Chernysh R. Modified additive-averaged splitting algorithm, its parallel realization and application to meteorological problems.

The thesis is for a scientific degree of a candidate of Physics and Mathematics Sciences in the research area 01.05.02 - mathematical modeling and numerical analysis. - Kyiv National Taras Shevchenko University, Kyiv, 2010. The thesis deals with improvement of numerical methods used for mathematical modeling. The conducted scientific researches concern the modification of additive-averaged splitting algorithm. This method provides a possibility to control the informational interdependency of subproblems. The existence of the control parameter makes it possible to find its optimal value for the best realization of particular problem and to apply parallel computations more effectively. This approach helped to determine optimal values sets of this parameter. It also gave proof of expediency and importance of the algorithm modification. The present thesis also constructs a special coordinate-wise domain decomposition and suggests to coordinate it with the subproblem operator. Such combination grants an advantageous possibility to avoid the need adjusting the solutions of adjacent subdomains. As a consistent consequence of this modification the three-level parallel algorithm was constructed. Its distinctive features are high-level parallelism and controllability of asynchronous lines connections. However the described parallel algorithm applies only to a specific range of problems. The present work illustrates this algorithm used for realization of the mathematical model of atmosphere circulation.