{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002090894,0.0007144113,0.0008063171,0.0006390397,0.0005032963,0.0009447333,0.000686422,0.001424659,0.003030833],"category_scores_gemma":[0.00656014,0.0003575527,0.0005625708,0.0003849154,0.001755335,0.00136732,0.002359651,0.001335283,0.0002015131],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008527543,"about_ca_system_score_gemma":0.000952253,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001784234,"about_ca_topic_score_gemma":0.001065581,"domain_scores_codex":[0.9991573,0.0003840253,0.00002508523,0.0001015546,0.0002327505,0.00009919963],"domain_scores_gemma":[0.9972731,0.001790266,0.0002670025,0.0001408912,0.0003445032,0.0001841396],"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":[0.0003574411,0.0001086691,0.001222464,0.0003011079,0.00005638376,0.0004638606,0.0002457385,0.5207868,0.01733269,0.4293319,0.002769623,0.02702332],"study_design_scores_gemma":[0.00000967046,0.00003728581,0.0001443712,0.0000155486,0.000008089046,0.00003191613,0.00003270037,0.9661829,0.001832024,0.03069049,0.001007332,0.000007726488],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08393469,0.000355914,0.8992954,0.0009495033,0.0001079731,0.00008660075,0.00007662084,0.0001814512,0.01501181],"genre_scores_gemma":[0.8470161,0.0003550852,0.1407933,0.0003316078,0.0001187947,0.0001093095,0.0001798658,0.0002078,0.01088818],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003030833,"threshold_uncertainty_score":0.01105785,"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."}}