{"id":"https://openalex.org/W2169235784","doi":"https://doi.org/10.1145/1629911.1630010","title":"A robust and efficient harmonic balance (HB) using direct solution of HB Jacobian","display_name":"A robust and efficient harmonic balance (HB) using direct solution of HB Jacobian","publication_year":2009,"publication_date":"2009-07-26","ids":{"openalex":"https://openalex.org/W2169235784","doi":"https://doi.org/10.1145/1629911.1630010","mag":"2169235784"},"language":"en","primary_location":{"id":"doi:10.1145/1629911.1630010","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1629911.1630010","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 46th Annual Design Automation Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04492655","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110736159","display_name":"Amit Mehrotra","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Amit Mehrotra","raw_affiliation_strings":["Berkeley Design Automation"],"affiliations":[{"raw_affiliation_string":"Berkeley Design Automation","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089431228","display_name":"Abhishek Somani","orcid":"https://orcid.org/0000-0002-3785-7660"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abhishek Somani","raw_affiliation_strings":["Berkeley Design Automation"],"affiliations":[{"raw_affiliation_string":"Berkeley Design Automation","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110736159"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4095,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.82665081,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"370","last_page":"375"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9976000189781189,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.9189995527267456},{"id":"https://openalex.org/keywords/harmonics","display_name":"Harmonics","score":0.8150923848152161},{"id":"https://openalex.org/keywords/harmonic-balance","display_name":"Harmonic balance","score":0.7922505736351013},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7383423447608948},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5612760782241821},{"id":"https://openalex.org/keywords/harmonic-analysis","display_name":"Harmonic analysis","score":0.5254805684089661},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.493224561214447},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.474151074886322},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4613727331161499},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.43373459577560425},{"id":"https://openalex.org/keywords/envelope","display_name":"Envelope (radar)","score":0.412424772977829},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40126684308052063},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3545103371143341},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34838226437568665},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17691823840141296},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09298884868621826},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09133362770080566},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.08855921030044556},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.0866636335849762},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.07565587759017944},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.053267329931259155}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.9189995527267456},{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.8150923848152161},{"id":"https://openalex.org/C121758426","wikidata":"https://www.wikidata.org/wiki/Q5659248","display_name":"Harmonic balance","level":3,"score":0.7922505736351013},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7383423447608948},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5612760782241821},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.5254805684089661},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.493224561214447},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.474151074886322},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4613727331161499},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.43373459577560425},{"id":"https://openalex.org/C65155139","wikidata":"https://www.wikidata.org/wiki/Q5380912","display_name":"Envelope (radar)","level":3,"score":0.412424772977829},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40126684308052063},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3545103371143341},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34838226437568665},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17691823840141296},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09298884868621826},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09133362770080566},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.08855921030044556},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0866636335849762},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.07565587759017944},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.053267329931259155},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1629911.1630010","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1629911.1630010","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 46th Annual Design Automation Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.164.6949","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.164.6949","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dac.com/46th/PDFs/2009_Best_Paper_23.2.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-04492655v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04492655","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DAC '09: The 46th Annual Design Automation Conference 2009, Jul 2009, San Francisco, United States. pp.370-375, &#x27E8;10.1145/1629911.1630010&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04492655v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04492655","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DAC '09: The 46th Annual Design Automation Conference 2009, Jul 2009, San Francisco, United States. pp.370-375, &#x27E8;10.1145/1629911.1630010&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1480928214","https://openalex.org/W1495851026","https://openalex.org/W1506342804","https://openalex.org/W1532360728","https://openalex.org/W1983077080","https://openalex.org/W1985106294","https://openalex.org/W1992143597","https://openalex.org/W2100384730","https://openalex.org/W2120101160","https://openalex.org/W2133029208","https://openalex.org/W2143797322","https://openalex.org/W2145320787","https://openalex.org/W2149381887","https://openalex.org/W2161235036","https://openalex.org/W2162810287","https://openalex.org/W2172185550","https://openalex.org/W4239881334"],"related_works":["https://openalex.org/W2158091184","https://openalex.org/W2382140662","https://openalex.org/W2063574925","https://openalex.org/W3179723297","https://openalex.org/W197510432","https://openalex.org/W3021098778","https://openalex.org/W4310236371","https://openalex.org/W3148401657","https://openalex.org/W2103328473","https://openalex.org/W2735732156"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,29],"introduce":[4],"a":[5,40,119],"new":[6],"method":[7],"of":[8,12,22,64,85,110],"performing":[9],"direct":[10,33,108],"solution":[11,109],"the":[13,32,47,62,92,98,116],"harmonic":[14,111],"balance":[15,112],"Jacobian.":[16],"For":[17,80],"examples":[18,81],"with":[19,39,82,118],"moderate":[20,25,41,88],"number":[21,63,84],"harmonics":[23,65,86],"and":[24,71,87],"to":[26,46,89],"strong":[27,90],"nonlinearities,":[28,91],"demonstrate":[30],"that":[31],"solver":[34,53],"has":[35],"far":[36],"superior":[37],"performance":[38,93],"increase":[42],"in":[43],"memory":[44,99],"compared":[45],"best":[48],"preconditioned":[49],"iterative":[50],"solvers.":[51],"This":[52],"is":[54,66,95],"especially":[55],"suited":[56],"for":[57,77],"Fourier":[58],"envelope":[59],"analysis":[60],"where":[61],"small,":[67],"circuits":[68],"are":[69],"nonlinear":[70],"Jacobian":[72],"bypass":[73],"can":[74],"be":[75],"used":[76],"additional":[78],"speed.":[79],"large":[83],"advantage":[94],"maintained":[96],"but":[97],"requirements":[100],"increase.":[101],"We":[102],"propose":[103],"efficient":[104],"preconditioners":[105],"based":[106],"on":[107],"matrices":[113],"which":[114],"provide":[115],"user":[117],"memory-speed":[120],"trade-off.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
