{"id":"https://openalex.org/W2152146081","doi":"https://doi.org/10.1109/tcad.1985.1270141","title":"A Multilevel Solver for Boundary Value Problems","display_name":"A Multilevel Solver for Boundary Value Problems","publication_year":1985,"publication_date":"1985-10-01","ids":{"openalex":"https://openalex.org/W2152146081","doi":"https://doi.org/10.1109/tcad.1985.1270141","mag":"2152146081"},"language":"en","primary_location":{"id":"doi:10.1109/tcad.1985.1270141","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.1985.1270141","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","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/A5110454875","display_name":"Craig C. Douglas","orcid":null},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C.C. Douglas","raw_affiliation_strings":["Department of Computer Science, Duke University, Durham, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110454875"],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2108978,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":"4","first_page":"431","last_page":"435"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9990000128746033,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.7137271165847778},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6850951910018921},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5764749050140381},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5418975353240967},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4782537519931793},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4542671740055084},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.4356520175933838},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4050646424293518},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3599002957344055},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18076780438423157}],"concepts":[{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.7137271165847778},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6850951910018921},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5764749050140381},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5418975353240967},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4782537519931793},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4542671740055084},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.4356520175933838},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4050646424293518},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3599002957344055},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18076780438423157}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcad.1985.1270141","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.1985.1270141","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W137867401","https://openalex.org/W1975664127","https://openalex.org/W1993629555","https://openalex.org/W1998461805","https://openalex.org/W2021453599","https://openalex.org/W2026541804","https://openalex.org/W2064625750","https://openalex.org/W2072598943","https://openalex.org/W2165630134"],"related_works":["https://openalex.org/W2077078424","https://openalex.org/W2573021234","https://openalex.org/W2106610492","https://openalex.org/W2383355899","https://openalex.org/W1524119935","https://openalex.org/W3011358647","https://openalex.org/W2155760131","https://openalex.org/W2161759000","https://openalex.org/W2196719869","https://openalex.org/W2029287765"],"abstract_inverted_index":{"Multilevel":[0],"methods":[1,77],"have":[2,16],"been":[3,17],"studied":[4],"extensively":[5],"for":[6,36],"solving":[7,37],"certain":[8],"partial":[9,57],"differential":[10,58],"equations,":[11],"and":[12,27,51,69,78],"such":[13],"equation":[14],"solvers":[15],"successfully":[18],"applied":[19],"to":[20],"major":[21],"computational":[22],"problems":[23],"of":[24,34,43,55,75,81],"physical":[25],"interest":[26],"technological":[28],"importance.":[29],"KLEV":[30],"is":[31],"a":[32,64],"collection":[33],"routines":[35],"the":[38,82],"N":[39,41],"X":[40],"system":[42],"linear":[44],"equations":[45],"Az":[46],"=":[47],"g":[48,52],"when":[49],"A":[50,72],"are":[53,84],"discretizations":[54],"some":[56],"equation.":[59],"The":[60],"current":[61],"release":[62],"includes":[63],"direct":[65],"method,":[66],"iterative":[67],"methods,":[68],"multilevel":[70,76],"methods.":[71],"brief":[73],"review":[74],"an":[79],"overview":[80],"implementation":[83],"presented.":[85]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}