{"id":"W2328773821","doi":"10.2514/6.2015-2915","title":"Development of Generalized Summation-by-Parts Operators for the Second Derivative with Variable Coefficients","year":2015,"lang":"en","type":"article","venue":"22nd AIAA Computational Fluid Dynamics Conference","topic":"Numerical methods for differential equations","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Constant coefficients; Partial derivative; Operator (biology); Differential operator; Variable (mathematics); Mathematics; Applied mathematics; Derivative (finance); Operator theory; Mathematical analysis; Partial differential equation; Variable coefficient; Dissipative system; Material derivative; Summation by parts; Physics","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":[0.0005407659,0.0002148663,0.0003189441,0.000066885,0.0002432876,0.00008043603,0.0003094902,0.00006234538,0.0000981118],"category_scores_gemma":[0.0004664105,0.0001538329,0.00004384373,0.0003117852,0.000147934,0.0001247068,0.00005964334,0.0000951137,0.000005309002],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001602104,"about_ca_system_score_gemma":0.000805017,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001176836,"about_ca_topic_score_gemma":0.00007260074,"domain_scores_codex":[0.9983023,0.0001211734,0.0005683282,0.0002735374,0.0005040561,0.0002305653],"domain_scores_gemma":[0.9966013,0.001524176,0.0002599087,0.0002048687,0.001289874,0.000119909],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001428544,0.0003588629,0.0001597436,0.0001203927,0.0003104271,3.111089e-7,0.003613282,0.0394979,0.001640075,0.9471915,0.0007438265,0.006220758],"study_design_scores_gemma":[0.001180317,0.00008449521,0.0001219836,0.00004748561,0.00004601611,0.00000190944,0.0004621767,0.7747101,0.001512712,0.2203971,0.001205545,0.0002301541],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.1353777,0.00001634381,0.8631835,0.0001411972,0.0001406281,0.0006605293,0.0002460515,0.00003458025,0.0001994665],"genre_scores_gemma":[0.3598537,3.804831e-7,0.6392736,0.00005782083,0.00001387317,0.00006469544,0.0003154246,0.00002139402,0.0003991334],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.7352121,"threshold_uncertainty_score":0.6273124,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07264775250010978,"score_gpt":0.3268645969518437,"score_spread":0.2542168444517339,"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."}}