The exaproblems of mathematical modeling

The questions of the development of scientific software for solving mathematical modeling problems on the multi-processor computational systems are considered. The analysis and classification of the mathematical statements from various applications, as well as methods and technologies for the main stages of numerical experiments are presented. The conception and the structure of the Basic System of Modeling (BSM), which includes the problem-independent components for geometric and functional modeling, grid generation, approximation of the initial-boundary value problems, algebraic solvers, post-processing and visualization of the results, and control of computational process, are proposed. The applied program products can be constructed from the described components.