{"id":"https://openalex.org/W1854729830","doi":"https://doi.org/10.1137/140975310","title":"Multiple Galerkin Adaptive Algebraic Multigrid Algorithm for the Helmholtz Equations","display_name":"Multiple Galerkin Adaptive Algebraic Multigrid Algorithm for the Helmholtz Equations","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1854729830","doi":"https://doi.org/10.1137/140975310","mag":"1854729830"},"language":"en","primary_location":{"id":"doi:10.1137/140975310","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140975310","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":true,"raw_author_name":"I. Livshits","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5091798887"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6464,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68226974,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"37","issue":"5","first_page":"S195","last_page":"S215"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9993000030517578,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/multigrid-method","display_name":"Multigrid method","score":0.9140734672546387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7261747717857361},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6804078221321106},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.6447163224220276},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6332836151123047},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6220982074737549},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.5442720651626587},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.531478226184845},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5092970132827759},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.5050049424171448},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4539191722869873},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.41185200214385986},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2446783483028412},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.23664388060569763},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2202916443347931},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.13599571585655212},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.08836725354194641}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.9140734672546387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7261747717857361},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6804078221321106},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.6447163224220276},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6332836151123047},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6220982074737549},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.5442720651626587},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.531478226184845},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5092970132827759},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5050049424171448},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4539191722869873},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.41185200214385986},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2446783483028412},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.23664388060569763},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2202916443347931},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.13599571585655212},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.08836725354194641},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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":1,"locations":[{"id":"doi:10.1137/140975310","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140975310","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W4509327","https://openalex.org/W175176216","https://openalex.org/W1967983557","https://openalex.org/W1968873140","https://openalex.org/W1969600280","https://openalex.org/W1972866386","https://openalex.org/W1992935956","https://openalex.org/W2001099567","https://openalex.org/W2014065899","https://openalex.org/W2016859361","https://openalex.org/W2030729182","https://openalex.org/W2032718616","https://openalex.org/W2042199958","https://openalex.org/W2069595221","https://openalex.org/W2089886276","https://openalex.org/W2113633232","https://openalex.org/W2118796777","https://openalex.org/W2142094322","https://openalex.org/W2151478420","https://openalex.org/W2174736763","https://openalex.org/W2912759508","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2358905935","https://openalex.org/W3046241855","https://openalex.org/W2139875628","https://openalex.org/W1995427418","https://openalex.org/W4365420316","https://openalex.org/W3193896743","https://openalex.org/W3126389985","https://openalex.org/W3176862315","https://openalex.org/W3120022531","https://openalex.org/W2047719014"],"abstract_inverted_index":{"Introduced":[0],"in":[1,131,154],"this":[2],"paper":[3],"is":[4,56,122],"a":[5,25,108],"multiple":[6,84,104],"Galerkin":[7,105],"adaptive":[8],"algebraic":[9],"multigrid":[10,31,110,117],"algorithm":[11,98,121],"for":[12,61,144],"solving":[13,35],"linear":[14],"discrete":[15],"equations":[16,37],"arising":[17],"from":[18],"discretization":[19],"of":[20,65,77,100,141,149],"partial":[21],"differential":[22],"operators":[23,60,86],"with":[24,34,103,146],"rich":[26],"and":[27,87,133,156],"diverse":[28],"near-kernel.":[29,96],"Standard":[30],"methods":[32],"struggle":[33],"such":[36],"due":[38],"to":[39,42,47,82,125],"their":[40],"inability":[41],"produce":[43],"accurate":[44],"coarse":[45,89],"correction":[46],"all":[48],"near-kernel":[49,66],"components.":[50],"The":[51,97,119],"motivating":[52],"model":[53],"problem":[54],"here":[55],"the":[57,63,74,94,127,139,142,158,162],"indefinite":[58],"Helmholtz":[59],"which":[62,91],"character":[64],"components":[67,79],"is,":[68],"at":[69],"least":[70],"approximately,":[71],"known.":[72],"In":[73],"algorithm,":[75],"some":[76],"these":[78],"are":[80,136],"used":[81,124],"create":[83],"prolongation":[85],"consecutive":[88],"descriptions":[90],"collectively":[92],"approximate":[93],"entire":[95],"consists":[99],"two":[101,134],"parts,":[102],"corrections":[106],"accelerating":[107],"standard":[109,116],"V-cycle.":[111],"Both":[112],"parts":[113],"largely":[114],"employ":[115],"techniques.":[118],"resulting":[120],"then":[123],"precondition":[126],"GMRES.":[128],"Numerical":[129],"experiments":[130],"one":[132],"dimensions":[135],"presented,":[137],"demonstrating":[138],"applicability":[140],"method":[143],"problems":[145],"different":[147],"types":[148],"wave":[150],"numbers.":[151],"Further":[152],"leads":[153],"improving":[155],"extending":[157],"proposed":[159],"approach":[160],"conclude":[161],"paper.":[163]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
