{"id":"https://openalex.org/W3082716427","doi":"https://doi.org/10.1137/19m128377x","title":"Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains","display_name":"Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3082716427","doi":"https://doi.org/10.1137/19m128377x","mag":"3082716427"},"language":"en","primary_location":{"id":"doi:10.1137/19m128377x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m128377x","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":true,"oa_status":"green","oa_url":"https://dr.ntu.edu.sg/bitstream/10356/146051/2/19m128377x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084260114","display_name":"Changtao Sheng","orcid":"https://orcid.org/0000-0002-7089-5044"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]},{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN","SG","US"],"is_corresponding":true,"raw_author_name":"Changtao Sheng","raw_affiliation_strings":["\\ddagger Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957","Nanyang Technological University, Singapore","\\S Division of Science and Technology, BNU-HKBU United International College, Zhuhai, Guang-dong, China, and SUSTech International Center for Mathematics,","\\dagger Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore","Southern University of Science and Technology, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\ddagger Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"\\S Division of Science and Technology, BNU-HKBU United International College, Zhuhai, Guang-dong, China, and SUSTech International Center for Mathematics,","institution_ids":["https://openalex.org/I12615008","https://openalex.org/I3045169105"]},{"raw_affiliation_string":"\\dagger Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028981574","display_name":"Jie Shen","orcid":"https://orcid.org/0000-0002-4885-5732"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]},{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN","SG","US"],"is_corresponding":false,"raw_author_name":"Jie Shen","raw_affiliation_strings":["Southern University of Science and Technology, Shenzhen, China","\\S Division of Science and Technology, BNU-HKBU United International College, Zhuhai, Guang-dong, China, and SUSTech International Center for Mathematics,","\\dagger Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore","\\ddagger Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957","Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-4885-5732","affiliations":[{"raw_affiliation_string":"Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]},{"raw_affiliation_string":"\\S Division of Science and Technology, BNU-HKBU United International College, Zhuhai, Guang-dong, China, and SUSTech International Center for Mathematics,","institution_ids":["https://openalex.org/I12615008","https://openalex.org/I3045169105"]},{"raw_affiliation_string":"\\dagger Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058967726","display_name":"Tao Tang","orcid":"https://orcid.org/0000-0003-2919-2774"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]},{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN","SG","US"],"is_corresponding":false,"raw_author_name":"Tao Tang","raw_affiliation_strings":["\\dagger Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore","\\S Division of Science and Technology, BNU-HKBU United International College, Zhuhai, Guang-dong, China, and SUSTech International Center for Mathematics,","Southern University of Science and Technology, Shenzhen, China","Nanyang Technological University, Singapore","\\ddagger Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\\dagger Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"\\S Division of Science and Technology, BNU-HKBU United International College, Zhuhai, Guang-dong, China, and SUSTech International Center for Mathematics,","institution_ids":["https://openalex.org/I12615008","https://openalex.org/I3045169105"]},{"raw_affiliation_string":"Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]},{"raw_affiliation_string":"Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112395743","display_name":"Li-Lian Wang","orcid":"https://orcid.org/0000-0002-2735-9019"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]},{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]},{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN","SG","US"],"is_corresponding":false,"raw_author_name":"Li-Lian Wang","raw_affiliation_strings":["Southern University of Science and Technology, Shenzhen, China","Nanyang Technological University, Singapore","\\S Division of Science and Technology, BNU-HKBU United International College, Zhuhai, Guang-dong, China, and SUSTech International Center for Mathematics,","\\ddagger Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957","\\dagger Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]},{"raw_affiliation_string":"Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"\\S Division of Science and Technology, BNU-HKBU United International College, Zhuhai, Guang-dong, China, and SUSTech International Center for Mathematics,","institution_ids":["https://openalex.org/I12615008","https://openalex.org/I3045169105"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics, Purdue University, West Lafayette, IN 47907-1957","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"\\dagger Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019097739","display_name":"Huifang