{"id":"https://openalex.org/W2745247114","doi":"https://doi.org/10.1080/00207160.2017.1366463","title":"An adaptive FEM with ITP approach for steady Schr\u00f6dinger equation","display_name":"An adaptive FEM with ITP approach for steady Schr\u00f6dinger equation","publication_year":2017,"publication_date":"2017-08-10","ids":{"openalex":"https://openalex.org/W2745247114","doi":"https://doi.org/10.1080/00207160.2017.1366463","mag":"2745247114"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1366463","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1366463","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5007818254","display_name":"Yang Kuang","orcid":"https://orcid.org/0000-0003-3680-736X"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Yang Kuang","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao SAR, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao SAR, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100750983","display_name":"Guanghui Hu","orcid":"https://orcid.org/0000-0003-1522-1888"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":true,"raw_author_name":"Guanghui Hu","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao SAR, China","UM Zhuhai Research Institute, Guangdong, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao SAR, China","institution_ids":["https://openalex.org/I204512498"]},{"raw_affiliation_string":"UM Zhuhai Research Institute, Guangdong, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100750983"],"corresponding_institution_ids":["https://openalex.org/I204512498"],"apc_list":null,"apc_paid":null,"fwci":0.709,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.68083004,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"95","issue":"1","first_page":"187","last_page":"201"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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":0.9994000196456909,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9991999864578247,"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":0.9979000091552734,"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/mathematics","display_name":"Mathematics","score":0.7588735818862915},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6155605316162109},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5746265053749084},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5737891793251038},{"id":"https://openalex.org/keywords/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.5666972994804382},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5609533786773682},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5506542921066284},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5415374040603638},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39518114924430847},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1007363498210907}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7588735818862915},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6155605316162109},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5746265053749084},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5737891793251038},{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.5666972994804382},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5609533786773682},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5506542921066284},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5415374040603638},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39518114924430847},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1007363498210907},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1366463","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1366463","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1974228548","https://openalex.org/W1975919340","https://openalex.org/W1985448567","https://openalex.org/W2003656569","https://openalex.org/W2006572775","https://openalex.org/W2022614303","https://openalex.org/W2026106782","https://openalex.org/W2043581751","https://openalex.org/W2045905391","https://openalex.org/W2047622701","https://openalex.org/W2049161806","https://openalex.org/W2063446817","https://openalex.org/W2073125394","https://openalex.org/W2083222334","https://openalex.org/W2089719986","https://openalex.org/W2095908597","https://openalex.org/W2119617200","https://openalex.org/W2122716160","https://openalex.org/W2155498635","https://openalex.org/W2170930163","https://openalex.org/W2210503688","https://openalex.org/W2315148011","https://openalex.org/W2318378397","https://openalex.org/W2496111147","https://openalex.org/W3101253177","https://openalex.org/W4245463005"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W4223970227","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1988055643"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"an":[3,16,106],"adaptive":[4],"numerical":[5],"method":[6,104],"is":[7,24,54,77],"proposed":[8],"for":[9],"solving":[10],"a":[11,28,32,44,59,66],"2D":[12],"Schr\u00f6dinger":[13],"equation":[14,23,53],"with":[15],"imaginary":[17],"time":[18,48],"propagation":[19],"approach.":[20],"The":[21,51,98],"differential":[22],"first":[25],"transferred":[26],"via":[27,58],"Wick":[29],"rotation":[30],"to":[31,39,79,109],"real":[33],"time-dependent":[34],"equation,":[35],"whose":[36],"solution":[37],"corresponds":[38],"the":[40,85,111,115],"ground":[41,112],"state":[42,113],"of":[43,84,114],"given":[45],"system":[46],"when":[47],"approaches":[49],"infinity.":[50],"temporal":[52],"then":[55],"discretized":[56],"spatially":[57],"finite":[60],"element":[61],"method,":[62],"and":[63,89],"temporally":[64],"utilizing":[65],"Crank\u2013Nicolson":[67],"scheme.":[68],"A":[69],"moving":[70],"mesh":[71],"strategy":[72],"based":[73],"on":[74],"harmonic":[75],"maps":[76],"considered":[78],"eliminate":[80],"possible":[81],"singular":[82],"behaviour":[83],"solution.":[86],"Several":[87],"linear":[88],"nonlinear":[90],"examples":[91],"are":[92],"tested":[93],"by":[94],"using":[95],"our":[96,103],"method.":[97],"experiments":[99],"demonstrate":[100],"clearly":[101],"that":[102],"provides":[105],"effective":[107],"way":[108],"locate":[110],"equations":[116],"through":[117],"underlying":[118],"eigenvalue":[119],"problems.":[120]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}