{"id":"https://openalex.org/W1986211946","doi":"https://doi.org/10.1090/s0025-5718-06-01869-2","title":"A two-grid discretization method for decoupling systems of partial differential equations","display_name":"A two-grid discretization method for decoupling systems of partial differential equations","publication_year":2006,"publication_date":"2006-07-11","ids":{"openalex":"https://openalex.org/W1986211946","doi":"https://doi.org/10.1090/s0025-5718-06-01869-2","mag":"1986211946"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-06-01869-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01869-2","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01869-2/S0025-5718-06-01869-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01869-2/S0025-5718-06-01869-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091913691","display_name":"Jicheng Jin","orcid":"https://orcid.org/0000-0002-1572-0006"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jicheng Jin","raw_affiliation_strings":["Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People\u00e2\u0080\u0099s Republic of China","Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People's Republic of China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102767325","display_name":"Shi Shu","orcid":"https://orcid.org/0000-0002-5552-3840"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shi Shu","raw_affiliation_strings":["Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People\u00e2\u0080\u0099s Republic of China","Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People's Republic of China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101494424","display_name":"Jinchao Xu","orcid":"https://orcid.org/0009-0004-4132-0227"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]},{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Jinchao Xu","raw_affiliation_strings":["Institute for Computational and Applied Mathematics, Xiangtan University, People\u00e2\u0080\u0099s Republic of China; and Center for Computational Mathematics and Applications, Pennsylvania State University, Pennsylvania","Center for Computational Mathematics and Applications, Pennsylvania State University, Pennsylvania","Institute for Computational and Applied Mathematics, Xiangtan University, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute for Computational and Applied Mathematics, Xiangtan University, People\u00e2\u0080\u0099s Republic of China; and Center for Computational Mathematics and Applications, Pennsylvania State University, Pennsylvania","institution_ids":[]},{"raw_affiliation_string":"Center for Computational Mathematics and Applications, Pennsylvania State University, Pennsylvania","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Institute for Computational and Applied Mathematics, Xiangtan University, People's Republic of China","institution_ids":["https://openalex.org/I4610292"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5091913691"],"corresponding_institution_ids":["https://openalex.org/I4610292"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":56,"citation_normalized_percentile":{"value":0.09840535,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"75","issue":"256","first_page":"1617","last_page":"1626"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9991000294685364,"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":0.7911211252212524},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7270324230194092},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.7024831771850586},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.6918152570724487},{"id":"https://openalex.org/keywords/decoupling","display_name":"Decoupling (probability)","score":0.6873736381530762},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.5764972567558289},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4822143316268921},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.48166191577911377},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.47114863991737366},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.45787546038627625},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4345543384552002},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10080775618553162},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06229513883590698}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7911211252212524},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7270324230194092},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.7024831771850586},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6918152570724487},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.6873736381530762},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.5764972567558289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4822143316268921},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.48166191577911377},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.47114863991737366},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.45787546038627625},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4345543384552002},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10080775618553162},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06229513883590698},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-06-01869-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01869-2","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01869-2/S0025-5718-06-01869-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.2643","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.2643","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2006-75-256/S0025-5718-06-01869-2/S0025-5718-06-01869-2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.482.8313","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.482.8313","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.psu.edu/ccma/Reports/Publications/Publications2006/Pdf_files/AM289.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-06-01869-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01869-2","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01869-2/S0025-5718-06-01869-2.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6404512901","display_name":"Multiscale Methods for Partial Differential Equations","funder_award_id":"0209497","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7791612409","display_name":"Scientific Computing Research Environments for the Mathematical Sciences","funder_award_id":"0215392","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"},{"id":"https://openalex.org/F4320324780","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62"},{"id":"https://openalex.org/F4320336475","display_name":"National Safety Academic Fund","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1986211946.pdf","grobid_xml":"https://content.openalex.org/works/W1986211946.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W189377493","https://openalex.org/W228399867","https://openalex.org/W1633205748","https://openalex.org/W1866311589","https://openalex.org/W1966862259","https://openalex.org/W1980455776","https://openalex.org/W1982691309","https://openalex.org/W1989343938","https://openalex.org/W1997640799","https://openalex.org/W2002284134","https://openalex.org/W2017786109","https://openalex.org/W2031387765","https://openalex.org/W2033653234","https://openalex.org/W2058525241","https://openalex.org/W2069961480","https://openalex.org/W2070441252","https://openalex.org/W2070719255","https://openalex.org/W2084681089","https://openalex.org/W2086085861","https://openalex.org/W2099936591","https://openalex.org/W2192056604","https://openalex.org/W3149695743","https://openalex.org/W4239611225","https://openalex.org/W4252716533","https://openalex.org/W4292360407","https://openalex.org/W6636851861"],"related_works":["https://openalex.org/W1758121264","https://openalex.org/W2383355899","https://openalex.org/W1501940787","https://openalex.org/W3022010538","https://openalex.org/W1524119935","https://openalex.org/W1533062418","https://openalex.org/W2161759000","https://openalex.org/W2525918155","https://openalex.org/W2167386686","https://openalex.org/W2785989279"],"abstract_inverted_index":{"In":[0],"this":[1,21],"paper,":[2],"we":[3],"propose":[4],"a":[5,30,42],"two-grid":[6],"finite":[7],"element":[8],"method":[9],"for":[10],"solving":[11],"coupled":[12,27,39],"partial":[13],"differential":[14],"equations,":[15],"e.g.,":[16],"the":[17,23,26,36,48,54,65],"Schr\u00f6dinger-type":[18],"equation.":[19],"With":[20],"method,":[22],"solution":[24,37,49,67],"of":[25,38,50],"equations":[28,40,52],"on":[29,41,53],"fine":[31,55],"grid":[32,45],"is":[33,58],"reduced":[34],"to":[35],"much":[43],"coarser":[44],"together":[46],"with":[47],"decoupled":[51],"grid.":[56],"It":[57],"shown,":[59],"both":[60],"theoretically":[61],"and":[62],"numerically,":[63],"that":[64],"resulting":[66],"still":[68],"achieves":[69],"asymptotically":[70],"optimal":[71],"accuracy.":[72]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}