The project "Development and study of new Monte Carlo methods for modeling of complex systems" is funded by the National Science Fund, National Competition "Young Researchers" - 2011. The project leader is Dr. Rayna Georgieva.

Objectives

The objectives of the project proposal are to develop new efficient Monte Carlo and quasi-Monte Carlo methods and algorithms for numerical integration and solving of integral equations. Research will focus on modelling of semiconductor devices and realistic image creation in computer graphics. The methods and algorithms developed will be applied for providing sensitivity analysis of mathematical models under consideration. Efficiency of the algorithms will be studied on modern computer architectures, such as the existing grid infrastructure and/or the supercomputer IBM BlueGene/P.

Annotation

Monte Carlo and quasi-Monte Carlo methods is an extremely dynamic discipline, influenced by the intensive development of modern computing systems. It is becoming more widespread practical application in areas where finding the unknown variables is reduced to calculation of integrals or solving integral equations. Sensitivity analysis is an useful approach for verification and improvement of mathematical models. It leads to an increased efficiency and reliable results produced by the model.

Approaches for global sensitivity analysis on compact models for simulation of circuits and transistors will be applied for the first time. As a result, it is expected that the set of input parameters necessary to determine the unknown distribution will be identified more quickly and reliably. This will contribute to the development of new tool useful for design and analysis of chips.

It is expected that scientific research within the framework of the project proposal makes a valuable contribution to the theory and practice of realistic images creation using Monte Carlo methods, approaches to sensitivity analysis and high-performance architectures. It is envisaged that the experience gained in solving rendering equation can be applied successfully in solving the problem of gamma photons transport during computer tomography simulations for medical studies.

Publications

• I. T. Dimov, R. Georgieva, Tz. Ostromsky, Z. Zlatev. Advanced Algorithms for Multidimensional Sensitivity Studies of Large-scale Air Pollution Models based on Sobol Sequences. Special issue of Computers and Mathematics with Applications, "Efficient Numerical Methods for Scientific Applications". Elsevier. ISSN: 0898-1221. Doi: 10.1016/j.camwa.2012.07.005. IF (2011): 1.747. 5-year IF: 1.643 (accepted).

• P. Schwaha, M. Nedjalkov, S. Selberherr, I. Dimov. Particle-grid Techniques for Semiclassical and Quantum Transport Simulations. - In: Proceedings of The 15th International Workshop on Computational Electronics". IEEE Xplore, 2012, 1-3. ISBN: 978-1-4673-0705-5.

• I. T. Dimov, R. Georgieva, Tz. Ostromsky, Z. Zlatev. Variance-based Sensitivity Analysis of the Unified Danish Eulerian Model Acc ording to Variations of Chemical Rates, LNCS, Springer. SJR (2011): 0.331 (accepted).

• I. Dimov, R. Georgieva, Multidimensional Sensitivity Analysis of Large-scale Mathematical Models, Springer Series in Mathematics and Statistics (submitted).

Participation in international conferences

• 15th International Workshop on Computational Electronics, May 22 - 25, 2012, University of Wisconsin–Madison, USA.

• Fourth Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, June 11 - 16, 2012, St. St. Constantine and Helena, Varna, Bulgaria.

• Fifth Conference on Numerical Analysis and Applications, June 15 - 20, 2012, Lozenetz, Bulgaria.

• XV-th International Summer Conference on "Probability and Statistics", June 23 - 30, 2012, Pomorie, Bulgaria.