{"id":"https://openalex.org/W2030947573","doi":"https://doi.org/10.1007/s00211-007-0074-1","title":"Domain decomposition for multiscale PDEs","display_name":"Domain decomposition for multiscale PDEs","publication_year":2007,"publication_date":"2007-04-19","ids":{"openalex":"https://openalex.org/W2030947573","doi":"https://doi.org/10.1007/s00211-007-0074-1","mag":"2030947573"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-007-0074-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-007-0074-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5064637859","display_name":"Ivan G. Graham","orcid":"https://orcid.org/0000-0002-5730-676X"},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"I. G. Graham","raw_affiliation_strings":["Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK","University of Bath, Mathematical Sciences, BA2 7AY, Bath, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]},{"raw_affiliation_string":"University of Bath, Mathematical Sciences, BA2 7AY, Bath, UK#TAB#","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018201344","display_name":"Patrick O. Lechner","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108329","display_name":"d-fine (Germany)","ror":"https://ror.org/01tppr291","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210108329"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"P. O. Lechner","raw_affiliation_strings":["d-fine GmbH, Opernplatz 2, 60313, Frankfurt am Main, Germany","d-fine GmbH, Opernplatz 2, 60313, Frankfurt am Main, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"d-fine GmbH, Opernplatz 2, 60313, Frankfurt am Main, Germany","institution_ids":["https://openalex.org/I4210108329"]},{"raw_affiliation_string":"d-fine GmbH, Opernplatz 2, 60313, Frankfurt am Main, Germany#TAB#","institution_ids":["https://openalex.org/I4210108329"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050544926","display_name":"Robert Scheichl","orcid":"https://orcid.org/0000-0001-8493-4393"},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"R. Scheichl","raw_affiliation_strings":["Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK","University of Bath, Mathematical Sciences, BA2 7AY, Bath, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]},{"raw_affiliation_string":"University of Bath, Mathematical Sciences, BA2 7AY, Bath, UK#TAB#","institution_ids":["https://openalex.org/I51601045"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064637859"],"corresponding_institution_ids":["https://openalex.org/I51601045"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":12.2819,"has_fulltext":false,"cited_by_count":158,"citation_normalized_percentile":{"value":0.9907653,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"106","issue":"4","first_page":"589","last_page":"626"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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/T11558","display_name":"Composite Material Mechanics","score":0.9975000023841858,"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/preconditioner","display_name":"Preconditioner","score":0.9340216517448425},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.7556629180908203},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7187310457229614},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.5674769282341003},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5621913075447083},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5535618662834167},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.5166400074958801},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.48522329330444336},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.44867372512817383},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.445400208234787},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.42772233486175537},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.42056939005851746},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4202170968055725},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37386757135391235},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.3687041997909546},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28129687905311584},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23361331224441528}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9340216517448425},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.7556629180908203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7187310457229614},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.5674769282341003},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5621913075447083},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5535618662834167},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.5166400074958801},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.48522329330444336},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.44867372512817383},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.445400208234787},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.42772233486175537},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.42056939005851746},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4202170968055725},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37386757135391235},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3687041997909546},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28129687905311584},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23361331224441528},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00211-007-0074-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-007-0074-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.368.6406","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.368.6406","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.bath.ac.uk/~masrs/gra_lec_sch_preprint_1106.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.626.7095","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.626.7095","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.bath.ac.uk/~masigg/publications/preprints/gra_lec_sch_preprint.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.6299999952316284,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W12888405","https://openalex.org/W1522252579","https://openalex.org/W1548589512","https://openalex.org/W1602383637","https://openalex.org/W1966480196","https://openalex.org/W1973061863","https://openalex.org/W1973095123","https://openalex.org/W1977699116","https://openalex.org/W1979057228","https://openalex.org/W1986746311","https://openalex.org/W1997180308","https://openalex.org/W1997596109","https://openalex.org/W2003116365","https://openalex.org/W2009985306","https://openalex.org/W2029918260","https://openalex.org/W2041065439","https://openalex.org/W2065385312","https://openalex.org/W2066276925","https://openalex.org/W2066858310","https://openalex.org/W2074189597","https://openalex.org/W2077157253","https://openalex.org/W2083401186","https://openalex.org/W2096646948","https://openalex.org/W2101032783","https://openalex.org/W2102369828","https://openalex.org/W2115424171","https://openalex.org/W2117293438","https://openalex.org/W2314343349","https://openalex.org/W2509362106","https://openalex.org/W2557433803","https://openalex.org/W2731458684","https://openalex.org/W3015587769","https://openalex.org/W3214098784","https://openalex.org/W4245007249"],"related_works":["https://openalex.org/W2640255794","https://openalex.org/W2743060302","https://openalex.org/W2054089597","https://openalex.org/W2117656216","https://openalex.org/W2626358056","https://openalex.org/W3047336714","https://openalex.org/W1480631731","https://openalex.org/W2554183881","https://openalex.org/W4229577910","https://openalex.org/W2901959480"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":21}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}