{"id":"W4289281834","doi":"10.48550/arxiv.1811.09351","title":"A variationally separable splitting for the generalized-$α$ method for parabolic equations","year":2018,"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":"","funders":"Curtin Institute for Computation, Curtin University of Technology; American Chemical Society Petroleum Research Fund; Curtin University of Technology; Australian Government; Commonwealth Scientific and Industrial Research Organisation; Natural Sciences and Engineering Research Council of Canada; European Commission; Megagrants; University of Texas at Austin","keywords":"Discretization; Separable space; Mathematics; Solver; Norm (philosophy); Dissipation; Nabla symbol; Partial differential equation; Tensor product; Applied mathematics; Degrees of freedom (physics and chemistry); Mathematical analysis; Mathematical optimization; Physics; Pure mathematics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0007379057,0.0002822227,0.0003479625,0.0001079063,0.0002948884,0.00005427604,0.0005576625,0.0002013389,0.00002575563],"category_scores_gemma":[0.0008363971,0.000277313,0.0002729276,0.00030079,0.00006124657,0.00009334164,0.0001988369,0.0002561846,0.0000130625],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001913479,"about_ca_system_score_gemma":0.00009355824,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007430868,"about_ca_topic_score_gemma":0.000003341224,"domain_scores_codex":[0.9987264,0.0000922851,0.000314508,0.0004740928,0.00008182797,0.0003108805],"domain_scores_gemma":[0.9915607,0.007311489,0.0002047354,0.0004966819,0.0003526568,0.0000737122],"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":[0.00001486959,0.00001431564,0.000004286651,0.0001623496,0.0001726782,4.600734e-7,0.00007197789,0.7238331,0.00002598951,0.2745129,0.0003152267,0.0008717669],"study_design_scores_gemma":[0.0002092772,0.00001154567,0.0000111828,0.00002621859,0.0001415311,5.508468e-7,0.00001649029,0.5535486,0.00005322334,0.4436002,0.002208393,0.0001727077],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0007111066,0.0001256078,0.9961858,0.00008881462,0.0007623564,0.001256812,0.0001765671,0.000275904,0.0004170373],"genre_scores_gemma":[0.05191887,0.00005246591,0.9466854,0.00009472146,0.0005040309,0.00008553225,0.00006561486,0.00007479552,0.0005185553],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.1702845,"threshold_uncertainty_score":0.9999679,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1430149751047057,"score_gpt":0.2896863654150864,"score_spread":0.1466713903103806,"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."}}