{"id":"https://openalex.org/W1966165223","doi":"https://doi.org/10.1137/050647256","title":"Using High\u2010Order Methods on Adaptively Refined Block\u2010Structured Meshes: Derivatives, Interpolations, and Filters","display_name":"Using High\u2010Order Methods on Adaptively Refined Block\u2010Structured Meshes: Derivatives, Interpolations, and Filters","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1966165223","doi":"https://doi.org/10.1137/050647256","mag":"1966165223"},"language":"en","primary_location":{"id":"doi:10.1137/050647256","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050647256","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/A5075624899","display_name":"Jaideep Ray","orcid":"https://orcid.org/0009-0000-9908-7035"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jaideep Ray","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053086368","display_name":"Christopher Kennedy","orcid":"https://orcid.org/0000-0001-8812-4451"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christopher A. Kennedy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057730779","display_name":"Sophia Lefantzi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sophia Lefantzi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075501406","display_name":"Habib N. Najm","orcid":"https://orcid.org/0000-0002-6338-7260"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Habib N. Najm","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":3.3258,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.90842727,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","issue":"1","first_page":"139","last_page":"181"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994000196456909,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994000196456909,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"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/T10514","display_name":"Numerical methods in engineering","score":0.9980000257492065,"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/stencil","display_name":"Stencil","score":0.930456817150116},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6880925297737122},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5759341716766357},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.574260950088501},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5726763010025024},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5395109057426453},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.49387890100479126},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.49011000990867615},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.46794524788856506},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.44922935962677},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4314143657684326},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.42932936549186707},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.4125911593437195},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3985070288181305},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.32193756103515625},{"id":"https://openalex.org/keywords/multivariate-interpolation","display_name":"Multivariate interpolation","score":0.29929018020629883},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.1584438681602478},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15021532773971558},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13339832425117493},{"id":"https://openalex.org/keywords/method-of-characteristics","display_name":"Method of characteristics","score":0.09669375419616699}],"concepts":[{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.930456817150116},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6880925297737122},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5759341716766357},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.574260950088501},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5726763010025024},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5395109057426453},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.49387890100479126},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.49011000990867615},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.46794524788856506},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.44922935962677},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4314143657684326},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.42932936549186707},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.4125911593437195},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3985070288181305},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.32193756103515625},{"id":"https://openalex.org/C203332170","wikidata":"https://www.wikidata.org/wiki/Q6334079","display_name":"Multivariate interpolation","level":3,"score":0.29929018020629883},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.1584438681602478},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15021532773971558},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13339832425117493},{"id":"https://openalex.org/C33163149","wikidata":"https://www.wikidata.org/wiki/Q1785085","display_name":"Method