{"id":"https://openalex.org/W7163539928","doi":"https://doi.org/10.48550/arxiv.2606.04864","title":"An algebraic multiscale preconditioner for large sparse SPD matrices","display_name":"An algebraic multiscale preconditioner for large sparse SPD matrices","publication_year":2026,"publication_date":"2026-06-03","ids":{"openalex":"https://openalex.org/W7163539928","doi":"https://doi.org/10.48550/arxiv.2606.04864"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.04864","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.04864","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.04864","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137832563","display_name":"Yingjie Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Yingjie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137767154","display_name":"Shubin Fu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fu, Shubin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102701820","display_name":"Eric Tsz Shun Chung","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chung, Eric Tsz Shun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.7041000127792358,"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":0.7041000127792358,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.1485999971628189,"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":0.10769999772310257,"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/preconditioner","display_name":"Preconditioner","score":0.8758000135421753},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6593000292778015},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.6491000056266785},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5778999924659729},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5577999949455261},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4593000113964081},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.444599986076355},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.4334999918937683}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8758000135421753},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6593000292778015},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6491000056266785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5950999855995178},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5778999924659729},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5577999949455261},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4593000113964081},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45170000195503235},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.444599986076355},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.4334999918937683},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.3853999972343445},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C554573382","wikidata":"https://www.wikidata.org/wiki/Q4723988","display_name":"Algebraic analysis","level":5,"score":0.32350000739097595},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2676999866962433},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25440001487731934},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2508000135421753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.04864","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.04864","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.04864","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.04864","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.40371423959732056,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2],"two-grid":[3],"algebraic":[4,93],"multiscale":[5],"preconditioner":[6],"for":[7,49,61,74],"large":[8],"sparse":[9],"symmetric":[10],"positive":[11],"definite":[12],"systems":[13],"arising":[14],"from":[15,28],"elliptic":[16],"problems":[17,78],"with":[18,81],"highly":[19],"heterogeneous":[20,75],"coefficients.":[21],"The":[22,52],"coarse":[23],"space":[24],"is":[25,69],"constructed":[26],"directly":[27],"the":[29,45],"system":[30],"matrix":[31],"by":[32],"graph":[33],"partitioning":[34],"and":[35,63,66,86,99],"local":[36],"generalized":[37],"eigenvalue":[38],"solvers,":[39],"yielding":[40],"basis":[41],"functions":[42],"that":[43],"capture":[44],"low-energy":[46],"modes":[47],"responsible":[48],"slow":[50],"convergence.":[51],"method":[53],"requires":[54],"no":[55],"geometric":[56],"information,":[57],"making":[58],"it":[59],"suitable":[60],"unstructured":[62],"matrix-only":[64],"settings,":[65],"its":[67],"construction":[68],"naturally":[70],"parallelizable.":[71],"Numerical":[72],"results":[73],"Darcy":[76],"flow":[77],"show":[79],"robustness":[80],"respect":[82],"to":[83],"coefficient":[84],"contrast":[85],"problem":[87],"size,":[88],"better":[89],"performance":[90],"than":[91],"standard":[92],"multigrid":[94],"on":[95],"challenging":[96],"large-scale":[97],"cases,":[98],"good":[100],"parallel":[101],"scalability.":[102]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-05T00:00:00"}