{"id":"https://openalex.org/W2990423170","doi":"https://doi.org/10.1090/mcom/3510","title":"An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids","display_name":"An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids","publication_year":2019,"publication_date":"2019-11-20","ids":{"openalex":"https://openalex.org/W2990423170","doi":"https://doi.org/10.1090/mcom/3510","mag":"2990423170"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3510","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3510","pdf_url":null,"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":null,"license_id":null,"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":"green","oa_url":"https://nottingham-repository.worktribe.com/output/3078436","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063675442","display_name":"Paola F. Antonietti","orcid":"https://orcid.org/0000-0002-2138-3878"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Paola F. Antonietti","raw_affiliation_strings":["MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy"],"affiliations":[{"raw_affiliation_string":"MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035584552","display_name":"Paul Houston","orcid":"https://orcid.org/0000-0002-3588-2029"},"institutions":[{"id":"https://openalex.org/I142263535","display_name":"University of Nottingham","ror":"https://ror.org/01ee9ar58","country_code":"GB","type":"education","lineage":["https://openalex.org/I142263535"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Paul Houston","raw_affiliation_strings":["School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom","institution_ids":["https://openalex.org/I142263535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065701859","display_name":"Giorgio Pennesi","orcid":"https://orcid.org/0000-0003-3118-9283"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giorgio Pennesi","raw_affiliation_strings":["MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy"],"affiliations":[{"raw_affiliation_string":"MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064002486","display_name":"Endre S\u00fcli","orcid":"https://orcid.org/0000-0002-0812-6105"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Endre S\u00fcli","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063675442"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":3.0267,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.92230954,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"89","issue":"325","first_page":"2047","last_page":"2083"},"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":1.0,"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":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983999729156494,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9973000288009644,"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/preconditioner","display_name":"Preconditioner","score":0.8888325095176697},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7961590886116028},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7323900461196899},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6953010559082031},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5485185384750366},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5225690603256226},{"id":"https://openalex.org/keywords/massively-parallel","display_name":"Massively parallel","score":0.4632920026779175},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46102461218833923},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.43676960468292236},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.43195319175720215},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.42816030979156494},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.42057913541793823},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.37173759937286377},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32747483253479004},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.26754626631736755},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2328609824180603},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13909688591957092},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13690516352653503},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.11375734210014343}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8888325095176697},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7961590886116028},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7323900461196899},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6953010559082031},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5485185384750366},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5225690603256226},{"id":"https://openalex.org/C190475519","wikidata":"https://www.wikidata.org/wiki/Q544384","display_name":"Massively