{"id":"W3028879718","doi":"10.1007/s10444-021-09889-0","title":"Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification","year":2021,"lang":"en","type":"preprint","venue":"Advances in Computational Mathematics","topic":"Electromagnetic Scattering and Analysis","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Centre for Doctoral Training in Statistical Applied Mathematics, University of Bath; Universität Heidelberg; Universität Zürich; Simon Fraser University; Engineering and Physical Sciences Research Council; Eidgenössische Technische Hochschule Zürich; Institut national de recherche en informatique et en automatique (INRIA)","keywords":"Nabla symbol; Preconditioner; Helmholtz equation; Mathematics; Galerkin method; Dirichlet distribution; Helmholtz free energy; Inverse; Discontinuous Galerkin method; Combinatorics; Finite element method; Mathematical analysis; Applied mathematics; Physics; Geometry; Quantum mechanics; Linear system; Omega; Thermodynamics","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":[],"consensus_categories":[],"category_scores_codex":[0.0002001919,0.0002054286,0.0006167818,0.0003288842,0.00004693313,0.00006778946,0.000206913,0.00006222499,0.0002434292],"category_scores_gemma":[0.00001840015,0.0002202693,0.0002451811,0.0009321899,0.00005826142,0.0001054925,0.00009848605,0.0002353725,0.000001701881],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004630633,"about_ca_system_score_gemma":0.00008594841,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009421262,"about_ca_topic_score_gemma":0.00001723854,"domain_scores_codex":[0.9983473,0.00006829855,0.0007500052,0.0003869501,0.0002866818,0.0001607411],"domain_scores_gemma":[0.9983757,0.0003982664,0.000687638,0.0002623702,0.0002441352,0.00003193217],"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":[0.000001691081,0.0003200002,0.008164471,0.0002202165,0.0008239497,2.502825e-7,0.0005239027,0.9838683,0.0002372822,0.003207665,0.00001991843,0.00261237],"study_design_scores_gemma":[0.0002032521,0.00002087541,0.002263248,0.0004748464,0.0008937871,3.250667e-7,0.0006529324,0.8645514,0.0005802759,0.130042,0.00001459892,0.000302403],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5237417,0.0006693429,0.4743131,0.00007019269,0.00004255551,0.0001764386,0.0002390291,0.00002116322,0.000726576],"genre_scores_gemma":[0.9409302,0.00002534246,0.05375589,0.000008282726,0.00002179167,0.00007349098,0.005097704,0.00001466273,0.00007263017],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4205572,"threshold_uncertainty_score":0.8982323,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009491627207898075,"score_gpt":0.2834346868438386,"score_spread":0.2739430596359405,"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."}}