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Advanced Quasi-Monte Carlo Algorithms for Multidimensional Integrals in Air Pollution Modelling

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Advances in High Performance Computing (HPC 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 902))

Abstract

Sensitivity analysis is a powerful tool for studying and improving the reliability of mathematical models. Air pollution and meteorological models are in front places among the examples of mathematical models with a lot of natural uncertainties in their input data sets and parameters. In this work some results of the global sensitivity study of the Unified Danish Eulerian Model (UNI-DEM) have been presented. One of the most attractive features of UNI-DEM is its advanced chemical scheme – the Condensed CBM IV, which consider a large number of chemical species and numerous reactions between them, of which the ozone is one of the most important pollutants for its central role in many practical applications of the results. A comprehensive experimental study of quasi-Monte Carlo algorithms based on lattice sequences with different generating vectors for multidimensional numerical integration has been done. The Fibonacci based lattice rule is compared with other types of lattice rules. The performance of a lattice rule depends on the choice of the generator vectors. When the integrand is sufficiently regular the lattice rules outperform not only the standard Monte Carlo methods, but also other types of methods using low discrepancy sequences.

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Acknowledgements

Venelin Todorov is supported by the Bulgarian National Science Fund under Young Scientists Project KP-06-M32/2 - 17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics” and by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICT in SES)”, Task 1.2.5., financed by the Ministry of Education and Science in Bulgaria. The work is also supported by the Bulgarian National Science Fund under Project DN 12/5-2017 “Efficient Stochastic Methods and Algorithms for Large-Scale Problems”.

Author information

Authors and Affiliations

  1. Institute of Information and Communication Technologies, Department of Parallel Algorithms, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Venelin Todorov, Ivan Dimov & Tzvetan Ostromsky

  2. Institute of Mathematics and Informatics, Department of Information Modeling, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Venelin Todorov

  3. National Centre for Environment and Energy, University of Århus, Frederiksborgvej 399, P. O. Box 358, 4000, Roskilde, Denmark

    Zahari Zlatev

Authors
  1. Venelin Todorov
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  2. Ivan Dimov
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  3. Tzvetan Ostromsky
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  4. Zahari Zlatev
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Corresponding author

Correspondence to Venelin Todorov .

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Todorov, V., Dimov, I., Ostromsky, T., Zlatev, Z. (2021). Advanced Quasi-Monte Carlo Algorithms for Multidimensional Integrals in Air Pollution Modelling. In: Dimov, I., Fidanova, S. (eds) Advances in High Performance Computing. HPC 2019. Studies in Computational Intelligence, vol 902. Springer, Cham. https://doi.org/10.1007/978-3-030-55347-0_14

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