{"id":"W4382359695","doi":"10.1137/21m1431199","title":"Local Fourier Analysis of p-Multigrid for High-Order Finite Element Operators","year":2023,"lang":"en","type":"article","venue":"SIAM Journal on Scientific Computing","topic":"Advanced Numerical Methods in Computational Mathematics","field":"Engineering","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"U.S. Department of Energy","keywords":"Multigrid method; Finite element method; Discretization; Applied mathematics; Mathematics; Partial differential equation; Smoothing; Smoothed finite element method; Laplace operator; Mathematical analysis; Boundary knot method; Boundary element method","routes":{"ca_aff":true,"ca_fund":false,"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":[0.001777828,0.0001616868,0.0003895833,0.0008659957,0.0002769747,0.0001250528,0.0002715748,0.00004134277,0.00004400881],"category_scores_gemma":[0.0006072752,0.0001448969,0.0001778889,0.0034661,0.0000905402,0.00008255141,0.00006802844,0.0002232119,0.00002427181],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009726513,"about_ca_system_score_gemma":0.00003517275,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":3.512045e-7,"about_ca_topic_score_gemma":6.047897e-7,"domain_scores_codex":[0.9980698,0.00006230257,0.0007082905,0.0002389673,0.0005652468,0.0003554584],"domain_scores_gemma":[0.9970954,0.001964544,0.0001905216,0.000224813,0.0004060985,0.0001186164],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000004537696,0.00002341809,0.00003461349,0.00003822695,0.0002808234,0.000003674066,0.0002331092,0.9365,0.0003721869,0.001078173,0.0005457294,0.06088549],"study_design_scores_gemma":[0.0002547697,0.00005719663,0.000303732,0.00006256388,0.0001111803,0.000002020424,0.0001632207,0.9905824,0.001371774,0.004843796,0.002096149,0.0001512081],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09628818,0.0000344924,0.9013368,0.00004951268,0.001948798,0.0001340818,0.00002799288,0.0001127446,0.00006738253],"genre_scores_gemma":[0.5883028,0.000003804047,0.4114416,0.00002486487,0.0001110731,0.000002784113,0.00001971112,0.00002632474,0.0000670895],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.4920146,"threshold_uncertainty_score":0.5908725,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03755450190679228,"score_gpt":0.3413912804011748,"score_spread":0.3038367784943825,"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."}}