{"id":"https://openalex.org/W2037838607","doi":"https://doi.org/10.1137/s0036142901399793","title":"A Nonoverlapping Domain Decomposition Method for Orthogonal Spline Collocation Problems","display_name":"A Nonoverlapping Domain Decomposition Method for Orthogonal Spline Collocation Problems","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2037838607","doi":"https://doi.org/10.1137/s0036142901399793","mag":"2037838607"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901399793","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901399793","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5066709922","display_name":"Bernard Bialecki","orcid":null},"institutions":[{"id":"https://openalex.org/I167576493","display_name":"Colorado School of Mines","ror":"https://ror.org/04raf6v53","country_code":"US","type":"education","lineage":["https://openalex.org/I167576493"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bernard Bialecki","raw_affiliation_strings":["Colorado School Of Mines"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Colorado School Of Mines","institution_ids":["https://openalex.org/I167576493"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111838056","display_name":"Maksymilian Dryja","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maksymilian Dryja","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8948,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74340583,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"41","issue":"5","first_page":"1709","last_page":"1728"},"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":0.9975000023841858,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8363592624664307},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.7209242582321167},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6113386750221252},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.574583113193512},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.46760764718055725},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.45858144760131836},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44395965337753296},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4327091574668884},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4310798645019531},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.4261524975299835},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4146574139595032},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1986319124698639},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.17741039395332336},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.14744064211845398},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.07636329531669617},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.0744662880897522}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8363592624664307},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.7209242582321167},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6113386750221252},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.574583113193512},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.46760764718055725},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.45858144760131836},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44395965337753296},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4327091574668884},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4310798645019531},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.4261524975299835},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4146574139595032},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1986319124698639},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.17741039395332336},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.14744064211845398},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.07636329531669617},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0744662880897522},{"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/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142901399793","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901399793","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W241441376","https://openalex.org/W577962163","https://openalex.org/W1542243431","https://openalex.org/W1970643355","https://openalex.org/W1989485818","https://openalex.org/W1995531080","https://openalex.org/W2000582360","https://openalex.org/W2025591043","https://openalex.org/W2041523977","https://openalex.org/W2045662757","https://openalex.org/W2051392682","https://openalex.org/W2062618977","https://openalex.org/W2065907281","https://openalex.org/W2086296535","https://openalex.org/W2090072162","https://openalex.org/W2104126767","https://openalex.org/W2166217501","https://openalex.org/W4244835284"],"related_works":["https://openalex.org/W1482343169","https://openalex.org/W2021938426","https://openalex.org/W4206513033","https://openalex.org/W2327379900","https://openalex.org/W2296924041","https://openalex.org/W2890254931","https://openalex.org/W2791210196","https://openalex.org/W2313741786","https://openalex.org/W2347304635","https://openalex.org/W1972581143"],"abstract_inverted_index":{"Anonoverlapping":[0],"domain":[1],"decomposition":[2,80],"approach":[3],"is":[4,60,75,93,106],"used":[5],"on":[6,32,57,72],"uniform":[7],"and":[8,14,39,45,68],"matching":[9],"grids":[10],"to":[11,16],"first":[12],"define":[13],"then":[15],"compute":[17],"the":[18,24,42,63,69,91,98,103],"orthogonal":[19],"spline":[20],"collocation":[21,43,55,70,104],"solution":[22,44,56,71,105],"of":[23,41,90,100],"Dirichlet":[25],"boundary":[26],"value":[27],"problem":[28],"for":[29,52],"Poisson's":[30],"equation":[31],"an":[33],"L-shaped":[34],"region.":[35],"We":[36],"prove":[37],"existence":[38],"uniqueness":[40],"derive":[46],"optimal":[47],"order":[48],"Hs-norm":[49],"error":[50],"bounds":[51],"s=0,1,2$.":[53],"The":[54,87],"two":[58],"interfaces":[59],"computed":[61,76],"using":[62],"preconditioned":[64],"conjugate":[65],"gradient":[66],"method,":[67],"three":[73],"squares":[74],"by":[77],"a":[78],"matrix":[79],"method":[81],"that":[82],"uses":[83],"fast":[84],"Fourier":[85],"transforms.":[86],"total":[88],"cost":[89],"algorithm":[92],"O(N2":[94,107],"\\log":[95],"N),":[96],"where":[97],"number":[99],"unknowns":[101],"in":[102],")$.":[108]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
