{"id":"https://openalex.org/W4360611653","doi":"https://doi.org/10.1007/s11227-023-05189-0","title":"Efficient GPU implementation of a Boltzmann-Schr\u00f6dinger-Poisson solver for the simulation of nanoscale DG MOSFETs","display_name":"Efficient GPU implementation of a Boltzmann-Schr\u00f6dinger-Poisson solver for the simulation of nanoscale DG MOSFETs","publication_year":2023,"publication_date":"2023-03-23","ids":{"openalex":"https://openalex.org/W4360611653","doi":"https://doi.org/10.1007/s11227-023-05189-0"},"language":"en","primary_location":{"id":"doi:10.1007/s11227-023-05189-0","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11227-023-05189-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11227-023-05189-0.pdf","source":{"id":"https://openalex.org/S32326811","display_name":"The Journal of Supercomputing","issn_l":"0920-8542","issn":["0920-8542","1573-0484"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Supercomputing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11227-023-05189-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001623766","display_name":"Francesco Vecil","orcid":null},"institutions":[{"id":"https://openalex.org/I198244214","display_name":"Universit\u00e9 Clermont Auvergne","ror":"https://ror.org/01a8ajp46","country_code":"FR","type":"education","lineage":["https://openalex.org/I198244214"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Francesco Vecil","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Blaise Pascal, Universit\u00e9 Clermont Auvergne, Clermont-Ferrand, France","LMBP - Laboratoire de Math\u00e9matiques Blaise Pascal (Campus universitaire des C\u00e9zeaux, 3 place Vasarely, TSA 60026 / CS 60026, 63178 Aubi\u00e8re Cedex - France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Blaise Pascal, Universit\u00e9 Clermont Auvergne, Clermont-Ferrand, France","institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I198244214"]},{"raw_affiliation_string":"LMBP - Laboratoire de Math\u00e9matiques Blaise Pascal (Campus universitaire des C\u00e9zeaux, 3 place Vasarely, TSA 60026 / CS 60026, 63178 Aubi\u00e8re Cedex - France)","institution_ids":["https://openalex.org/I4210155549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009583807","display_name":"Jos\u00e9 M. Mantas","orcid":"https://orcid.org/0000-0002-4465-938X"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Miguel Mantas","raw_affiliation_strings":["Departamento de Lenguajes y Sistemas Inform\u00e1ticos, Universidad de Granada, Granada, Spain","UGR - Universidad de Granada = University of Granada (Avda. del Hospicio, s/n C.P. 18010 Granada - Spain)"],"affiliations":[{"raw_affiliation_string":"Departamento de Lenguajes y Sistemas Inform\u00e1ticos, Universidad de Granada, Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"UGR - Universidad de Granada = University of Granada (Avda. del Hospicio, s/n C.P. 18010 Granada - Spain)","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040153798","display_name":"Pedro Alonso","orcid":"https://orcid.org/0000-0002-6882-6592"},"institutions":[{"id":"https://openalex.org/I60053951","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859","country_code":"ES","type":"education","lineage":["https://openalex.org/I60053951"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Pedro Alonso-Jord\u00e1","raw_affiliation_strings":["Departamento de Sistemas Inform\u00e1ticos y Computaci\u00f3n, Universitat Polit\u00e8cnica de Val\u00e8ncia, Valencia, Spain","UPV - Universitat Polit\u00e8cnica de Val\u00e8ncia = Universitad Politecnica de Valencia = Polytechnic University of Valencia (Camino de Vera, s/n 46022 Valencia - Spain)"],"affiliations":[{"raw_affiliation_string":"Departamento de Sistemas Inform\u00e1ticos y Computaci\u00f3n, Universitat Polit\u00e8cnica de Val\u00e8ncia, Valencia, Spain","institution_ids":["https://openalex.org/I60053951"]},{"raw_affiliation_string":"UPV - Universitat Polit\u00e8cnica de Val\u00e8ncia = Universitad Politecnica de Valencia = Polytechnic University of Valencia (Camino de Vera, s/n 46022 Valencia - Spain)","institution_ids":["https://openalex.org/I60053951"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001623766"],"corresponding_institution_ids":["https://openalex.org/I198244214","https://openalex.org/I4210155549"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.131,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.39945263,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"79","issue":"12","first_page":"13370","last_page":"13401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10558","display_name":"Advancements in Semiconductor Devices and Circuit Design","score":0.9988999962806702,"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/T10558","display_name":"Advancements in Semiconductor Devices and Circuit