Baranov I. Structural methods for mathematical modelling and computer simulation of physico-mechanical fields in complex-shape domains

Physico-mechanical processes such as hydrodynamic, in complex-shape domains. Increasing the analysis accuracy in the neighbourhood of corner points in the solution region of boundary problems, developing local structures to account for boundary conditions on the domain boundary and interface with the standard basis inside the domain, application of structural methods to problems in modelling physico-mechanical fields. Elements of mathematical analysis, analytic and differential geometry, functional analysis, linear algebra, and variational methods of mathematical physics. The new systems of R-operations and R-operations with rounded of different classes smoothness are built; the behavior of smooth and normalized R-operations in the neighborhood of point (0,0) is studied; the new method of construction of smooth basis functions which are satisfy the homogeneous Dirichlet boundary condition is developed; the method of construction of boundary basic elements which satisfy the boundary conditions of the problem and interface with the standard basis inside the domain is first developed. The methods developed and the approaches were used in problems of modelling hydrodynamic fields in complex-shape domains. Results of the thesis is planned to apply in IPMash of NASU for developing new hydrovortex injectors. Application: power engineering.