Ivan Dimov: Multidimensional Sensitivity Analysis of Large-scale Mathematical Models
The aim of the talk is to present various approximation Sensitivity Analysis techniques of Large-scale Mathematical Models. A concept of Sensitivity Analysis and complexity in classes of algorithms will be presented. More precisely, randomized Quasi-Monte Carlo and modified Sobol sequences will be analyzed. As a case study the Unified Danish Eulerian model of air pollution transport (UNI-DEM) will be considered. UNI-DEM is carried out to compute more precisely interaction effects of inputs and sensitivity measures. Various Monte Carlo algorithms have been applied for numerical integration of multidimensional integrals to estimate the sensitivity measures. A comparison of their efficiency will be discussed.
Venelin Todorov: High-accuracy numerical methods for parabolic systems in air pollution modeling
We present different approach es for enhancing the accuracy of the second-order finite difference approximations of two dimensional semilinear parabolic systems. These are the fourth-order compact difference scheme and the fourth-order scheme based on Richardson extrapolation. Our interest is concentrated on a system of ten parabolic partial differential equations in air pollution modeling. We analyze numerical experiments to compare the two approaches with respect to accuracy, computational complexity, nonnegativity preserving, etc. The sixth-order approximation based on the fourth order compact difference scheme combined with Richardson extrapolation is also discussed numerically.
(Joint work with Juri Kandilarov, Ivan Dimov and Luben Vulkov.)