{"id":"https://openalex.org/W7129691343","doi":"https://doi.org/10.48550/arxiv.2602.13841","title":"A Monolithic hp Space-Time Multigrid Preconditioned Newton-Krylov Solver for Space-Time FEM applied to the Incompressible Navier-Stokes Equations","display_name":"A Monolithic hp Space-Time Multigrid Preconditioned Newton-Krylov Solver for Space-Time FEM applied to the Incompressible Navier-Stokes Equations","publication_year":2026,"publication_date":"2026-02-14","ids":{"openalex":"https://openalex.org/W7129691343","doi":"https://doi.org/10.48550/arxiv.2602.13841"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.13841","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.13841","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":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.2602.13841","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Margenberg, Nils","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Margenberg, Nils","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Bause, Markus","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bause, Markus","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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.5665000081062317,"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":0.5665000081062317,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.2745000123977661,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.03550000116229057,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.8913000226020813},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7067000269889832},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6227999925613403},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6104000210762024},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5846999883651733},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5412999987602234},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4699000120162964},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.4287000000476837}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8913000226020813},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7067000269889832},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6227999925613403},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6104000210762024},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.608299970626831},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5860999822616577},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5846999883651733},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5412999987602234},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4699000120162964},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.4287000000476837},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.42080000042915344},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4020000100135803},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.37279999256134033},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35899999737739563},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.34119999408721924},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3334999978542328},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.32190001010894775},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.30309998989105225},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.2897999882698059},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27489998936653137},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.265500009059906},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25540000200271606}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.13841","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.13841","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.13841","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.13841","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,20],"present":[1],"a":[2,32,97,142],"monolithic":[3],"hp":[4],"space-time":[5,11,76,108],"multigrid":[6,77,127],"method":[7,121],"(hp-STMG)":[8],"for":[9],"tensor-product":[10],"finite":[12],"element":[13],"discretizations":[14],"of":[15,75,129,144],"the":[16,90,125],"incompressible":[17],"Navier-Stokes":[18],"equations.":[19],"employ":[21],"mapped":[22],"inf-sup":[23],"stable":[24],"pairs":[25],"$\\mathbb":[26],"Q_{r+1}/\\mathbb":[27],"P_{r}^{\\mathrm{disc}}$":[28],"in":[29,38,56,61,124,152],"space":[30,57,62],"and":[31,63,71,131,134],"slabwise":[33],"discontinuous":[34],"Galerkin":[35],"DG($k$)":[36],"discretization":[37],"time.":[39,64],"The":[40,120],"resulting":[41],"fully":[42],"coupled":[43],"nonlinear":[44,91],"systems":[45],"are":[46],"solved":[47],"by":[48,96,105],"Newton-GMRES":[49],"preconditioned":[50],"with":[51,58,115,137],"hp-STMG,":[52],"combining":[53],"geometric":[54],"coarsening":[55,60],"polynomial":[59],"Our":[65],"main":[66],"contribution":[67],"is":[68,83,94,103,122],"an":[69,106],"hp-robust":[70],"practically":[72],"efficient":[73],"extension":[74],"to":[78],"Navier-Stokes:":[79],"matrix-free":[80,126],"operator":[81],"evaluation":[82],"retained":[84],"via":[85],"column-wise,":[86],"state-dependent":[87],"spatial":[88],"kernels;":[89],"convective":[92],"term":[93],"handled":[95],"reduced,":[98],"order-preserving":[99],"time":[100,117],"quadrature.":[101],"Robustness":[102],"ensured":[104],"inexact":[107],"Vanka":[109],"smoother":[110],"based":[111],"on":[112],"patch":[113],"models":[114],"single":[116],"point":[118],"evaluation.":[119],"implemented":[123],"framework":[128],"deal.II":[130],"demonstrates":[132],"h-":[133],"p-robust":[135],"convergence":[136],"robust":[138],"solver":[139],"performance":[140],"across":[141],"range":[143],"Reynolds":[145],"numbers,":[146],"as":[147,149],"well":[148],"high":[150],"throughput":[151],"large-scale":[153],"MPI-parallel":[154],"experiments.":[155]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-02-16T00:00:00"}