040144","https://openalex.org/W2014864771","https://openalex.org/W2015119048","https://openalex.org/W2028085547","https://openalex.org/W2039893955","https://openalex.org/W2045974403","https://openalex.org/W2051615510","https://openalex.org/W2051915213","https://openalex.org/W2062790549","https://openalex.org/W2066093260","https://openalex.org/W2083206954","https://openalex.org/W2477810599","https://openalex.org/W4256665807"],"related_works":["https://openalex.org/W4383816821","https://openalex.org/W4283382972","https://openalex.org/W4367557258","https://openalex.org/W2059014664","https://openalex.org/W118848820","https://openalex.org/W3148891486","https://openalex.org/W4282968753","https://openalex.org/W2065245699","https://openalex.org/W1541736886","https://openalex.org/W3216866263"],"abstract_inverted_index":{"The":[0,17,24,133,153,166],"paper":[1,134],"contains":[2],"a":[3,15,36,48,85,146],"noniterative":[4],"solver":[5,18],"for":[6,61,141,148,158],"the":[7,10,40,76,79,91,99,105,109,112,115,138,149,163,176],"Helmholtz":[8,12,42],"and":[9,160],"modified":[11],"equations":[13],"in":[14,56,136,181],"hexahedron.":[16],"is":[19,27,44,73,145,156,175],"based":[20,74],"on":[21,75],"domain":[22,26,150],"decomposition.":[23],"solution":[25,38],"divided":[28],"into":[29,130],"mostly":[30],"parallelepiped":[31],"subdomains.":[32],"In":[33,111],"each":[34,122,182],"subdomain":[35,92],"particular":[37],"of":[39,78,107,125,178],"nonhomogeneous":[41],"equation":[43],"first":[45],"computed":[46],"by":[47,84],"fast":[49],"spectral":[50],"3-D":[51],"method":[52,72],"which":[53,144],"was":[54],"developed":[55],"our":[57],"earlier":[58],"papers":[59],"(see,":[60],"example,":[62],"SIAM":[63],"J.":[64],"Sci.":[65],"Comput.,":[66],"20":[67],"(1999),":[68],"pp.":[69],"2237--2260).":[70],"This":[71],"application":[77],"discrete":[80],"Fourier":[81],"transform":[82],"accompanied":[83],"subtraction":[86],"technique.":[87],"For":[88],"high":[89],"accuracy":[90],"boundary":[93],"conditions":[94],"must":[95],"be":[96],"compatible":[97],"with":[98],"specified":[100],"inhomogeneous":[101],"right-hand":[102],"side":[103],"at":[104],"edges":[106],"all":[108],"interfaces.":[110],"following":[113],"steps":[114],"partial":[116],"solutions":[117],"are":[118,128],"hierarchically":[119],"matched.":[120],"At":[121],"step":[123],"pairs":[124],"adjacent":[126],"subdomains":[127],"merged":[129],"larger":[131],"units.":[132],"describes":[135],"detail":[137],"matching":[139],"algorithm":[140,167],"two":[142],"boxes":[143],"basis":[147],"decomposition":[151],"scheme.":[152],"hierarchical":[154],"approach":[155],"convenient":[157],"parallelization":[159],"can":[161],"minimize":[162],"global":[164],"communication.":[165],"requires":[168],"O(N3":[169],",":[170],"log,N)":[171],"operations,":[172],"where":[173],"N":[174],"number":[177],"grid":[179],"points":[180],"direction.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-11T18:08:03.149640","created_date":"2025-10-10T00:00:00"}
