{"id":"W4366774998","doi":"10.1002/nla.2500","title":"A closed‐form multigrid smoothing factor for an additive Vanka‐type smoother applied to the Poisson equation","year":2023,"lang":"en","type":"article","venue":"Numerical Linear Algebra with Applications","topic":"Numerical methods in engineering","field":"Engineering","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Poisson's equation; Smoothing; Finite element method; Mathematical analysis; Multigrid method; Applied mathematics; Discretization; Discrete Poisson equation; Partial differential equation; Mixed finite element method; Mass matrix; Laplace's equation","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002285334,0.0003132108,0.0002949715,0.0001504549,0.0002362013,0.00006185732,0.0004246183,0.0001238522,0.00004950235],"category_scores_gemma":[0.0001445504,0.0002381211,0.00007114072,0.001708383,0.0000431191,0.0001333643,0.00004858831,0.0003287639,0.0003913331],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001171466,"about_ca_system_score_gemma":0.00002694798,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001370407,"about_ca_topic_score_gemma":0.000007173167,"domain_scores_codex":[0.9983354,0.00002789662,0.000340587,0.000447055,0.0003062043,0.0005428477],"domain_scores_gemma":[0.9983243,0.0006227921,0.00006007436,0.0006097758,0.0001202056,0.0002628282],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001383485,0.0001364237,0.00005580768,0.0001125292,0.0002063231,0.000001057454,0.003409732,0.4724203,0.0164347,0.01107905,0.001785348,0.4942203],"study_design_scores_gemma":[0.0005265484,0.0002575342,0.002245731,0.00002437897,0.00005855197,0.000002150718,0.0003312006,0.715124,0.005838426,0.002013496,0.2728923,0.0006857419],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.006537445,0.00002470699,0.9881756,0.0004134899,0.0001763573,0.002256298,0.0001992582,0.001618301,0.0005985495],"genre_scores_gemma":[0.6479748,0.00001580004,0.3455301,0.0003698639,0.0007764697,0.0047889,0.000223512,0.0002285595,0.00009198485],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.6426455,"threshold_uncertainty_score":0.9710295,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03566184032007813,"score_gpt":0.2983817119453563,"score_spread":0.2627198716252782,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}