{"id":"https://openalex.org/W1996356934","doi":"https://doi.org/10.1137/070700905","title":"Factorization Techniques for Nodal Spectral Elements in Curved Domains","display_name":"Factorization Techniques for Nodal Spectral Elements in Curved Domains","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1996356934","doi":"https://doi.org/10.1137/070700905","mag":"1996356934"},"language":"en","primary_location":{"id":"doi:10.1137/070700905","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070700905","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/A5035669714","display_name":"J\u00f6rg Stiller","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J\u00f6rg Stiller","raw_affiliation_strings":["joerg.stiller@tu-dresden.de#TAB#"],"affiliations":[{"raw_affiliation_string":"joerg.stiller@tu-dresden.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082796420","display_name":"Uwe Fladrich","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Uwe Fladrich","raw_affiliation_strings":["uwe.fladrich@tu-dresden.de#TAB#"],"affiliations":[{"raw_affiliation_string":"uwe.fladrich@tu-dresden.de#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035669714"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4629,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62692986,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"5","first_page":"2286","last_page":"2301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9987000226974487,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9986000061035156,"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":0.9930999875068665,"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/mathematics","display_name":"Mathematics","score":0.7662904262542725},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.7043837904930115},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6209996342658997},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4760546386241913},{"id":"https://openalex.org/keywords/curvilinear-coordinates","display_name":"Curvilinear coordinates","score":0.4431541860103607},{"id":"https://openalex.org/keywords/rotational-symmetry","display_name":"Rotational symmetry","score":0.44173744320869446},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4368906617164612},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4154888689517975},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3803745210170746},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2578532099723816},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.252675861120224},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09761705994606018}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7662904262542725},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.7043837904930115},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6209996342658997},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4760546386241913},{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.4431541860103607},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.44173744320869446},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4368906617164612},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4154888689517975},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3803745210170746},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2578532099723816},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.252675861120224},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09761705994606018},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070700905","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070700905","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":[{"score":0.6600000262260437,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1968345767","https://openalex.org/W1973681957","https://openalex.org/W1987498275","https://openalex.org/W1991950983","https://openalex.org/W2003408966","https://openalex.org/W2008021403","https://openalex.org/W2021442891","https://openalex.org/W2041640855","https://openalex.org/W2044695077","https://openalex.org/W2047352485","https://openalex.org/W2049487270","https://openalex.org/W2049548546","https://openalex.org/W2066985111","https://openalex.org/W2076987291","https://openalex.org/W2081163355","https://openalex.org/W2104724067","https://openalex.org/W2106828713","https://openalex.org/W2107940133","https://openalex.org/W2142296733"],"related_works":["https://openalex.org/W1639593894","https://openalex.org/W63200814","https://openalex.org/W2367601375","https://openalex.org/W2371750680","https://openalex.org/W2360227361","https://openalex.org/W2067779234","https://openalex.org/W1999171692","https://openalex.org/W1600077717","https://openalex.org/W60226892","https://openalex.org/W2149042794"],"abstract_inverted_index":{"Spectral":[0],"element":[1,169,181],"methods":[2],"on":[3,34,89],"tetrahedra":[4],"with":[5,73],"symmetric":[6],"collocation":[7,83],"points":[8],"can":[9,108],"be":[10,109],"accelerated":[11],"by":[12,82,131,155],"factorizing":[13],"the":[14,38,58,79,100,105,118,123,127,132,147,157,160,167,179],"discrete":[15,106],"operators":[16,107],"according":[17],"to":[18,44,71,111,122],"Hesthaven":[19],"and":[20],"Teng":[21],"[SIAM":[22],"J.":[23],"Sci.":[24],"Comput.,":[25],"21":[26],"(2000),":[27],"pp.":[28],"2352\u20132380].":[29],"While":[30],"these":[31],"authors":[32],"focused":[33],"first-order":[35],"conservation":[36],"laws,":[37],"present":[39],"paper":[40],"provides":[41],"an":[42],"extension":[43],"second-order":[45],"problems.":[46],"Though":[47],"factorization":[48,152],"is":[49,120,129,153,171],"easily":[50],"accomplished":[51],"for":[52],"planar":[53,124,180],"elements,":[54],"difficulties":[55],"arise":[56],"from":[57],"presence":[59],"of":[60,78,99],"variable":[61],"metric":[62,80,101],"coefficients":[63],"in":[64,146,159],"curved":[65,168],"tetrahedra.":[66],"Two":[67],"approaches":[68],"are":[69,143],"considered":[70],"cope":[72],"this":[74],"peculiarity:":[75],"(i)":[76],"approximation":[77],"terms":[81,102,142],"projection,":[84],"(ii)":[85],"Gauss":[86],"quadrature":[87,148,161],"based":[88],"axisymmetric":[90],"point":[91],"sets.":[92],"The":[93,135],"first":[94],"method":[95],"achieves":[96],"a":[97,116],"separation":[98],"such":[103],"that":[104,166],"reduced":[110],"factorizable":[112],"standard":[113],"matrices.":[114],"As":[115],"consequence,":[117],"performance":[119],"comparable":[121],"case,":[125],"whereas":[126],"accuracy":[128,139],"limited":[130],"projection":[133],"step.":[134],"second":[136],"approach":[137],"maintains":[138],"since":[140],"all":[141],"evaluated":[144],"individually":[145],"points.":[149,162],"Nonetheless,":[150],"complete":[151],"achieved":[154],"exploiting":[156],"symmetry":[158],"Performance":[163],"analysis":[164],"shows":[165],"operator":[170],"less":[172],"than":[173],"three":[174],"times":[175],"as":[176,178],"costly":[177],"counterpart.":[182]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