Yuan","orcid":"https://orcid.org/0000-0003-2267-9387"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]},{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huifang Yuan","raw_affiliation_strings":["Wuhan University, Wuhan, 430072, China","Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China and School of Mathematics and Statistics,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wuhan University, Wuhan, 430072, China","institution_ids":["https://openalex.org/I37461747"]},{"raw_affiliation_string":"Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China and School of Mathematics and Statistics,","institution_ids":["https://openalex.org/I3045169105"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5084260114"],"corresponding_institution_ids":["https://openalex.org/I12615008","https://openalex.org/I172675005","https://openalex.org/I219193219","https://openalex.org/I3045169105"],"apc_list":null,"apc_paid":null,"fwci":1.19,"has_fulltext":true,"cited_by_count":59,"citation_normalized_percentile":{"value":0.85154295,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"58","issue":"5","first_page":"2435","last_page":"2464"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9995999932289124,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8353974223136902},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5858716368675232},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5723857283592224},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.544303297996521},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5372744798660278},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5009407997131348},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.49712327122688293},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4911019802093506},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48705318570137024},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.4707525372505188},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46377032995224},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.43814817070961},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.43323689699172974},{"id":"https://openalex.org/keywords/pseudo-spectral-method","display_name":"Pseudo-spectral method","score":0.42459559440612793},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.41783997416496277},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4153834879398346},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.2453291416168213},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.15906411409378052},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1317794919013977},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07569178938865662}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8353974223136902},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5858716368675232},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5723857283592224},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.544303297996521},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5372744798660278},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5009407997131348},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.49712327122688293},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4911019802093506},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48705318570137024},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.4707525372505188},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46377032995224},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.43814817070961},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.43323689699172974},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.42459559440612793},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.41783997416496277},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4153834879398346},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2453291416168213},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.15906411409378052},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1317794919013977},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07569178938865662},{"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},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m128377x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m128377x","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"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/146051","is_oa":true,"landing_page_url":"https://hdl.handle.net/10356/146051","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/146051/2/19m128377x.pdf","source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:dr.ntu.edu.sg:10356/146051","is_oa":true,"landing_page_url":"https://hdl.handle.net/10356/146051","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/146051/2/19m128377x.pdf","source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Journal Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2621865199","display_name":null,"funder_award_id":"11731006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G36446433","display_name":null,"funder_award_id":"FA9550-20-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G417982304","display_name":null,"funder_award_id":"DMS-1620262","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G442931909","display_name":null,"funder_award_id":"MOE2018-T2-1-059","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G5146864000","display_name":null,"funder_award_id":"MOE2017-T2-2-144","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G5414121631","display_name":"Design