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Modeling physical and technical processes based on parallel computing

Work number - M 49 FILED

Presented Institute of Cybernetics of VM Glushkov NAS of Ukraine

Ph.D. Sedoruk VA, Ph.D. Chistyakov OV, Ph.D. Ivanenko PA

The purpose of the work is to develop new mathematical methods, computer algorithms and software for modeling physical and technical processes based on parallel computing, as well as, to develop new methods for efficient setup (Tuning) of parallel programs for computing environment.

Solving the problems of linear algebra - systems of linear algebraic equations (SLAE) and algebraic eigenvalue problem are one of the fundamental problems of numerical modeling in many subject areas. Studies of mathematical models of many physical-technical problems are reduced to solving these problems with matrices, which usually have a sparse structure. Experience shows that the useing existing linear algebra software has shown, a prerequisite for creating efficient parallel algorithms and programs for sparse matrices is to take into account the architecture of hybrid computers and the features of the matrix structure, bringing it into structure if necessary, which provides high efficiency and balancing of computations processors.

For this purpose, mathematical modeling of physics and technical processes on hybrid computers has developed and investigated new parallel methods and computer algorithms for solving of SLAE and eigenvalue problem based on the structural regularization of sparse matrices. The efficiency of the created algorithms has been proved theoretically and through practical experiments. The developed algorithmic-software toolkit is tested in the mathematical modeling of the following physical and technical processes: strength of two-component composite materials of regular structure with uniaxial compression; strength of structures in electric welding; short-term meteorological forecasting. A significant reduction in the time of mathematical modeling by more than 20 times was obtained.

When creating parallel applications for modern supercomputers have trouble effectively setting them on computer resources. The disadvantages of the current methodology of self-tuning (program tuning) program on the computer architecture are considerable time of writing and work of the auto-tuner. The paper develops a formal approach to the automatic creation of autotuners from the source code of the program, which is achieved by using the technique of copying rules. A software system (auto-tuner) has been created that optimizes software products for different computer operating systems. The system was used to optimize the parallel algorithm of short-term meteorological forecasting, which is used in the Internet portal of the Institute of Software Systems of NAS of Ukraine.

Number of publications: 22 articles in professional journals, 13 publications in conference materials. The total number of references to publications of authors presented in the work, according to Scopus bases is 9/2; according to Google Scholar 70/5. 4 copyrights have been obtained for computer programs created.