Design","score":0.9988999962806702,"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9968000054359436,"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/solver","display_name":"Solver","score":0.7182494401931763},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6729272603988647},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6251967549324036},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.5914188623428345},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.47906455397605896},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.4680950939655304},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4524279534816742},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.42308276891708374},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.237106055021286},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19883206486701965},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13793328404426575},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09658968448638916}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7182494401931763},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6729272603988647},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6251967549324036},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.5914188623428345},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.47906455397605896},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.4680950939655304},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4524279534816742},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.42308276891708374},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.237106055021286},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19883206486701965},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13793328404426575},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09658968448638916},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11227-023-05189-0","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11227-023-05189-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11227-023-05189-0.pdf","source":{"id":"https://openalex.org/S32326811","display_name":"The Journal of Supercomputing","issn_l":"0920-8542","issn":["0920-8542","1573-0484"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Supercomputing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04907803v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04907803","pdf_url":"https://hal.science/hal-04907803v1/document","source":{"id":"https://openalex.org/S4406922466","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":"Journal of Supercomputing, 2023, 79, pp.13370 - 13401. ⟨10.1007/s11227-023-05189-0⟩","raw_type":"Journal articles"},{"id":"pmh:oai:digibug.ugr.es:10481/81597","is_oa":true,"landing_page_url":"https://hdl.handle.net/10481/81597","pdf_url":"https://digibug.ugr.es/bitstream/10481/81597/1/s11227-023-05189-0.pdf","source":{"id":"https://openalex.org/S4306400567","display_name":"Institutional Repository of the University of Granada (University of Granada)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I173304897","host_organization_name":"Universidad de Granada","host_organization_lineage":["https://openalex.org/I173304897"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"VoR"}],"best_oa_location":{"id":"doi:10.1007/s11227-023-05189-0","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11227-023-05189-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11227-023-05189-0.pdf","source":{"id":"https://openalex.org/S32326811","display_name":"The Journal of Supercomputing","issn_l":"0920-8542","issn":["0920-8542","1573-0484"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Supercomputing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.7400000095367432,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1224945033","display_name":null,"funder_award_id":"FEDER","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G1258440726","display_name":null,"funder_award_id":"(MINECO","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G1419670400","display_name":null,"funder_award_id":"GB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G1428725115","display_name":null,"funder_award_id":"UGR20","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G1650125035","display_name":null,"funder_award_id":"B-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2016851323","display_name":null,"funder_award_id":"MINECO","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2387244833","display_name":null,"funder_award_id":"A-TIC-344-UGR20","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G2894098041","display_name":null,"funder_award_id":"PID2020-117846GB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G3145880764","display_name":null,"funder_award_id":"MTM2017","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G3991634671","display_name":null,"funder_award_id":"PID2020-117846GB-I00","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G4996922997","display_name":null,"funder_award_id":"MTM2017-85067-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G5805502524","display_name":null,"funder_award_id":"PID2020","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