{"id":"https://openalex.org/W4396585876","doi":"https://doi.org/10.1137/23m1568806","title":"Matrix-Free High-Performance Saddle-Point Solvers for High-Order Problems in \\(\\boldsymbol{H}(\\operatorname{\\textbf{div}})\\)","display_name":"Matrix-Free High-Performance Saddle-Point Solvers for High-Order Problems in \\(\\boldsymbol{H}(\\operatorname{\\textbf{div}})\\)","publication_year":2024,"publication_date":"2024-05-02","ids":{"openalex":"https://openalex.org/W4396585876","doi":"https://doi.org/10.1137/23m1568806"},"language":"en","primary_location":{"id":"doi:10.1137/23m1568806","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1568806","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/2440339","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030630927","display_name":"Will Pazner","orcid":"https://orcid.org/0000-0003-4885-2934"},"institutions":[{"id":"https://openalex.org/I126345244","display_name":"Portland State University","ror":"https://ror.org/00yn2fy02","country_code":"US","type":"education","lineage":["https://openalex.org/I126345244"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Will Pazner","raw_affiliation_strings":["Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 USA"],"raw_orcid":"https://orcid.org/0000-0003-4885-2934","affiliations":[{"raw_affiliation_string":"Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 USA","institution_ids":["https://openalex.org/I126345244"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003911272","display_name":"Tzanio Kolev","orcid":"https://orcid.org/0000-0002-2810-3090"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tzanio Kolev","raw_affiliation_strings":["Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94550 USA"],"raw_orcid":"https://orcid.org/0000-0002-2810-3090","affiliations":[{"raw_affiliation_string":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94550 USA","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027636165","display_name":"Panayot S. Vassilevski","orcid":"https://orcid.org/0000-0002-5294-7242"},"institutions":[{"id":"https://openalex.org/I126345244","display_name":"Portland State University","ror":"https://ror.org/00yn2fy02","country_code":"US","type":"education","lineage":["https://openalex.org/I126345244"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Panayot S. Vassilevski","raw_affiliation_strings":["Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 USA","institution_ids":["https://openalex.org/I126345244"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030630927"],"corresponding_institution_ids":["https://openalex.org/I126345244"],"apc_list":null,"apc_paid":null,"fwci":2.1497,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.85225298,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"46","issue":"3","first_page":"B179","last_page":"B204"},"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":0.9998000264167786,"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"}},"topics":[{"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9988999962806702,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9962999820709229,"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/schur-complement","display_name":"Schur complement","score":0.8168138265609741},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7242547869682312},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.6652187705039978},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.5538967251777649},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.5435199737548828},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4961300790309906},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48624172806739807},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.45444709062576294},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42395684123039246},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3755371570587158},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23037859797477722},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.22567948698997498},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18563947081565857},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.17722871899604797}],"concepts":[{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.8168138265609741},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7242547869682312},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.6652187705039978},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.5538967251777649},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.5435199737548828},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4961300790309906},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48624172806739807},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.45444709062576294},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42395684123039246},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3755371570587158},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23037859797477722},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.22567948698997498},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18563