and Analysis of Highly Efficient Algorithms for Complex Nonlinear Systems","funder_award_id":"2012585","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5729145195","display_name":null,"funder_award_id":"FA9550-20","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6422365594","display_name":null,"funder_award_id":"NSFC/RGC 11961160718","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7068715445","display_name":null,"funder_award_id":"FA9550-16-1-0102","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7163321403","display_name":null,"funder_award_id":"DMS-1720442","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G729797197","display_name":null,"funder_award_id":"11731006","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7839367162","display_name":null,"funder_award_id":"FA9550-20-1-0309","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8512854826","display_name":null,"funder_award_id":"TZ2018001","funder_id":"https://openalex.org/F4320336025","funder_display_name":"Science Challenge Project"},{"id":"https://openalex.org/G8536560856","display_name":null,"funder_award_id":"TZ2018001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8747941999","display_name":null,"funder_award_id":"FA9550-20-1-0309","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"},{"id":"https://openalex.org/F4320336025","display_name":"Science Challenge Project","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3082716427.pdf","grobid_xml":"https://content.openalex.org/works/W3082716427.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W1977360274","https://openalex.org/W1979983774","https://openalex.org/W1984898295","https://openalex.org/W1989941945","https://openalex.org/W2004872575","https://openalex.org/W2011095781","https://openalex.org/W2012828992","https://openalex.org/W2022382654","https://openalex.org/W2039427414","https://openalex.org/W2056284729","https://openalex.org/W2057646856","https://openalex.org/W2078959912","https://openalex.org/W2084980626","https://openalex.org/W2091313463","https://openalex.org/W2093685032","https://openalex.org/W2099111135","https://openalex.org/W2104736025","https://openalex.org/W2111271983","https://openalex.org/W2134061862","https://openalex.org/W2163257413","https://openalex.org/W2171629345","https://openalex.org/W2172034033","https://openalex.org/W2243218848","https://openalex.org/W2342026602","https://openalex.org/W2395085125","https://openalex.org/W2532859297","https://openalex.org/W2571966495","https://openalex.org/W2596900639","https://openalex.org/W2619423951","https://openalex.org/W2728907612","https://openalex.org/W2749611175","https://openalex.org/W2751463447","https://openalex.org/W2755519002","https://openalex.org/W2758600160","https://openalex.org/W2896765605","https://openalex.org/W2901814426","https://openalex.org/W2957713991","https://openalex.org/W2963055256","https://openalex.org/W2963145184","https://openalex.org/W2963196588","https://openalex.org/W2963301529","https://openalex.org/W2963714816","https://openalex.org/W2982546823","https://openalex.org/W3011053680","https://openalex.org/W3100586835","https://openalex.org/W3103130534","https://openalex.org/W3105657163","https://openalex.org/W3123275897"],"related_works":["https://openalex.org/W2043686470","https://openalex.org/W2096756136","https://openalex.org/W2896642768","https://openalex.org/W2410898212","https://openalex.org/W2056658486","https://openalex.org/W3121536649","https://openalex.org/W1972164677","https://openalex.org/W2042296795","https://openalex.org/W2118767500","https://openalex.org/W2970795967"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,126],"propose":[4],"a":[5,46,104,116],"fast":[6,93,109],"spectral-Galerkin":[7],"method":[8,138],"for":[9,82],"solving":[10,59],"PDEs":[11],"involving":[12],"an":[13,60,124],"integral":[14],"fractional":[15,32,49,62,121,129],"Laplacian":[16,50],"in":[17,75],"$\\mathbb{R}^d$,":[18],"which":[19],"is":[20,64],"built":[21],"upon":[22],"two":[23],"essential":[24],"components:":[25],"(i)":[26],"the":[27,31,48,56,71,89,92,97,108,128,135,141],"Dunford--Taylor":[28],"formulation":[29],"of":[30,58,73,91,99,119],"Laplacian;":[33],"and":[34,55],"(ii)":[35],"Fourier-like":[36],"biorthogonal":[37],"mapped":[38],"Chebyshev":[39],"functions":[40],"(MCFs)":[41],"as":[42],"basis":[43],"functions.":[44],"As":[45,123],"result,":[47],"can":[51,111],"be":[52,112],"fully":[53],"diagonalized,":[54],"complexity":[57],"elliptic":[61],"PDE":[63],"quasi-optimal,":[65],"i.e.,":[66],"$O((N\\log_2N)^d)$":[67],"with":[68,140],"$N$":[69],"being":[70],"number":[72],"modes":[74],"each":[76],"spatial":[77],"direction.":[78],"Ample":[79],"numerical":[80],"tests":[81],"various":[83],"decaying":[84],"exact":[85],"solutions":[86],"show":[87],"that":[88],"convergence":[90],"solver":[94,110],"perfectly":[95],"matches":[96],"order":[98],"theoretical":[100],"error":[101],"estimates.":[102],"With":[103],"suitable":[105],"time":[106],"discretization,":[107],"directly":[113],"applied":[114],"to":[115],"large":[117],"class":[118],"nonlinear":[120,130],"PDEs.":[122],"example,":[125],"solve":[127],"Schr\u00f6dinger":[131],"equation":[132],"by":[133],"using":[134],"fourth-order":[136],"time-splitting":[137],"together":[139],"proposed":[142],"MCF--spectral-Galerkin":[143],"method.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-30T09:15:22.047038","created_date":"2025-10-10T00:00:00"}