{"id":"https://openalex.org/W2987432592","doi":"https://doi.org/10.1109/cluster.2019.8891018","title":"Scalable, High-Order Continuity Across Block Boundaries of Functional Approximations Computed in Parallel","display_name":"Scalable, High-Order Continuity Across Block Boundaries of Functional Approximations Computed in Parallel","publication_year":2019,"publication_date":"2019-09-01","ids":{"openalex":"https://openalex.org/W2987432592","doi":"https://doi.org/10.1109/cluster.2019.8891018","mag":"2987432592"},"language":"en","primary_location":{"id":"doi:10.1109/cluster.2019.8891018","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cluster.2019.8891018","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Conference on Cluster Computing (CLUSTER)","raw_type":"proceedings-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/A5058960340","display_name":"Iulian Grindeanu","orcid":"https://orcid.org/0000-0002-0264-8236"},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Iulian Grindeanu","raw_affiliation_strings":["Argonne National Laboratory, Lemont, IL, USA"],"affiliations":[{"raw_affiliation_string":"Argonne National Laboratory, Lemont, IL, USA","institution_ids":["https://openalex.org/I1282105669"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057612088","display_name":"Tom Peterka","orcid":null},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tom Peterka","raw_affiliation_strings":["Argonne National Laboratory, Lemont, IL, USA"],"affiliations":[{"raw_affiliation_string":"Argonne National Laboratory, Lemont, IL, USA","institution_ids":["https://openalex.org/I1282105669"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034282541","display_name":"Vijay Mahadevan","orcid":"https://orcid.org/0000-0002-3337-2607"},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vijay S. Mahadevan","raw_affiliation_strings":["Argonne National Laboratory, Lemont, IL, USA"],"affiliations":[{"raw_affiliation_string":"Argonne National Laboratory, Lemont, IL, USA","institution_ids":["https://openalex.org/I1282105669"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023994860","display_name":"Youssef S. G. Nashed","orcid":"https://orcid.org/0000-0001-6146-3939"},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Youssef S. G. Nashed","raw_affiliation_strings":["Argonne National Laboratory, Lemont, IL, USA"],"affiliations":[{"raw_affiliation_string":"Argonne National Laboratory, Lemont, IL, USA","institution_ids":["https://openalex.org/I1282105669"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5058960340"],"corresponding_institution_ids":["https://openalex.org/I1282105669"],"apc_list":null,"apc_paid":null,"fwci":0.5675,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.65866354,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":null,"first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991000294685364,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991000294685364,"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":0.9944999814033508,"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/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6426217555999756},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5318909287452698},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45608800649642944},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4526975452899933},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.41278648376464844},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39723125100135803},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35106945037841797},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3418491780757904},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3007124960422516},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09145820140838623}],"concepts":[{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6426217555999756},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5318909287452698},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45608800649642944},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4526975452899933},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.41278648376464844},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39723125100135803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35106945037841797},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3418491780757904},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3007124960422516},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09145820140838623},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cluster.2019.8891018","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cluster.2019.8891018","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Conference on Cluster Computing (CLUSTER)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1507807393","https://openalex.org/W1542243431","https://openalex.org/W1583788335","https://openalex.org/W1603304768","https://openalex.org/W1861537833","https://openalex.org/W1960418590","https://openalex.org/W1965697623","https://openalex.org/W1981812667","https://openalex.org/W2009997314","https://openalex.org/W2018039791","https://openalex.org/W2030907924","https://openalex.org/W2036463286","https://openalex.org/W2039470961","https://openalex.org/W2074189597","https://openalex.org/W2089001914","https://openalex.org/W2112066591","https://openalex.org/W2123224804","https://openalex.org/W2126777570","https://openalex.org/W2146417834","https://openalex.org/W2291283624","https://openalex.org/W2336396212","https://openalex.org/W2622745967","https://openalex.org/W2739589480","https://openalex.org/W2953027876","https://openalex.org/W2954055238","https://openalex.org/W3130894512","https://openalex.org/W4205462863","https://openalex.org/W4205649593","https://openalex.org/W4249019869"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2389214306","https://openalex.org/W4235240664","https://openalex.org/W2965083567","https://openalex.org/W1838576100","https://openalex.org/W2095886385","https://openalex.org/W2889616422","https://openalex.org/W2089704382","https://openalex.org/W1983399550","https://openalex.org/W2348315137"],"abstract_inverted_index":{"We":[0,86,108,148],"investigate":[1],"the":[2,61,75,113,131,139],"representation":[3],"of":[4,63,126,161],"discrete":[5],"scientific":[6],"data":[7],"with":[8],"a":[9,26,37,57,135],"C":[10,17,68,100],"<sup":[11,18,69,101],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[12,19,70,102],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</sup>":[13,20,71,103],"functional":[14,39],"model,":[15],"where":[16],"denotes":[21],"k-th":[22],"order":[23],"continuity,":[24],"in":[25,51,56,115,134],"distributed-memory":[27],"parallel":[28,52],"setting.":[29],"The":[30],"Multivariate":[31],"Functional":[32],"Approximation":[33],"(MFA)":[34],"model":[35],"is":[36,165],"piecewise-continuous":[38],"approximation":[40,50,163],"based":[41],"on":[42,167],"multi-variate":[43],"high-dimensional":[44],"B-splines.":[45],"When":[46],"computing":[47,169],"an":[48,88,158],"MFA":[49],"over":[53],"multiple":[54],"blocks":[55,118,121],"spatial":[58],"domain":[59,114,141],"decomposition,":[60],"interior":[62],"each":[64],"block":[65,84,106],"will":[66],"be":[67,155],",":[72],"k":[73],"being":[74],"B-spline":[76],"polynomial":[77],"degree,":[78],"but":[79],"discontinuities":[80],"exist":[81],"across":[82,105],"neighboring":[83,96],"boundaries.":[85,107],"present":[87],"efficient":[89],"and":[90,119],"scalable":[91,166],"solution":[92],"that":[93,110,150],"involves":[94],"blending":[95],"approximations":[97],"to":[98,123,138],"ensure":[99],"continuity":[104],"show":[109],"after":[111],"decomposing":[112],"structured,":[116],"overlapping":[117],"approximating":[120],"independently":[122],"high":[124],"degrees":[125],"accuracy,":[127],"we":[128],"can":[129,154],"extend":[130],"local":[132],"solution,":[133],"postprocessing":[136],"step,":[137],"global":[140],"by":[142],"using":[143],"compact,":[144],"multidimensional":[145],"smoothstep":[146],"functions.":[147],"prove":[149],"this":[151],"approach,":[152],"which":[153],"viewed":[156],"as":[157],"extended":[159],"partition":[160],"unity":[162],"method,":[164],"high-performance":[168],"architectures.":[170]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