947081565857},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.17722871899604797},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/23m1568806","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1568806","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:pdxscholar.library.pdx.edu:mth_fac-1412","is_oa":false,"landing_page_url":"https://pdxscholar.library.pdx.edu/mth_fac/408","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:2440339","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/2440339","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":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:2440339","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/2440339","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":null,"raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G420278764","display_name":null,"funder_award_id":"DE-AC52-07NA27344 (LLNL-JRNL-848035)","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G8127111558","display_name":null,"funder_award_id":"20-ERD-002","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"}],"funders":[{"id":"https://openalex.org/F4320338286","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W592911714","https://openalex.org/W875678063","https://openalex.org/W1737435842","https://openalex.org/W1973312823","https://openalex.org/W1980053021","https://openalex.org/W1983139887","https://openalex.org/W1985144286","https://openalex.org/W2005789227","https://openalex.org/W2010804587","https://openalex.org/W2024307458","https://openalex.org/W2025359061","https://openalex.org/W2033986961","https://openalex.org/W2039789965","https://openalex.org/W2053572944","https://openalex.org/W2059880466","https://openalex.org/W2075237894","https://openalex.org/W2075896209","https://openalex.org/W2078842791","https://openalex.org/W2078843646","https://openalex.org/W2093842590","https://openalex.org/W2095039621","https://openalex.org/W2096894484","https://openalex.org/W2141870784","https://openalex.org/W2148551624","https://openalex.org/W2148594104","https://openalex.org/W2287612569","https://openalex.org/W2499931820","https://openalex.org/W2597480328","https://openalex.org/W2607476412","https://openalex.org/W2622428623","https://openalex.org/W2730469415","https://openalex.org/W2786313222","https://openalex.org/W2943869808","https://openalex.org/W2962888941","https://openalex.org/W2969466890","https://openalex.org/W3016268593","https://openalex.org/W3040786754","https://openalex.org/W3091293834","https://openalex.org/W3099186551","https://openalex.org/W3124354733","https://openalex.org/W3135853372","https://openalex.org/W3167826856","https://openalex.org/W3199141021","https://openalex.org/W3204468590","https://openalex.org/W3215122111","https://openalex.org/W4365455929","https://openalex.org/W4379013997"],"related_works":["https://openalex.org/W2804034492","https://openalex.org/W2040165403","https://openalex.org/W1524826225","https://openalex.org/W2138306359","https://openalex.org/W2028160813","https://openalex.org/W1965116625","https://openalex.org/W1990747776","https://openalex.org/W993433986","https://openalex.org/W1552250021","https://openalex.org/W177285201"],"abstract_inverted_index":{"Here,":[0],"this":[1],"work":[2],"describes":[3],"the":[4,43,53,60,78,89,114,134,139],"development":[5],"of":[6,59,72,77,91,113,129],"matrix-free":[7,47],"GPU-accelerated":[8,108],"solvers":[9,18],"for":[10,52,110],"high-order":[11],"finite":[12],"element":[13],"problems":[14,25],"in":[15,26,32,69],"H(div).":[16],"The":[17,84],"are":[19,117,124],"applicable":[20],"to":[21],"grad-div":[22,137],"and":[23,29,35,56,81,96,120,145],"Darcy":[24],"saddle-point":[27],"formulation,":[28],"have":[30],"applications":[31],"radiation":[33,148],"diffusion":[34,149],"porous":[36],"media":[37],"flow":[38],"problems,":[39],"among":[40],"others.":[41],"Using":[42],"interpolation\u2013histopolation":[44],"basis,":[45],"efficient":[46],"preconditioners":[48],"can":[49,98],"be":[50,99],"constructed":[51],"(1,":[54],"1)-block":[55],"Schur":[57,86],"complement":[58,87],"block":[61],"system.":[62],"With":[63],"these":[64],"approximations,":[65],"block-preconditioned":[66],"MINRES":[67],"converges":[68],"a":[70,127,146],"number":[71,128],"iterations":[73],"that":[74],"is":[75],"independent":[76],"mesh":[79],"size":[80],"polynomial":[82],"degree.":[83],"approximate":[85],"takes":[88],"form":[90],"an":[92],"M-matrix":[93],"graph":[94],"Laplacian":[95],"therefore":[97],"well-preconditioned":[100],"by":[101],"highly":[102],"scalable":[103],"algebraic":[104],"multigrid":[105],"methods.":[106],"High-performance":[107],"algorithms":[109],"all":[111],"components":[112],"solution":[115],"algorithm":[116],"developed,":[118],"discussed,":[119],"benchmarked.":[121],"Numerical":[122],"results":[123],"presented":[125],"on":[126],"challenging":[130],"test":[131,150],"cases,":[132],"including":[133],"\u201ccrooked":[135],"pipe\u201d":[136],"problem,":[138,144],"SPE10":[140],"reservoir":[141],"modeling":[142],"benchmark":[143],"nonlinear":[147],"case.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2024-05-03T00:00:00"}