{"id":"https://openalex.org/W3125933139","doi":"https://doi.org/10.1137/20m1333018","title":"Preconditioning the Mass Matrix for High Order Finite Element Approximation on Tetrahedra","display_name":"Preconditioning the Mass Matrix for High Order Finite Element Approximation on Tetrahedra","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3125933139","doi":"https://doi.org/10.1137/20m1333018","mag":"3125933139"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1333018","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091196582","display_name":"Mark Ainsworth","orcid":"https://orcid.org/0000-0002-4899-1048"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark Ainsworth","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101430629","display_name":"Shuai Jiang","orcid":"https://orcid.org/0000-0001-6395-9209"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shuai Jiang","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.888,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.805927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":80,"max":82},"biblio":{"volume":"43","issue":"1","first_page":"A384","last_page":"A414"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9996,"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":0.9996,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.999,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9987,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/basis","display_name":"Basis (linear algebra)","score":0.7672616},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.6302865},{"id":"https://openalex.org/keywords/mass-matrix","display_name":"Mass matrix","score":0.5912091},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.5855576},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5647421},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.54807097}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.91585964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.77959925},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7672616},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6313138},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.6302865},{"id":"https://openalex.org/C135585149","wikidata":"https://www.wikidata.org/wiki/Q339704","display_name":"Mass matrix","level":3,"score":0.5912091},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.5855576},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5647421},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.54807097},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.47072497},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.47059026},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46907443},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33680168},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22920093},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.16623452},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.120482564},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.063679636},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0},{"id":"https://openalex.org/C185544564","wikidata":"https://www.wikidata.org/wiki/Q81197","display_name":"Nuclear physics","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1333018","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320333566","funder_display_name":"National Defense Science and Engineering Graduate","award_id":null}],"datasets":[],"versions":[],"referenced_works_count":25,"referenced_works":["https://openalex.org/W122787279","https://openalex.org/W1592415565","https://openalex.org/W1969745760","https://openalex.org/W1981807311","https://openalex.org/W1988228958","https://openalex.org/W1992121802","https://openalex.org/W1995795749","https://openalex.org/W2000479313","https://openalex.org/W2006640177","https://openalex.org/W2008848819","https://openalex.org/W2023954922","https://openalex.org/W2032255647","https://openalex.org/W2038220764","https://openalex.org/W2057235948","https://openalex.org/W2061253771","https://openalex.org/W2064307182","https://openalex.org/W2071289502","https://openalex.org/W2074250763","https://openalex.org/W2077670970","https://openalex.org/W2088353152","https://openalex.org/W2104126767","https://openalex.org/W2133278728","https://openalex.org/W2135723931","https://openalex.org/W2915180890","https://openalex.org/W2923440116"],"related_works":["https://openalex.org/W3124183851","https://openalex.org/W2772495847","https://openalex.org/W2466318204","https://openalex.org/W2337689163","https://openalex.org/W2283733296","https://openalex.org/W2117618344","https://openalex.org/W2117324810","https://openalex.org/W2108653069","https://openalex.org/W1979539876","https://openalex.org/W1518768192"],"abstract_inverted_index":{"A":[0],"preconditioner":[1,39,106,136],"for":[2,6],"the":[3,28,32,36,52,65,71,74,78,97,105,117,135],"mass":[4,80],"matrix":[5,81],"high":[7,47],"order":[8,34,48,132],"finite":[9],"element":[10],"discretization":[11],"on":[12,101],"tetrahedra":[13],"is":[14,24,40,68,82,99],"presented":[15],"and":[16,31,94],"shown":[17,69],"to":[18,85,110,122,133,137,144],"give":[19],"a":[20,45,124],"condition":[21],"number":[22],"that":[23,70,77],"independent":[25,91],"of":[26,35,44,64,92,113,149],"both":[27],"mesh":[29],"size":[30],"polynomial":[33],"elements.":[37],"The":[38],"described":[41],"in":[42,131],"terms":[43],"new,":[46],"basis":[49,72,118],"which":[50],"has":[51],"usual":[53],"property":[54,76],"whereby":[55],"individual":[56],"functions":[57],"are":[58],"associated":[59],"with":[60,89],"distinct":[61],"geometric":[62],"entities":[63],"tetrahedron.":[66],"It":[67],"enjoys":[73],"novel":[75],"resulting":[79],"spectrally":[83],"equivalent":[84],"its":[86],"own":[87],"diagonal":[88],"constants":[90],"h":[93],"p.":[95],"Although":[96],"exposition":[98],"based":[100],"an":[102,138,146],"explicit":[103],"basis,":[104,140],"can":[107,119],"be":[108,120],"applied":[109],"any":[111],"choice":[112],"basis.":[114,150],"In":[115],"particular,":[116],"used":[121],"specify":[123],"basis-independent":[125],"additive":[126],"Schwarz":[127],"method,":[128],"meaning":[129],"that,":[130],"apply":[134],"alternative":[139],"one":[141],"only":[142],"need":[143],"implement":[145],"appropriate":[147],"change":[148]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3125933139","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2025-03-22T21:24:09.422677","created_date":"2021-02-01"}