An advanced lattice rules with prime number of points with product weights for multidimensional sensitivity analysis.

In this paper an advanced stochastic approach based a lattice rule with improved generating vector has been obtained and studied. The Unified Danish Eulerian Model (UNI-DEM) is a key element in our investigation since it is one of the most advanced large-scale mathematical models that describes adequately all physical and chemical processes. The calculations are done in a large spatial domain, which covers completely the European region and the Mediterranean, for certain time period. What is more, it studies the transportation of a number of pollutants and all these make it a perfect case study. The paper compares the described lattice rule and demonstrates its superiority over the plain Monte Carlo approach and Fibonacci based lattice rule. The proposed approach is robust and computationally efficient in estimating multidimensional integrals and thus sensitivity indices, which is vital in scientific computing. [ABSTRACT FROM AUTHOR]