{"id":"https://openalex.org/W2989503034","doi":"https://doi.org/10.1137/18m1207879","title":"Strang Splitting in Combination with Rank-1 and Rank-<i>r</i> Lattices for the Time-Dependent Schr\u00f6dinger Equation","display_name":"Strang Splitting in Combination with Rank-1 and Rank-<i>r</i> Lattices for the Time-Dependent Schr\u00f6dinger Equation","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2989503034","doi":"https://doi.org/10.1137/18m1207879","mag":"2989503034"},"language":"en","primary_location":{"id":"doi:10.1137/18m1207879","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1207879","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/643396","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004676873","display_name":"Yuya Suzuki","orcid":"https://orcid.org/0000-0002-4988-8106"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Yuya Suzuki","raw_affiliation_strings":["KU Leuven, Belgium"],"affiliations":[{"raw_affiliation_string":"KU Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103712586","display_name":"Gowri Suryanarayana","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gowri Suryanarayana","raw_affiliation_strings":["EnergyVille and VITO, Belgium"],"affiliations":[{"raw_affiliation_string":"EnergyVille and VITO, Belgium","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045125806","display_name":"Dirk Nuyens","orcid":"https://orcid.org/0000-0002-4555-2314"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Dirk Nuyens","raw_affiliation_strings":["KU Leuven, Belgium"],"affiliations":[{"raw_affiliation_string":"KU Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004676873"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":0.6083,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.70935619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"41","issue":"6","first_page":"B1254","last_page":"B1283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9995999932289124,"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":0.9994999766349792,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8469460010528564},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7099264860153198},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5647202730178833},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.552688479423523},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5017697811126709},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.49764516949653625},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4628870189189911},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45327815413475037},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.45002466440200806},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.43495672941207886},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4333392381668091},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4223836660385132},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4161977767944336},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.31043100357055664},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1329905390739441},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12857863306999207}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8469460010528564},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7099264860153198},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5647202730178833},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.552688479423523},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5017697811126709},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.49764516949653625},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4628870189189911},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45327815413475037},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.45002466440200806},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.43495672941207886},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4333392381668091},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4223836660385132},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4161977767944336},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.31043100357055664},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1329905390739441},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12857863306999207},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/18m1207879","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1207879","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/643396","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/643396","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Siam Journal On Scientific Computing, vol. 41 (6), Art.No. 6, (B1254-B1283)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1808.06357","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.06357","pdf_url":"https://arxiv.org/pdf/1808.06357","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/643396","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/643396","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Siam Journal On Scientific Computing, vol. 41 (6), Art.No. 6, (B1254-B1283)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W7132561","https://openalex.org/W13364258","https://openalex.org/W52854976","https://openalex.org/W116055073","https://openalex.org/W227029647","https://openalex.org/W602313805","https://openalex.org/W916565236","https://openalex.org/W1515678755","https://openalex.org/W1531371725","https://openalex.org/W1592378316","https://openalex.org/W1592958377","https://openalex.org/W1632462863","https://openalex.org/W1820164671","https://openalex.org/W1976544585","https://openalex.org/W1980482577","https://openalex.org/W2011023754","https://openalex.org/W2012708209","https://openalex.org/W2035455944","https://openalex.org/W2036017515","https://openalex.org/W2041905900","https://openalex.org/W2049161806","https://openalex.org/W2050545584","https://openalex.org/W2055715492","https://openalex.org/W2072216330","https://openalex.org/W2076120296","https://openalex.org/W2083191882","https://openalex.org/W2095100077","https://openalex.org/W2099747558","https://openalex.org/W2132119675","https://openalex.org/W2148093730","https://openalex.org/W2157831252","https://openalex.org/W2160346753","https://openalex.org/W2166634029","https://openalex.org/W2392207747","https://openalex.org/W2963814522","https://openalex.org/W3104310777","https://openalex.org/W3122016199","https://openalex.org/W3124681825","https://openalex.org/W4241566164"],"related_works":["https://openalex.org/W4296209631","https://openalex.org/W3097449145","https://openalex.org/W2561617217","https://openalex.org/W4294811468","https://openalex.org/W2355801475","https://openalex.org/W4206659427","https://openalex.org/W2170062176","https://openalex.org/W2148135840","https://openalex.org/W106004901","https://openalex.org/W2973622563"],"abstract_inverted_index":{"We":[0,13,32,56,105],"approximate":[1],"the":[2,5,24,52,59,68,74,82,92,100,103,133,142,162,177,181],"solution":[3,182],"for":[4,136,171],"time":[6,50,69,166,189],"dependent":[7],"Schr\u00f6dinger":[8],"equation":[9],"in":[10,41,49,77],"two":[11,151],"steps.":[12],"first":[14],"use":[15],"a":[16,35,78,155],"pseudospectral":[17],"collocation":[18],"method":[19,109,139,149],"that":[20,58,73,91],"uses":[21],"samples":[22],"of":[23,37,95,99,102,165],"functions":[25],"on":[26],"rank-$1$":[27,178],"or":[28],"rank-$r$":[29],"lattice":[30,179],"points.":[31],"then":[33],"get":[34],"system":[36],"ordinary":[38],"differential":[39],"equations":[40],"time,":[42],"which":[43],"we":[44,89],"solve":[45],"approximately":[46],"by":[47,110,175],"stepping":[48],"using":[51,114,176,191],"Strang":[53],"splitting":[54],"method.":[55],"prove":[57,90],"numerical":[60,130,156,159],"scheme":[61],"proposed":[62,148],"converges":[63],"quadratically":[64],"with":[65,81,112,128],"respect":[66],"to":[67,144],"step":[70],"size,":[71],"given":[72],"potential":[75],"is":[76,97,168],"Korobov":[79],"space":[80],"smoothness":[83,96],"parameter":[84],"greater":[85],"than":[86],"$9/2$.":[87],"Particularly,":[88],"required":[93],"degree":[94],"independent":[98],"dimension":[101],"problem.":[104],"demonstrate":[106],"our":[107,137],"new":[108,138],"comparing":[111],"results":[113,160],"sparse":[115],"grids":[116],"from":[117,154],"[V.":[118],"Gradinaru,":[119],"SIAM":[120],"J.":[121],"Numer.":[122],"Anal.,":[123],"46":[124],"(2007),":[125],"pp.":[126],"103--123],":[127],"several":[129],"examples":[131,143],"showing":[132],"large":[134],"advantage":[135],"and":[140],"pushing":[141],"higher":[145],"dimensionality.":[146],"The":[147],"has":[150],"distinctive":[152],"features":[153],"perspective:":[157],"(i)":[158],"show":[161],"error":[163],"convergence":[164],"discretization":[167],"consistent":[169],"even":[170],"higher-dimensional":[172],"problems;":[173],"(ii)":[174],"points,":[180],"can":[183],"be":[184],"efficiently":[185],"computed":[186],"(and":[187],"further":[188],"stepped)":[190],"only":[192],"one-dimensional":[193],"fast":[194],"Fourier":[195],"transforms.":[196]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-31T07:56:22.981413","created_date":"2019-11-22T00:00:00"}
