Lisin D. Synthesis of adaptive methods for modeling of the heat processes with the use of R-functions and atomic functions

Non-stationary heat fields, the development of mathematical tools for solving 3D boundary value problems of heat conduction, mathematical tools of the R-functions theory, atomic radial basis function, the methods of computational mathematics and computer modeling; new meshfree methods for solving boundary value problems of heat conduction for 3D regions using ARBF are created and numerically implemented, the system of computer modeling of heat transfer processes on the basis of meshless approach using atomic radial basis functions and mathematical tools of the theory of R-functions is developed, the system for finding and fast visualizing the set of nodes on the surface of the object described by means of R-functions theory is developed and implemented. Results of thesis were introduced in the educational process at KhNU. Application: machine construction, automobile construction, aeronautics.