parallel","level":2,"score":0.4632920026779175},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46102461218833923},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.43676960468292236},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.43195319175720215},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.42816030979156494},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.42057913541793823},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.37173759937286377},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32747483253479004},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.26754626631736755},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2328609824180603},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13909688591957092},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13690516352653503},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.11375734210014343},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/mcom/3510","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3510","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:3078436","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/3078436","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:re.public.polimi.it:11311/1131527","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1131527","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:nottingham-repository.worktribe.com:3078436","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/3078436","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1127862405","display_name":null,"funder_award_id":"GNCS","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G267408053","display_name":null,"funder_award_id":"EP/R030707/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6261345112","display_name":null,"funder_award_id":"SIR Project n. RBSI14VT0S","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W158882822","https://openalex.org/W178921856","https://openalex.org/W1488877410","https://openalex.org/W1493036607","https://openalex.org/W1548589512","https://openalex.org/W1565176587","https://openalex.org/W1586623601","https://openalex.org/W1646532324","https://openalex.org/W1950919561","https://openalex.org/W1963803848","https://openalex.org/W1968754888","https://openalex.org/W1978682560","https://openalex.org/W1982576260","https://openalex.org/W1984473207","https://openalex.org/W1985863010","https://openalex.org/W1990319748","https://openalex.org/W1992066344","https://openalex.org/W1998894128","https://openalex.org/W2009012285","https://openalex.org/W2021666101","https://openalex.org/W2022811246","https://openalex.org/W2029725158","https://openalex.org/W2031088298","https://openalex.org/W2040382997","https://openalex.org/W2042387166","https://openalex.org/W2062839853","https://openalex.org/W2063884077","https://openalex.org/W2073237186","https://openalex.org/W2077617493","https://openalex.org/W2083820570","https://openalex.org/W2086501907","https://openalex.org/W2097964994","https://openalex.org/W2099760642","https://openalex.org/W2100520873","https://openalex.org/W2116404756","https://openalex.org/W2117496726","https://openalex.org/W2130350269","https://openalex.org/W2135297899","https://openalex.org/W2158943855","https://openalex.org/W2167745263","https://openalex.org/W2168914934","https://openalex.org/W2280689009","https://openalex.org/W2404390473","https://openalex.org/W2519971170","https://openalex.org/W2558016433","https://openalex.org/W2562030788","https://openalex.org/W2589767494","https://openalex.org/W2883313970","https://openalex.org/W2887880955","https://openalex.org/W2922002644","https://openalex.org/W2962814658","https://openalex.org/W2962924286","https://openalex.org/W2963313365","https://openalex.org/W2963487886","https://openalex.org/W2964307594","https://openalex.org/W2976972080","https://openalex.org/W4242960114","https://openalex.org/W4293028925","https://openalex.org/W4297968680","https://openalex.org/W4392818294"],"related_works":["https://openalex.org/W2471168230","https://openalex.org/W1986812736","https://openalex.org/W4389317411","https://openalex.org/W1492522302","https://openalex.org/W1554397852","https://openalex.org/W2096454229","https://openalex.org/W2477650282","https://openalex.org/W2773710110","https://openalex.org/W2042199958","https://openalex.org/W1877902382"],"abstract_inverted_index":{"In":[0,61],"this":[1],"article":[2],"we":[3],"design":[4],"and":[5,46,91,113,121,128],"analyze":[6],"a":[7,43,47],"class":[8],"of":[9,18,22,29,50,99,103,125],"two-level":[10],"non-overlapping":[11,48],"additive":[12],"Schwarz":[13],"preconditioners":[14],"for":[15],"the":[16,19,51,63,76,85,97,100,104,110,114,118,122,126,137],"solution":[17],"linear":[20],"system":[21,106],"equations":[23,34],"stemming":[24],"from":[25,84],"discontinuous":[26],"Galerkin":[27],"discretizations":[28],"second-order":[30],"elliptic":[31],"partial":[32],"differential":[33],"on":[35,42],"polytopic":[36],"meshes.":[37],"The":[38],"preconditioner":[39],"is":[40],"based":[41],"coarse":[44,64,129],"space":[45,65],"partition":[49],"computational":[52],"domain":[53],"where":[54],"local":[55],"solvers":[56],"are":[57,133],"applied":[58],"in":[59],"parallel.":[60],"particular,":[62],"can":[66,81],"potentially":[67],"be":[68,71,82],"chosen":[69],"to":[70,75,109],"non-embedded":[72],"with":[73,107],"respect":[74,108],"finer":[77],"space;":[78],"indeed":[79],"it":[80],"obtained":[83],"fine":[86,127],"grid":[87],"by":[88],"employing":[89],"agglomeration":[90],"edge":[92],"coarsening":[93],"techniques.":[94],"We":[95],"investigate":[96],"dependence":[98],"condition":[101],"number":[102],"preconditioned":[105],"diffusion":[111],"coefficient":[112],"discretization":[115],"parameters,":[116],"i.e.,":[117],"mesh":[119],"size":[120],"polynomial":[123],"degree":[124],"spaces.":[130],"Numerical":[131],"examples":[132],"presented":[134],"which":[135],"confirm":[136],"theoretical":[138],"bounds.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
