{"id":"https://openalex.org/W4404047479","doi":"https://doi.org/10.1137/23m1597496","title":"An Energy-Based Discontinuous Galerkin Method for the Nonlinear Schr\u00f6dinger Equation with Wave Operator","display_name":"An Energy-Based Discontinuous Galerkin Method for the Nonlinear Schr\u00f6dinger Equation with Wave Operator","publication_year":2024,"publication_date":"2024-11-04","ids":{"openalex":"https://openalex.org/W4404047479","doi":"https://doi.org/10.1137/23m1597496"},"language":"en","primary_location":{"id":"doi:10.1137/23m1597496","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1597496","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5065391648","display_name":"Kui Ren","orcid":"https://orcid.org/0000-0001-6463-4561"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kui Ren","raw_affiliation_strings":["Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 USA"],"raw_orcid":"https://orcid.org/0000-0001-6463-4561","affiliations":[{"raw_affiliation_string":"Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032078745","display_name":"Lu Zhang","orcid":"https://orcid.org/0000-0002-2940-6261"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lu Zhang","raw_affiliation_strings":["Department of Computational Applied Mathematics and Operations Research, Rice University, Houston, TX 77005 USA, and Ken Kennedy Institute, Rice University, Houston, TX 77005 USA"],"raw_orcid":"https://orcid.org/0000-0002-2940-6261","affiliations":[{"raw_affiliation_string":"Department of Computational Applied Mathematics and Operations Research, Rice University, Houston, TX 77005 USA, and Ken Kennedy Institute, Rice University, Houston, TX 77005 USA","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100548968","display_name":"Yin Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yin Zhou","raw_affiliation_strings":["Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 USA","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1731,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50102931,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"62","issue":"6","first_page":"2459","last_page":"2483"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9986000061035156,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9986000061035156,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9955000281333923,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9940000176429749,"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":0.8111449480056763},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6260875463485718},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6251516342163086},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5850152373313904},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5714326500892639},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5466734170913696},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.4707180857658386},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.44883885979652405},{"id":"https://openalex.org/keywords/dalembert-operator","display_name":"D'Alembert operator","score":0.43937262892723083},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.4186112880706787},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.41650667786598206},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36132800579071045},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.22069326043128967},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12580418586730957},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0766235888004303}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8111449480056763},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6260875463485718},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6251516342163086},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5850152373313904},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5714326500892639},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5466734170913696},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.4707180857658386},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.44883885979652405},{"id":"https://openalex.org/C58677928","wikidata":"https://www.wikidata.org/wiki/Q911268","display_name":"D'Alembert operator","level":2,"score":0.43937262892723083},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.4186112880706787},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.41650667786598206},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36132800579071045},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.22069326043128967},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12580418586730957},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0766235888004303},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1597496","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1597496","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8199999928474426}],"awards":[{"id":"https://openalex.org/G544448365","display_name":null,"funder_award_id":"DMS-2309802","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6049973117","display_name":null,"funder_award_id":"DMS-1913309","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7335263447","display_name":null,"funder_award_id":"DMS-1937254","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1987077205","https://openalex.org/W1999077739","https://openalex.org/W2021207474","https://openalex.org/W2036516029","https://openalex.org/W2039318241","https://openalex.org/W2039951077","https://openalex.org/W2055514331","https://openalex.org/W2055824650","https://openalex.org/W2061274519","https://openalex.org/W2065560314","https://openalex.org/W2087705056","https://openalex.org/W2091754351","https://openalex.org/W2109218138","https://openalex.org/W2148330860","https://openalex.org/W2152799582","https://openalex.org/W2209133793","https://openalex.org/W2335116161","https://openalex.org/W2911359226","https://openalex.org/W2921034323","https://openalex.org/W2922898532","https://openalex.org/W2950426004","https://openalex.org/W3019726072","https://openalex.org/W3031945669","https://openalex.org/W3099782930","https://openalex.org/W3144660602","https://openalex.org/W3171386003","https://openalex.org/W3192430706","https://openalex.org/W3203424473","https://openalex.org/W3211924546","https://openalex.org/W4205634890","https://openalex.org/W4232654152","https://openalex.org/W4233665781","https://openalex.org/W4286267527","https://openalex.org/W4307259826","https://openalex.org/W4318472958","https://openalex.org/W4387663219"],"related_works":["https://openalex.org/W2245214771","https://openalex.org/W2073973926","https://openalex.org/W2333053900","https://openalex.org/W1975562467","https://openalex.org/W2951961089","https://openalex.org/W3101208931","https://openalex.org/W2181923191","https://openalex.org/W3213209941","https://openalex.org/W4293767864","https://openalex.org/W2074095400"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-12-22T23:10:17.713674","created_date":"2025-10-10T00:00:00"}