{"id":"https://openalex.org/W2033113310","doi":"https://doi.org/10.1016/s0167-8191(96)00089-0","title":"Parallel implementation of the Kronecker product technique for numerical solution of parabolic partial differential equations","display_name":"Parallel implementation of the Kronecker product technique for numerical solution of parabolic partial differential equations","publication_year":1997,"publication_date":"1997-03-01","ids":{"openalex":"https://openalex.org/W2033113310","doi":"https://doi.org/10.1016/s0167-8191(96)00089-0","mag":"2033113310"},"language":"en","primary_location":{"id":"doi:10.1016/s0167-8191(96)00089-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0167-8191(96)00089-0","pdf_url":null,"source":{"id":"https://openalex.org/S112708030","display_name":"Parallel Computing","issn_l":"0167-8191","issn":["0167-8191","1872-7336"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel 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/A5103516438","display_name":"Muhammad Amer","orcid":null},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"M.A. Amer","raw_affiliation_strings":["Mathematics and Computer Science Department, Faculty of Science, United Arab Emirates University, Al-Ain, United Arab Emirates"],"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science Department, Faculty of Science, United Arab Emirates University, Al-Ain, United Arab Emirates","institution_ids":["https://openalex.org/I201726411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085199538","display_name":"B.A. Abdel-Hamida","orcid":null},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":true,"raw_author_name":"B.A. Abdel-Hamida","raw_affiliation_strings":["Mathematics and Computer Science Department, Faculty of Science, United Arab Emirates University, Al-Ain, United Arab Emirates"],"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science Department, Faculty of Science, United Arab Emirates University, Al-Ain, United Arab Emirates","institution_ids":["https://openalex.org/I201726411"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035788057","display_name":"Donald W. Fausett","orcid":null},"institutions":[{"id":"https://openalex.org/I106959904","display_name":"Florida Institute of Technology","ror":"https://ror.org/04atsbb87","country_code":"US","type":"education","lineage":["https://openalex.org/I106959904"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Fausett","raw_affiliation_strings":["Applied Mathematics Department, Florida Institute of Technology, USA","Applied Mathematics Department, Florida Institute of Technology, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics Department, Florida Institute of Technology, USA","institution_ids":["https://openalex.org/I106959904"]},{"raw_affiliation_string":"Applied Mathematics Department, Florida Institute of Technology, USA#TAB#","institution_ids":["https://openalex.org/I106959904"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085199538"],"corresponding_institution_ids":["https://openalex.org/I201726411"],"apc_list":{"value":2680,"currency":"USD","value_usd":2680},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16571848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"14","first_page":"1997","last_page":"2005"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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":0.9993000030517578,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9907000064849854,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9855999946594238,"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/kronecker-product","display_name":"Kronecker product","score":0.7709442377090454},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7189072370529175},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6600964069366455},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.6317893266677856},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5540798306465149},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5362166166305542},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.522832453250885},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48736387491226196},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4865333139896393},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.43027523159980774},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31925153732299805},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22205564379692078},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2110656499862671},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1307685375213623},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07330211997032166}],"concepts":[{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.7709442377090454},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7189072370529175},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6600964069366455},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.6317893266677856},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5540798306465149},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5362166166305542},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.522832453250885},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48736387491226196},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4865333139896393},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.43027523159980774},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31925153732299805},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22205564379692078},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2110656499862671},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1307685375213623},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07330211997032166},{"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/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":1,"locations":[{"id":"doi:10.1016/s0167-8191(96)00089-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0167-8191(96)00089-0","pdf_url":null,"source":{"id":"https://openalex.org/S112708030","display_name":"Parallel Computing","issn_l":"0167-8191","issn":["0167-8191","1872-7336"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel 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":15,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1489661330","https://openalex.org/W1493749856","https://openalex.org/W1968352158","https://openalex.org/W2009193081","https://openalex.org/W2032861796","https://openalex.org/W2035885121","https://openalex.org/W2052903802","https://openalex.org/W2053440286","https://openalex.org/W2072422032","https://openalex.org/W2072572259","https://openalex.org/W2089588109","https://openalex.org/W2090398100","https://openalex.org/W2119233169","https://openalex.org/W3046452920"],"related_works":["https://openalex.org/W123417539","https://openalex.org/W2079407403","https://openalex.org/W2060299328","https://openalex.org/W2117336295","https://openalex.org/W4375957393","https://openalex.org/W4233239985","https://openalex.org/W3102722572","https://openalex.org/W2090103374","https://openalex.org/W577870507","https://openalex.org/W2073634779"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}