{"id":"https://openalex.org/W2126059216","doi":"https://doi.org/10.1090/s0025-5718-96-00740-5","title":"The frequency decomposition multilevel method: A robust additive hierarchical basis preconditioner","display_name":"The frequency decomposition multilevel method: A robust additive hierarchical basis preconditioner","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2126059216","doi":"https://doi.org/10.1090/s0025-5718-96-00740-5","mag":"2126059216"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-96-00740-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00740-5","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00740-5/S0025-5718-96-00740-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00740-5/S0025-5718-96-00740-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035602683","display_name":"Rob Stevenson","orcid":"https://orcid.org/0000-0001-7623-3060"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Rob Stevenson","raw_affiliation_strings":["Department of Mathematics, Nijmegen University, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Nijmegen University, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035602683"],"corresponding_institution_ids":["https://openalex.org/I145872427"],"apc_list":null,"apc_paid":null,"fwci":2.2603,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.87798974,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"65","issue":"215","first_page":"983","last_page":"997"},"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":1.0,"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":1.0,"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":0.9997000098228455,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9995999932289124,"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/preconditioner","display_name":"Preconditioner","score":0.8653192520141602},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7345539331436157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7033113241195679},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5648330450057983},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.5412070751190186},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.5323282480239868},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5240181684494019},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5167826414108276},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.49461767077445984},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.47808289527893066},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4697577953338623},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.41202592849731445},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22222933173179626},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12751904129981995},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.08856678009033203},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.08469343185424805},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.08272361755371094},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07824194431304932}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8653192520141602},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7345539331436157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7033113241195679},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5648330450057983},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.5412070751190186},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.5323282480239868},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5240181684494019},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5167826414108276},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.49461767077445984},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.47808289527893066},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4697577953338623},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.41202592849731445},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22222933173179626},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12751904129981995},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.08856678009033203},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.08469343185424805},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.08272361755371094},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07824194431304932},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-96-00740-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00740-5","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00740-5/S0025-5718-96-00740-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:repository.ubn.ru.nl:2066/286956","is_oa":false,"landing_page_url":"https://repository.ubn.ru.nl/handle/2066/286956","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, 65, 215, pp. 983-997","raw_type":"Article / Letter to editor"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-96-00740-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00740-5","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00740-5/S0025-5718-96-00740-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2126059216.pdf","grobid_xml":"https://content.openalex.org/works/W2126059216.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1607829564","https://openalex.org/W2017085690","https://openalex.org/W2019457556","https://openalex.org/W2028357997","https://openalex.org/W2071850876","https://openalex.org/W2113187309","https://openalex.org/W2113553363","https://openalex.org/W2153127767","https://openalex.org/W2505424974","https://openalex.org/W2788971267","https://openalex.org/W4242248336","https://openalex.org/W4251739310","https://openalex.org/W6636327480"],"related_works":["https://openalex.org/W1492522302","https://openalex.org/W2096454229","https://openalex.org/W2042199958","https://openalex.org/W2103149966","https://openalex.org/W2177482563","https://openalex.org/W4229577910","https://openalex.org/W2773710110","https://openalex.org/W1554397852","https://openalex.org/W1877902382","https://openalex.org/W2161243591"],"abstract_inverted_index":{"Hackbusch\u2019s":[0],"frequency":[1,35],"decomposition":[2],"multilevel":[3],"method":[4,75],"is":[5],"characterized":[6],"by":[7],"the":[8,18,34,58,62,65],"application":[9],"of":[10,33,45,64,73],"three":[11],"additional":[12],"coarse-grid":[13,22],"corrections":[14],"in":[15],"parallel":[16],"to":[17,26,80],"standard":[19],"one.":[20],"Each":[21],"correction":[23],"was":[24],"designed":[25],"damp":[27],"errors":[28],"from":[29],"a":[30,42,77],"different":[31],"part":[32],"spectrum.":[36],"In":[37],"this":[38,46],"paper,":[39],"we":[40,69],"introduce":[41],"cheap":[43],"variant":[44],"method,":[47],"partly":[48],"based":[49],"on":[50],"semicoarsening,":[51],"which":[52],"demands":[53],"fewer":[54],"recursive":[55],"calls":[56],"than":[57],"original":[59],"version.":[60],"Using":[61],"theory":[63],"additive":[66],"Schwarz":[67],"methods,":[68],"will":[70],"prove":[71],"robustness":[72],"our":[74],"as":[76],"preconditioner":[78],"applied":[79],"anisotropic":[81],"equations.":[82]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
