{"id":"https://openalex.org/W7143329982","doi":"https://doi.org/10.1007/s10915-026-03241-8","title":"A Spectral Method with Harmonic Map for Elliptic PDEs on General Two-Dimensional Domains","display_name":"A Spectral Method with Harmonic Map for Elliptic PDEs on General Two-Dimensional Domains","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7143329982","doi":"https://doi.org/10.1007/s10915-026-03241-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-026-03241-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-026-03241-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-026-03241-8.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-026-03241-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130948450","display_name":"Shan Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shan Shi","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan, 250100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan, 250100, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124227311","display_name":"Xiaoyun Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoyun Jiang","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan, 250100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan, 250100, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052906032","display_name":"Fanhai Zeng","orcid":"https://orcid.org/0000-0003-4507-1278"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fanhai Zeng","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan, 250100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan, 250100, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5130995207","display_name":"Hui Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Hui Zhang","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong"],"raw_orcid":"https://orcid.org/0009-0009-7334-772X","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5130995207"],"corresponding_institution_ids":["https://openalex.org/I14243506"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.73269876,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"107","issue":"2","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":0.7405999898910522,"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":0.7405999898910522,"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/T10514","display_name":"Numerical methods in engineering","score":0.08420000225305557,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.030899999663233757,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5996000170707703},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.545199990272522},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.49790000915527344},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.48890000581741333},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.4819999933242798},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.47279998660087585},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.4424000084400177},{"id":"https://openalex.org/keywords/harmonic-map","display_name":"Harmonic map","score":0.42640000581741333},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41830000281333923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8252000212669373},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5996000170707703},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.545199990272522},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.498199999332428},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.49790000915527344},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.48890000581741333},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.47279998660087585},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4602000117301941},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4424000084400177},{"id":"https://openalex.org/C6270764","wikidata":"https://www.wikidata.org/wiki/Q5659257","display_name":"Harmonic map","level":2,"score":0.42640000581741333},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41830000281333923},{"id":"https://openalex.org/C2780767217","wikidata":"https://www.wikidata.org/wiki/Q5532421","display_name":"Generality","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.36010000109672546},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.3515999913215637},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.3481999933719635},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.33649998903274536},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26030001044273376},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.26019999384880066},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2597000002861023}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-026-03241-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-026-03241-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-026-03241-8.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10915-026-03241-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-026-03241-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-026-03241-8.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1408897352","display_name":null,"funder_award_id":"12120101001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G17409056","display_name":null,"funder_award_id":"ZR2022JQ01","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G1951310221","display_name":null,"funder_award_id":"12171284","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G506018211","display_name":null,"funder_award_id":"12371447","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322598","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7143329982.pdf","grobid_xml":"https://content.openalex.org/works/W7143329982.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W579985084","https://openalex.org/W1975357829","https://openalex.org/W1978958642","https://openalex.org/W1983549191","https://openalex.org/W1985144286","https://openalex.org/W2008065952","https://openalex.org/W2020376322","https://openalex.org/W2040558735","https://openalex.org/W2044695077","https://openalex.org/W2047352485","https://openalex.org/W2058111044","https://openalex.org/W2066500060","https://openalex.org/W2080219236","https://openalex.org/W2082849992","https://openalex.org/W2083097852","https://openalex.org/W2093900303","https://openalex.org/W2130655033","https://openalex.org/W2553651416","https://openalex.org/W2770593113","https://openalex.org/W2885228491","https://openalex.org/W2963080509","https://openalex.org/W2981763651","https://openalex.org/W3011053680","https://openalex.org/W3026183760","https://openalex.org/W3123764437","https://openalex.org/W3165482041","https://openalex.org/W4214928334","https://openalex.org/W4239114676","https://openalex.org/W4247375400","https://openalex.org/W4253937035","https://openalex.org/W4316662276","https://openalex.org/W4361804108","https://openalex.org/W4376137564","https://openalex.org/W4401971012","https://openalex.org/W4405394823","https://openalex.org/W4405394858","https://openalex.org/W4406445840","https://openalex.org/W4408631936","https://openalex.org/W4410832418"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,57],"paper,":[3],"we":[4],"develop":[5],"an":[6],"efficient":[7],"Fourier-Legendre":[8],"spectral-Galerkin":[9],"method":[10,46,58],"for":[11,49],"solving":[12],"elliptic":[13],"partial":[14],"differential":[15],"equations":[16],"on":[17,98],"general":[18,35],"two-dimensional":[19],"domains.":[20,37,55],"A":[21],"key":[22],"core":[23],"of":[24,80,89,102],"our":[25],"approach":[26],"is":[27,59,78],"employing":[28],"a":[29,99],"harmonic":[30],"map":[31],"to":[32],"handle":[33],"the":[34,45,81,90],"physical":[36],"This":[38],"technique":[39],"ensures":[40],"broad":[41],"geometric":[42],"applicability,":[43],"making":[44],"highly":[47],"effective":[48],"both":[50],"complex":[51,103],"star-shaped":[52],"and":[53,87],"nonstar-shaped":[54],"Moreover,":[56],"rigorously":[60],"proved,":[61],"with":[62],"optimal":[63],"convergence":[64],"results":[65],"established":[66],"under":[67],"$$H^1$$":[68],"<mml:math":[69],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[70],"<mml:msup>":[71],"<mml:mi>H</mml:mi>":[72],"<mml:mn>1</mml:mn>":[73],"</mml:msup>":[74],"</mml:math>":[75],"-norm,":[76],"which":[77],"independent":[79],"domain":[82],"boundary\u2019s":[83],"smoothness.":[84],"The":[85],"effectiveness":[86],"generality":[88],"scheme":[91],"are":[92],"validated":[93],"through":[94],"some":[95],"numerical":[96],"examples":[97],"wide":[100],"variety":[101],"geometries.":[104]},"counts_by_year":[],"updated_date":"2026-04-01T02:31:24.031677","created_date":"2026-03-31T00:00:00"}