of characteristics","level":3,"score":0.09669375419616699},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050647256","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050647256","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":31,"referenced_works":["https://openalex.org/W830650959","https://openalex.org/W1564075061","https://openalex.org/W1575549230","https://openalex.org/W1969555281","https://openalex.org/W1972350124","https://openalex.org/W1976349874","https://openalex.org/W1988314584","https://openalex.org/W1991962363","https://openalex.org/W2006770307","https://openalex.org/W2017400139","https://openalex.org/W2021121593","https://openalex.org/W2029520499","https://openalex.org/W2029786748","https://openalex.org/W2031998851","https://openalex.org/W2051465806","https://openalex.org/W2054739989","https://openalex.org/W2057109824","https://openalex.org/W2065932192","https://openalex.org/W2066812059","https://openalex.org/W2076502454","https://openalex.org/W2077047259","https://openalex.org/W2101503265","https://openalex.org/W2108242008","https://openalex.org/W2155276545","https://openalex.org/W2166536848","https://openalex.org/W2176197873","https://openalex.org/W2334954231","https://openalex.org/W4234402868","https://openalex.org/W4240530219","https://openalex.org/W4292169137","https://openalex.org/W4382891143"],"related_works":["https://openalex.org/W4389319301","https://openalex.org/W4389116067","https://openalex.org/W2383156613","https://openalex.org/W2793633700","https://openalex.org/W3016193330","https://openalex.org/W4316371992","https://openalex.org/W2765282948","https://openalex.org/W2983482276","https://openalex.org/W2146791968","https://openalex.org/W2067136911"],"abstract_inverted_index":{"Block\u2010structured":[0],"adaptive":[1],"mesh":[2,22,205],"refinement":[3],"(AMR)":[4],"is":[5,147,163,188,206,227],"used":[6,274],"for":[7,84,93],"efficient":[8],"resolution":[9,202],"of":[10,48,141,182,184,197,203,212,217,252,257],"partial":[11],"differential":[12],"equations":[13],"(PDEs)":[14],"solved":[15],"on":[16,40,152],"large":[17,28],"computational":[18,59],"domains":[19],"by":[20,27,43,80,172,208],"clustering":[21],"points":[23],"only":[24],"where":[25],"required":[26],"gradients.":[29],"Previous":[30],"work":[31],"has":[32],"indicated":[33],"that":[34,121,124],"fourth\u2010order":[35],"convergence":[36],"can":[37,56,240],"be":[38,150,241],"achieved":[39],"such":[41],"meshes":[42],"using":[44,104,166],"a":[45,105,132,138,281],"suitable":[46],"combination":[47],"high\u2010order":[49,94,110],"derivative,":[50,95,218,235],"interpolation,":[51,96,219,236],"and":[52,55,87,97,168,220,229,237,247],"filter":[53,98,221,238],"stencils":[54,99,115,273],"deliver":[57],"significant":[58],"savings":[60],"over":[61],"conventional":[62],"second\u2010order":[63],"methods":[64,259],"at":[65],"engineering":[66],"error":[67],"tolerances.":[68],"In":[69],"this":[70,268,276],"paper,":[71],"we":[72],"explore":[73],"the":[74,77,81,119,122,143,153,158,174,180,185,193,200,204,234,250,272],"interactions":[75],"between":[76],"errors":[78],"introduced":[79],"discretized":[82],"operators":[83],"derivatives,":[85],"interpolations,":[86],"filters.":[88],"We":[89,190],"develop":[90],"general":[91],"expressions":[92],"applicable":[100],"in":[101,157,176,275],"multiple":[102],"dimensions,":[103],"Fourier":[106],"approach,":[107],"to":[108,128,149,244],"facilitate":[109],"block\u2010structured":[111],"AMR":[112],"implementations.":[113],"These":[114],"are":[116,126,129,278],"derived":[117],"under":[118],"assumption":[120],"fields":[123],"they":[125],"applied":[127],"smooth.":[130],"For":[131],"given":[133,139],"derivative":[134,156],"stencil":[135,187],"(and":[136],"thus":[137],"order":[140,146,181,196],"accuracy),":[142],"necessary":[144],"interpolation":[145,186,253],"found":[148],"dependent":[151],"highest":[154],"spatial":[155],"PDE":[159],"being":[160],"solved.":[161],"This":[162],"demonstrated":[164],"empirically,":[165],"one\u2010":[167],"two\u2010dimensional":[169],"model":[170],"equations,":[171],"observing":[173],"increase":[175],"delivered":[177],"accuracy":[178,183],"as":[179,199,280],"increased.":[189],"also":[191],"examine":[192],"empirically":[194],"observed":[195],"convergence,":[198],"effective":[201],"increased":[207],"successively":[209],"adding":[210],"levels":[211],"refinement,":[213],"with":[214,271],"different":[215],"orders":[216,246],"stencils.":[222],"The":[223,255],"procedure":[224],"devised":[225],"here":[226],"modular":[228],"its":[230],"various":[231],"pieces,":[232],"i.e.,":[233],"stencils,":[239],"extended":[242],"independently":[243],"higher":[245],"dimensions":[248],"(in":[249],"case":[251],"stencils).":[254],"application":[256],"these":[258],"often":[260],"requires":[261],"nontrivial":[262],"logic,":[263,269],"especially":[264],"near":[265],"domain":[266],"boundaries;":[267],"along":[270],"study,":[277],"available":[279],"freely":[282],"downloadable":[283],"software":[284],"library.":[285]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
