{"id":"https://openalex.org/W2021377936","doi":"https://doi.org/10.1137/0916076","title":"Multi-<i>P</i> Methods: Iterative Algorithms for the <i>P</i>-Version of the Finite Element Analysis","display_name":"Multi-<i>P</i> Methods: Iterative Algorithms for the <i>P</i>-Version of the Finite Element Analysis","publication_year":1995,"publication_date":"1995-11-01","ids":{"openalex":"https://openalex.org/W2021377936","doi":"https://doi.org/10.1137/0916076","mag":"2021377936"},"language":"en","primary_location":{"id":"doi:10.1137/0916076","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0916076","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100783980","display_name":"Ning Hu","orcid":"https://orcid.org/0000-0002-6444-8467"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ning Hu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109654487","display_name":"I. Norman Katz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"I. Norman Katz","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":1.0565,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.74227835,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"6","first_page":"1308","last_page":"1332"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9968000054359436,"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/mathematics","display_name":"Mathematics","score":0.7376836538314819},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6819690465927124},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5894687175750732},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.5373249650001526},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.497254878282547},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46996232867240906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20791274309158325},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.1242763102054596},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.08112969994544983}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7376836538314819},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6819690465927124},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5894687175750732},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.5373249650001526},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.497254878282547},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46996232867240906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20791274309158325},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.1242763102054596},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.08112969994544983},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0916076","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0916076","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1519938374","https://openalex.org/W1967820494","https://openalex.org/W1980158900","https://openalex.org/W1988913405","https://openalex.org/W1989009729","https://openalex.org/W2001415695","https://openalex.org/W2023630575","https://openalex.org/W2028357997","https://openalex.org/W2041607840","https://openalex.org/W2044809480","https://openalex.org/W2056040698","https://openalex.org/W2064625750","https://openalex.org/W2065651109","https://openalex.org/W2067484330","https://openalex.org/W2113700277","https://openalex.org/W2124387207","https://openalex.org/W2151317657","https://openalex.org/W2168329017","https://openalex.org/W2319687096","https://openalex.org/W2555826189","https://openalex.org/W3147736755","https://openalex.org/W4213380965","https://openalex.org/W4230055019","https://openalex.org/W4301859080"],"related_works":["https://openalex.org/W2113718785","https://openalex.org/W2182869042","https://openalex.org/W2110063879","https://openalex.org/W2052433444","https://openalex.org/W1987150538","https://openalex.org/W1519938374","https://openalex.org/W2182328658","https://openalex.org/W4205238550","https://openalex.org/W1987597427","https://openalex.org/W1527096857"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"classical":[2],"multigrid":[3],"methods,":[4,25,73],"which":[5,26],"are":[6,27,117],"based":[7,28],"on":[8,29,104],"either":[9],"the":[10,15,18,30,33,66,71,76,98],"finite":[11,19,34],"difference":[12],"method":[13,36],"or":[14],"h-version":[16],"of":[17,32,46,84],"element":[20,35],"method,":[21],"we":[22,74],"study":[23],"multi-p":[24,47,62,68,79,85,100,115],"p-version":[31],"and":[37,54,91,111],"hierarchical":[38],"shape":[39],"functions.":[40],"We":[41,57],"have":[42,58,88,108],"developed":[43],"a":[44],"class":[45],"V-cycle":[48,53,72,80,86],"algorithms:":[49],"standard":[50],"V-cycle,":[51],"modified":[52],"varying":[55],"V-cycle.":[56],"also":[59],"studied":[60],"nested":[61,67,99],"methods.":[63,101],"By":[64],"combining":[65],"methods":[69,87,116],"with":[70],"obtain":[75],"so-called":[77],"\u201caccelerated":[78],"methods.\u201d":[81],"The":[82],"convergence":[83],"been":[89,109],"investigated":[90],"an":[92],"error":[93],"estimate":[94],"is":[95],"given":[96],"for":[97],"Numerical":[102],"experiments":[103],"representative":[105],"sample":[106],"problems":[107],"conducted":[110],"indicate":[112],"that":[113],"our":[114],"very":[118],"efficient.":[119]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}