{"id":"W4380362597","doi":"10.48550/arxiv.2306.05975","title":"Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Numerical Methods in Computational Mathematics","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; University of Toronto","keywords":"Curvilinear coordinates; Mathematics; Spectral element method; Symmetric tensor; Cartesian tensor; Tensor product; Context (archaeology); Polygon mesh; Mathematical analysis; Finite element method; Pure mathematics; Geometry; Tensor density; Tensor field; Mixed finite element method; Exact solutions in general relativity","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007296042,0.0004603987,0.0004817076,0.0003987149,0.0003376049,0.0008416481,0.001022478,0.0006273596,0.002341908],"category_scores_gemma":[0.002100187,0.0002479233,0.0005936134,0.0006202325,0.001018926,0.001294049,0.001713783,0.0009403218,0.0008842726],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003274148,"about_ca_system_score_gemma":0.0006357097,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008103066,"about_ca_topic_score_gemma":0.0008981811,"domain_scores_codex":[0.999564,0.0001132279,0.00002317282,0.00003173705,0.0002355538,0.00003233672],"domain_scores_gemma":[0.9992737,0.0002385054,0.00006808496,0.0001761934,0.0001875342,0.00005595994],"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":[0.0001053867,0.00006971323,0.0006264953,0.000209611,0.00003173832,0.0002055633,0.0004883585,0.4202182,0.04912132,0.4247698,0.001774517,0.1023792],"study_design_scores_gemma":[0.000006280562,0.00002687806,0.00004341865,0.000008990486,0.000003473752,0.00004467029,0.00002634655,0.9594601,0.005506009,0.03231204,0.002554006,0.000007807859],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.01078271,0.0000482322,0.9871551,0.00003644846,0.00002100183,0.00001870225,0.00001853186,0.0001136514,0.001805676],"genre_scores_gemma":[0.299709,0.0002128839,0.6947311,0.00007067288,0.00003304722,0.0001210562,0.0001218348,0.000238129,0.004762324],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.002341908,"threshold_uncertainty_score":0.007834435,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08686783605224799,"score_gpt":0.2179742355345931,"score_spread":0.1311063994823451,"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."}}