{"id":"https://openalex.org/W3011950599","doi":"https://doi.org/10.1137/19m1296343","title":"Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation","display_name":"Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3011950599","doi":"https://doi.org/10.1137/19m1296343","mag":"3011950599"},"language":"en","primary_location":{"id":"doi:10.1137/19m1296343","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296343","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.04423","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071233708","display_name":"Andrew T. Barker","orcid":"https://orcid.org/0000-0003-3572-911X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrew T. Barker","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030195587","display_name":"Stephan V. Gelever","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stephan V. Gelever","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003575107","display_name":"Chak Shing Lee","orcid":"https://orcid.org/0000-0002-9573-3463"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chak S. Lee","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020792389","display_name":"Sarah Osborn","orcid":"https://orcid.org/0000-0003-3256-3337"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sarah V. Osborn","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5027636165","display_name":"Panayot S. Vassilevski","orcid":"https://orcid.org/0000-0002-5294-7242"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panayot S. Vassilevski","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5071233708"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.16009212,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.45721402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"43","issue":"4","first_page":"A2737","last_page":"A2765"},"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":0.9994000196456909,"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":0.9883000254631042,"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/saddle-point","display_name":"Saddle point","score":0.6450618505477905},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6367729902267456},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5749858617782593},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5462105870246887},{"id":"https://openalex.org/keywords/reservoir-simulation","display_name":"Reservoir simulation","score":0.5418201088905334},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.48033633828163147},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.44479674100875854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.439665824174881},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42326292395591736},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.42064422369003296},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.4200728237628937},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3800659775733948},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34243321418762207},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.17855745553970337},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17144480347633362},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11926138401031494},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08624973893165588}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.6450618505477905},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6367729902267456},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5749858617782593},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5462105870246887},{"id":"https://openalex.org/C2778668878","wikidata":"https://www.wikidata.org/wiki/Q6380338","display_name":"Reservoir simulation","level":2,"score":0.5418201088905334},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.48033633828163147},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.44479674100875854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.439665824174881},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42326292395591736},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.42064422369003296},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.4200728237628937},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3800659775733948},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34243321418762207},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.17855745553970337},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17144480347633362},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11926138401031494},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08624973893165588},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/19m1296343","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296343","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2003.04423","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.04423","pdf_url":"https://arxiv.org/pdf/2003.04423","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":null},{"id":"mag:3011950599","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2003.04423","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:pdxscholar.library.pdx.edu:mth_fac-1343","is_oa":false,"landing_page_url":"https://pdxscholar.library.pdx.edu/mth_fac/339","pdf_url":null,"source":{"id":"https://openalex.org/S4377196300","display_name":"PDXScholar  (Portland State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126345244","host_organization_name":"Portland State University","host_organization_lineage":["https://openalex.org/I126345244"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics and Statistics Faculty Publications and Presentations","raw_type":"text"},{"id":"pmh:oai:osti.gov:1824746","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1824746","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"doi:10.48550/arxiv.2003.04423","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.04423","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2003.04423","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.04423","pdf_url":"https://arxiv.org/pdf/2003.04423","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W362836892","https://openalex.org/W1526698283","https://openalex.org/W1665371634","https://openalex.org/W1837874438","https://openalex.org/W1970659509","https://openalex.org/W1974220164","https://openalex.org/W1981142209","https://openalex.org/W1990157709","https://openalex.org/W1994810579","https://openalex.org/W2000272165","https://openalex.org/W2003637147","https://openalex.org/W2009250131","https://openalex.org/W2029918260","https://openalex.org/W2050892063","https://openalex.org/W2069326881","https://openalex.org/W2070006753","https://openalex.org/W2070159602","https://openalex.org/W2070232376","https://openalex.org/W2070448527","https://openalex.org/W2082312113","https://openalex.org/W2089139137","https://openalex.org/W2108533624","https://openalex.org/W2112280313","https://openalex.org/W2126028850","https://openalex.org/W2131374225","https://openalex.org/W2135459060","https://openalex.org/W2138940269","https://openalex.org/W2142762932","https://openalex.org/W2318617894","https://openalex.org/W2339526232","https://openalex.org/W2401325911","https://openalex.org/W2491027544","https://openalex.org/W2523496060","https://openalex.org/W2590459043","https://openalex.org/W2613465422","https://openalex.org/W2762048197","https://openalex.org/W2765931382","https://openalex.org/W2766245020","https://openalex.org/W2962888941","https://openalex.org/W2964297483","https://openalex.org/W3022078055"],"related_works":["https://openalex.org/W12905223","https://openalex.org/W2963164483","https://openalex.org/W2952402321","https://openalex.org/W3135178051","https://openalex.org/W3035481208","https://openalex.org/W2077008103","https://openalex.org/W1499129909","https://openalex.org/W2291575397","https://openalex.org/W2092614367","https://openalex.org/W1485003658","https://openalex.org/W2106605796","https://openalex.org/W3122407115","https://openalex.org/W3169652463","https://openalex.org/W1515836157","https://openalex.org/W3154787082","https://openalex.org/W3152351374","https://openalex.org/W3021748939","https://openalex.org/W1895062987","https://openalex.org/W303839406","https://openalex.org/W2000700114"],"abstract_inverted_index":{"We":[0,109],"extend":[1],"previously":[2],"developed":[3],"two-level":[4],"coarsening":[5],"procedures":[6],"for":[7,85,97],"graph":[8],"Laplacian":[9],"problems":[10,128],"written":[11],"in":[12,37,44,59,72,92,118,130],"a":[13,32,70,87,123],"mixed":[14,50],"saddle":[15],"point":[16],"form":[17],"to":[18,31,56,79],"the":[19,38,45,49,104,111,114],"fully":[20],"recursive":[21],"multilevel":[22,73,116],"case.":[23],"The":[24],"resulting":[25],"hierarchy":[26,33],"of":[27,34,89,113,125],"discretizations":[28],"gives":[29],"rise":[30],"upscaled":[35],"models,":[36],"sense":[39],"that":[40],"they":[41],"provide":[42],"approximation":[43,95],"natural":[46],"norms":[47],"(in":[48,77],"setting).":[51],"This":[52],"property":[53],"enables":[54],"us":[55],"utilize":[57],"them":[58],"three":[60,120],"applications:":[61],"(i)":[62],"as":[63,69],"an":[64],"accurate":[65],"reduced":[66],"model,":[67],"(ii)":[68],"tool":[71],"Monte":[74],"Carlo":[75],"simulations":[76],"application":[78],"finite":[80],"volume":[81],"discretizations),":[82],"and":[83],"(iii)":[84],"providing":[86],"sequence":[88],"nonlinear":[90,99],"operators":[91],"FAS":[93],"(full":[94],"scheme)":[96],"solving":[98],"pressure":[100],"equations":[101],"discretized":[102],"by":[103],"conservative":[105],"two-point":[106],"flux":[107],"approximation.":[108],"illustrate":[110],"potential":[112],"proposed":[115],"technique":[117],"all":[119],"applications":[121],"on":[122],"number":[124],"popular":[126],"benchmark":[127],"used":[129],"reservoir":[131],"simulation.":[132]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
