"Efficient Monte Carlo Methods for Large-Scale Scientific Problems" Project

The project "Efficient Monte Carlo Methods for Large-Scale Scientific Problems" is funded by the National Science Fund, Thematical competition - 2009. The project leader is Prof. DSc Ivan Dimov.

Objectives

The main objective of the project is to develop efficient Monte Carlo methods and parallel implementation tools for large-scale mathematical models. We plan to implement the developed tools to four areas of groundbreaking applications: Environmental modeling, Semiconductor device modeling, Light propagation and Optimization of real-live and industrial problems. The main part of the investigation will be focused on the development of parallel Monte Carlo algorithms with an improved convergence rate for sensitivity analysis.

Annotation

Monte Carlo methods are very effective and power tools, and in some cases the only one option for simulation and conducting the research in various scientific and technological fields. The sensitivity analysis is an important step in the process of development, verification and improvement of large-scale mathematical models. Our study is based on variance-based methods that use variance as an indicator of the impact of the change of input parameters on the model output. It makes Monte Carlo approach applicable. Their main advantages are providing a global and quantitative sensitivity analysis and independence on the behavior of the analyzed computational model.

The main objective of the project is to develop efficient Monte Carlo methods and parallel implementation tools for large-scale mathematical models. We plan to implement the developed tools to four areas of groundbreaking applications: Environmental modeling, Semiconductor device modeling, Light propagation and Optimization of real-live and industrial problems. The main part of the investigation will be focused on the development of parallel Monte Carlo algorithms with improved convergence rates for sensitivity analysis. New variance-based sensitivity analysis technique is going to be used in the large-scale air pollution models for two separate multidimensional sensitivity analysis studies connected to the chemistry and emissions parts. The device modeling considers the importance of rare and random events for the performance of semiconductor devices - components of modern integral circuits. We also consider the rendering equation with uniform separation sampling. Ant Colony Optimization algorithms with different start strategies will be applied on several classes of optimization problems.

The use of the existing supercomputer IBM BlueGene/P, as well as EGEE and SEE-GRID Grid infrastructures is assumed.

The project is in the fundamental area of scientific research.

Publications during the first stage of the project