EPJ Web Conf.
Volume 226, 2020Mathematical Modeling and Computational Physics 2019 (MMCP 2019)
|Number of page(s)||8|
|Section||Plenary and Invited Lectures|
|Published online||20 January 2020|
Local Versus Global Decisions in Bayesian Automatic Adaptive Quadrature
Laboratory of Information Technologies, Joint Institute for Nuclear Research,
6, Joliot Curie St.,
2 Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering (IFIN-HH), 30, Reactorului St., Mâgurele – Bucharest, 077125, Romania
Published online: 20 January 2020
The paper reports new significant enhancement of the robustness and effectiveness of the Bayesian automatic adaptive quadrature over macroscopic integration ranges. The implementation of a classical m-panel rule (CC-32, Clenshaw-Curtis quadrature of algebraic degree of precision m = 32) is thought again. It involves new global and local decisions blocks which, on the one side, provide sharp diagnostics redirecting the advancement to the solution and, on the other side, take advantage of the progress in the available hardware to accelerate and to increase the accuracy of the computations. Where the decision power of CC-32 is exhausted, identification and precise characterization of the features of the integrand profile which prevent quick convergence are obtained by means of three-point Simpson rules spanned at triplets of successive CC-32 knots. This local complementary investigation tool provides scale insensitive diagnostics concerning the occurrence of integrand irregularities and prevents the activation of inappropriate decision blocks which would result in fake outputs.
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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