{"id":"https://openalex.org/W4256758023","doi":"https://doi.org/10.1155/2000/98424","title":"Discretization of Anisotropic Convection\u2010diffusionEquations, Convective M\u2010matrices and their IterativeSolution","display_name":"Discretization of Anisotropic Convection\u2010diffusionEquations, Convective M\u2010matrices and their IterativeSolution","publication_year":1999,"publication_date":"1999-12-14","ids":{"openalex":"https://openalex.org/W4256758023","doi":"https://doi.org/10.1155/2000/98424"},"language":"en","primary_location":{"id":"doi:10.1155/2000/98424","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2000/98424","pdf_url":"https://downloads.hindawi.com/archive/2000/098424.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/archive/2000/098424.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034711182","display_name":"Donald J. Rose","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":"Donald J. Rose","raw_affiliation_strings":["aDepartment of Computer Science,\" bDepartment of Biomedical Engineering, Duke University, Durham, NC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"aDepartment of Computer Science,\" bDepartment of Biomedical Engineering, Duke University, Durham, NC","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020925523","display_name":"Hai Shao","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":false,"raw_author_name":"Hai Shao","raw_affiliation_strings":["aDepartment of Computer Science,\" bDepartment of Biomedical Engineering, Duke University, Durham, NC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"aDepartment of Computer Science,\" bDepartment of Biomedical Engineering, Duke University, Durham, NC","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016723450","display_name":"Craig S. Henriquez","orcid":"https://orcid.org/0000-0002-5395-3767"},"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":false,"raw_author_name":"Craig S. Henriquez","raw_affiliation_strings":["aDepartment of Computer Science,\" bDepartment of Biomedical Engineering, Duke University, Durham, NC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"aDepartment of Computer Science,\" bDepartment of Biomedical Engineering, Duke University, Durham, NC","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034711182"],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":0.5054,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.71468035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"10","issue":"4","first_page":"485","last_page":"529"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991000294685364,"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":0.9987999796867371,"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":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6124380230903625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30929890275001526}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6124380230903625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30929890275001526}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2000/98424","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2000/98424","pdf_url":"https://downloads.hindawi.com/archive/2000/098424.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.39.9440","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.9440","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.duke.edu/~djr/p2.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1155/2000/98424","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2000/98424","pdf_url":"https://downloads.hindawi.com/archive/2000/098424.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VLSI Design","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309151","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34"},{"id":"https://openalex.org/F4320324852","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4256758023.pdf","grobid_xml":"https://content.openalex.org/works/W4256758023.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W2334249","https://openalex.org/W609598071","https://openalex.org/W1505377314","https://openalex.org/W1966532952","https://openalex.org/W1981885118","https://openalex.org/W1999585202","https://openalex.org/W2003116365","https://openalex.org/W2005882095","https://openalex.org/W2016121728","https://openalex.org/W2025221203","https://openalex.org/W2046877751","https://openalex.org/W2057041064","https://openalex.org/W2057084070","https://openalex.org/W2064114324","https://openalex.org/W2065725998","https://openalex.org/W2136969662","https://openalex.org/W2146266947","https://openalex.org/W2569133694","https://openalex.org/W2609880033","https://openalex.org/W2785458696","https://openalex.org/W2963516047","https://openalex.org/W4210300254","https://openalex.org/W4212951453","https://openalex.org/W4231075076","https://openalex.org/W4295016751","https://openalex.org/W4298132033","https://openalex.org/W6630227369","https://openalex.org/W6631554681","https://openalex.org/W6642624371","https://openalex.org/W6656608983","https://openalex.org/W6666489797","https://openalex.org/W6766054330","https://openalex.org/W7058433988"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W303980170","https://openalex.org/W2351491280","https://openalex.org/W2386767533","https://openalex.org/W2371447506","https://openalex.org/W3141679561"],"abstract_inverted_index":{"We":[0,64,97],"derive":[1],"the":[2,9,52,57,66,84,90,115,124],"constant\u2010":[3],"j":[4,13,18],"box":[5],"method":[6],"discretization":[7,55,91],"for":[8],"convection\u2010diffusion":[10],"equation,":[11],"\u2207":[12,22],"=":[14,19],"f":[15],",":[16,83,88],"with":[17],"\u2212":[20],"\u03b1":[21,31,80],"u":[23,26],"+":[24],"\u03b2":[25,43,82,128],".":[27],"In":[28],"two":[29],"dimensions,":[30],"is":[32,44,92],"a":[33,45,93],"2":[34,36],"\u00d7":[35],"symmetric,":[37],"positive":[38],"definite":[39],"tensor":[40],"field":[41],"and":[42,70,76,81,105],"two\u2010dimensional":[46],"vector":[47],"field.":[48],"This":[49],"derivation":[50],"generalizes":[51],"well\u2010known":[53],"Scharfetter\u2010Gummel":[54],"of":[56,79,89,103,117,119],"continuity":[58],"equations":[59],"in":[60],"semiconductor":[61],"device":[62],"simulation.":[63],"define":[65],"anisotropic":[67],"Delaunay":[68],"condition":[69,75],"show":[71,106],"that":[72,107],"under":[73,131],"this":[74],"appropriate":[77],"evaluations":[78],"stiffness":[85],"matrix,":[86],"M":[87,95,104],"convective":[94],"\u2010matrix.":[96],"then":[98],"examine":[99],"classical":[100],"iterative":[101],"splittings":[102],"convection":[108,110],"(even":[109],"dominance)":[111],"does":[112],"not":[113],"degrade":[114],"rate":[116],"convergence":[118],"such":[120],"iterations":[121],"relative":[122],"to":[123],"purely":[125],"diffusive":[126],"(":[127],"=0)":[129],"problem":[130],"certain":[132],"conditions.":[133]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
