On quasirandom sequences for numerical computations
USSR Computational Mathematics and Mathematical Physics
Quadrature formulae for functions of several variables satisfying a general Lipschitz condition
USSR Computational Mathematics and Mathematical Physics
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
On the L2-discrepancy for anchored boxes
Journal of Complexity
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Modeling the Long-Range Transport of Air Pollutants
IEEE Computational Science & Engineering
Algorithm 823: Implementing scrambled digital sequences
ACM Transactions on Mathematical Software (TOMS)
Monte Carlo Methods for Applied Scientists
Monte Carlo Methods for Applied Scientists
Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models
Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models
Operator splitting and commutativity analysis in the Danish Eulerian model
Mathematics and Computers in Simulation
Constructing Sobol Sequences with Better Two-Dimensional Projections
SIAM Journal on Scientific Computing
A Randomized Quasi-Monte Carlo Simulation Method for Markov Chains
Operations Research
Studying the sensitivity of pollutants' concentrations caused by variations of chemical rates
Journal of Computational and Applied Mathematics
Monte Carlo method for numerical integration based on Sobol's sequences
NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
On the scrambled soboĺ sequence
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
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In this paper advanced variance-based algorithms for global sensitivity analysis are studied. We consider efficient algorithms, such as Monte Carlo, quasi-Monte Carlo (QMC) and scrambled quasi-Monte Carlo algorithms based on Sobol sequences. Low discrepancy @L@P"@t Sobol sequences are considered as a basis. Two other approaches are also analyzed. The first one is an efficient Monte Carlo (MC) algorithm for multidimensional integration based on modified Sobol sequences (MCA-MSS) and proposed in an earlier work by some of the authors Dimov and Georgieva (2011) [28]. The second one is a randomized QMC algorithm proposed by Art Owen (1995) [20]. The procedure of randomization in the latter case is also known as Owen scrambling. The algorithms considered in this work are applied to sensitivity studies of air pollution levels calculated by the Unified Danish Eulerian Model (UNI-DEM) to some chemical reaction rates. UNI-DEM is chosen as a case study since it constitutes a typical large-scale mathematical model in which the chemical reactions are adequately presented. Extensive numerical experiments are performed to support the theoretical studies and to analyze applicability of algorithms under consideration to various classes of problems. Conclusions about the applicability and efficiency of the algorithms under consideration are drawn.