{"id":"https://openalex.org/W4220793576","doi":"https://doi.org/10.1137/21m1426079","title":"A space-time Trefftz discontinuous Galerkin method for the linear Schr\\\"odinger equation","display_name":"A space-time Trefftz discontinuous Galerkin method for the linear Schr\\\"odinger equation","publication_year":2021,"publication_date":"2021-06-08","ids":{"openalex":"https://openalex.org/W4220793576","doi":"https://doi.org/10.1137/21m1426079"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2106.04724","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.04724","pdf_url":"https://arxiv.org/pdf/2106.04724","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"},"type":"article","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2106.04724","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"G\\'omez, Sergio","orcid":null},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G\\'omez, Sergio","raw_affiliation_strings":["Dipartimento di Matematica \"F. Casorati\", Universit\u00e0 di Pavia, 27100 Pavia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \"F. Casorati\", Universit\u00e0 di Pavia, 27100 Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045318480","display_name":"Andrea Moiola","orcid":"https://orcid.org/0000-0002-6251-4440"},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Moiola, Andrea","raw_affiliation_strings":["Dipartimento di Matematica \"F. Casorati\", Universit\u00e0 di Pavia, 27100 Pavia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \"F. Casorati\", Universit\u00e0 di Pavia, 27100 Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045318480"],"corresponding_institution_ids":["https://openalex.org/I25217355"],"apc_list":null,"apc_paid":null,"fwci":1.0684,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.74627982,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9994000196456909,"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/T10514","display_name":"Numerical methods in engineering","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.879673957824707},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.703314483165741},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5679735541343689},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5535719990730286},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5246496200561523},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4941389858722687},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48979711532592773},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4384397864341736},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43317532539367676},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4110773801803589},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.39200812578201294},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3850078880786896},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1353362500667572}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.879673957824707},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.703314483165741},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5679735541343689},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5535719990730286},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5246496200561523},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4941389858722687},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48979711532592773},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4384397864341736},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43317532539367676},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4110773801803589},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.39200812578201294},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3850078880786896},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1353362500667572},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":1,"locations":[{"id":"pmh:oai:arXiv.org:2106.04724","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.04724","pdf_url":"https://arxiv.org/pdf/2106.04724","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:arXiv.org:2106.04724","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.04724","pdf_url":"https://arxiv.org/pdf/2106.04724","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"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8500000238418579}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W592504358","https://openalex.org/W1479683601","https://openalex.org/W1480253648","https://openalex.org/W1602383637","https://openalex.org/W1679644037","https://openalex.org/W1899086482","https://openalex.org/W1967469744","https://openalex.org/W2006718018","https://openalex.org/W2010605025","https://openalex.org/W2020804487","https://openalex.org/W2063863413","https://openalex.org/W2066909767","https://openalex.org/W2075828491","https://openalex.org/W2083719667","https://openalex.org/W2127600768","https://openalex.org/W2528346287","https://openalex.org/W2734915834","https://openalex.org/W3001250019","https://openalex.org/W3113258920","https://openalex.org/W4285584040","https://openalex.org/W4292166829","https://openalex.org/W4298356938","https://openalex.org/W4300528205","https://openalex.org/W4309680536"],"related_works":["https://openalex.org/W2982093746","https://openalex.org/W3043435143","https://openalex.org/W2158006240","https://openalex.org/W2162026849","https://openalex.org/W1967648380","https://openalex.org/W2394687667","https://openalex.org/W4308757930","https://openalex.org/W2383844134","https://openalex.org/W2887215440","https://openalex.org/W2374198922"],"abstract_inverted_index":{"A":[0],"space-time":[1,45],"Trefftz":[2,21],"discontinuous":[3],"Galerkin":[4],"method":[5],"for":[6,49,75],"the":[7,18,36,44,54,72,76,95],"Schr\\\"odinger":[8],"equation":[9,38],"with":[10,62],"piecewise-constant":[11],"potential":[12],"is":[13],"proposed":[14],"and":[15,24,69,78],"analyzed.":[16],"Following":[17],"spirit":[19],"of":[20,43,56,58,71],"methods,":[22],"trial":[23],"test":[25],"spaces":[26],"are":[27],"spanned":[28],"by":[29],"non-polynomial":[30],"complex":[31],"wave":[32],"functions":[33],"that":[34],"satisfy":[35],"Schro\\\"odinger":[37],"locally":[39],"on":[40],"each":[41],"element":[42],"mesh.":[46],"This":[47],"allows":[48],"a":[50,88],"significant":[51],"reduction":[52],"in":[53,60,87],"number":[55],"degrees":[57],"freedom":[59],"comparison":[61],"full":[63],"polynomial":[64],"spaces.":[65],"We":[66],"prove":[67],"well-posedness":[68],"stability":[70],"method,":[73],"and,":[74],"one-":[77],"two-":[79],"dimensional":[80],"cases,":[81],"optimal,":[82],"high-order,":[83],"h-convergence":[84],"error":[85],"estimates":[86],"skeleton":[89],"norm.":[90],"Some":[91],"numerical":[92],"experiments":[93],"validate":[94],"theoretical":[96],"results":[97],"presented.":[98]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2022-04-03T00:00:00"}
