Topics

Fundamental foundations of mathematical models in science and technology. Mathematical models accuracy assessment. Issues of existence, uniqueness and stability of solutions to applied problems. Numerical methods, theoretical analysis and substantiation of the convergence of computational algorithms. Methods of optimization and modeling of deterministic systems. Optimization algorithms for solving applied problems. Methods for modeling processes and phenomena in discrete-dynamic, functional systems and control systems.

Development and evaluation of computational algorithms for solving applied problems. Testing efficient computational methods using modern computer technologies. Effective numerical methods and algorithms as a form of complexes of problem-oriented programs. Development of simulation methods. Design and development of computer simulation systems. Comprehensive analysis of research and engineering questions with a modern technology of computational experiment.

Implicit patterns and hidden knowledge in data sets from various application areas based on the use of special algorithms and artificial intelligence tools (methodology of multivariate analysis; structuring large volumes of data in accordance with Data Mining technology; data clustering and categorization with methods of mathematical statistics, neural networks and fractal analysis, the use of neural networks for image and text analysis, etc.).

Hardware, software and mathematical support of computing systems. Design, configuration, and diagnostics of data transmission networks. Methods and algorithms for analyzing the efficiency of concentrated and distributed computing systems. Designing structures of parallel computing systems.

Multiprocessor computing systems: algorithms, technologies and solution of practical tasks. Principles of organizing parallel computing processes. Methods for programming virtual architectures for supercomputers, parallel algorithms for the numerical implementation of mathematical models and solving optimization problems. Application of multiprocessor systems in engineering, physics, biology, and medicine.