G6290219456","display_name":null,"funder_award_id":"ERDF/FEDER","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G6359393262","display_name":null,"funder_award_id":"MTM2017-85067-P","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G6589649124","display_name":null,"funder_award_id":"PID2020-","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G7420919289","display_name":null,"funder_award_id":"FEDER","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320323834","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449"},{"id":"https://openalex.org/F4320334905","display_name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","ror":"https://ror.org/01460j859"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4360611653.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W97921269","https://openalex.org/W1506342804","https://openalex.org/W1569090332","https://openalex.org/W1600301286","https://openalex.org/W1661842744","https://openalex.org/W1973375717","https://openalex.org/W1973728196","https://openalex.org/W1984626487","https://openalex.org/W2019733925","https://openalex.org/W2024446391","https://openalex.org/W2041670333","https://openalex.org/W2053062872","https://openalex.org/W2058041602","https://openalex.org/W2061793071","https://openalex.org/W2068434228","https://openalex.org/W2073605792","https://openalex.org/W2114011216","https://openalex.org/W2134262723","https://openalex.org/W2179329940","https://openalex.org/W2302931088","https://openalex.org/W2306356212","https://openalex.org/W2364308289","https://openalex.org/W2466537650","https://openalex.org/W2755651354","https://openalex.org/W2790573218","https://openalex.org/W2886485459","https://openalex.org/W2966012355","https://openalex.org/W2981692901","https://openalex.org/W3194347788","https://openalex.org/W4210415421","https://openalex.org/W4229666556","https://openalex.org/W4254591541","https://openalex.org/W4301491118"],"related_works":["https://openalex.org/W1604758548","https://openalex.org/W2804126825","https://openalex.org/W1549048322","https://openalex.org/W4367553810","https://openalex.org/W2104142636","https://openalex.org/W2731831065","https://openalex.org/W4283162424","https://openalex.org/W2271439649","https://openalex.org/W2011940952","https://openalex.org/W2144429051"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"previous":[2],"study":[3],"by":[4,91,136],"Mantas":[5],"and":[6,20,141,150,186],"Vecil":[7],"(Int":[8],"J":[9],"High":[10],"Perform":[11],"Comput":[12],"Appl":[13],"34(1):":[14],"81\u2013102,":[15],"2019)":[16],"describes":[17],"an":[18],"efficient":[19],"accurate":[21],"solver":[22,99,169],"for":[23,97,170,190,197,217],"nanoscale":[24],"DG":[25],"MOSFETs":[26],"through":[27],"a":[28,38,93,110,138,178],"deterministic":[29],"Boltzmann-Schr\u00f6dinger-Poisson":[30],"model":[31],"with":[32],"seven":[33],"electron\u2013phonon":[34],"scattering":[35],"mechanisms":[36],"on":[37,108,134],"hybrid":[39],"parallel":[40],"CPU/GPU":[41],"platform.":[42],"The":[43,128],"transport":[44,183],"computational":[45],"phase,":[46],"i.e.":[47,70],"the":[48,52,58,64,67,71,74,89,98,101,117,124,142,147,151,160,171,182,198],"time":[49],"integration":[50],"of":[51,66,73,100,181,195,203],"Boltzmann":[53],"equations,":[54],"was":[55,77],"ported":[56],"to":[57,83,95,115,145,158,165,211],"GPU":[59,96,109,135],"using":[60,80,192],"CUDA":[61],"extensions,":[62],"but":[63],"computation":[65],"system\u2019s":[68],"eigenstates,":[69],"solution":[72],"Schr\u00f6dinger-Poisson":[75,102,172],"block,":[76],"parallelized":[78],"only":[79],"OpenMP":[81],"due":[82],"its":[84],"complexity.":[85],"This":[86,104],"work":[87],"fills":[88],"gap":[90],"describing":[92],"port":[94],"block.":[103],"new":[105],"proposal":[106],"implements":[107],"Scheduled":[111],"Relaxation":[112],"Jacobi":[113],"method":[114],"solve":[116],"sparse":[118],"linear":[119],"systems":[120],"which":[121],"arise":[122],"in":[123],"2D":[125],"Poisson":[126],"equation.":[127],"1D":[129],"Schr\u00f6dinger":[130],"equation":[131],"is":[132,156,202],"solved":[133],"adapting":[137],"multi-section":[139],"iteration":[140],"Newton-Raphson":[143],"algorithm":[144],"approximate":[146,159],"energy":[148],"levels,":[149],"Inverse":[152],"Power":[153],"Iterative":[154],"Method":[155],"used":[157,189],"wave":[161],"vectors.":[162],"We":[163],"want":[164],"stress":[166],"that":[167],"this":[168],"block":[173],"can":[174,187,208],"be":[175,188,209],"thought":[176],"as":[177],"module":[179],"independent":[180],"phase":[184],"(Boltzmann)":[185],"solvers":[191,216],"different":[193],"levels":[194],"description":[196],"electrons;":[199],"therefore,":[200],"it":[201,207],"particular":[204],"interest":[205],"because":[206],"adapted":[210],"other":[212],"macroscopic,":[213],"hence":[214],"faster,":[215],"confined":[218],"devices":[219],"exploited":[220],"at":[221],"industrial":[222],"level.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-25T14:56:36.534964","created_date":"2025-10-10T00:00:00"}