Lisnyak A. Triangular Finite Elements in the Mathematical Modeling of Geometrical Objects on the Basis of R-functions

Object of research – formalization of the description and the building of discrete models of complex geometrical objects (engineering constructions, parts of machines and mechanisms, etc.). Subject of research – methods and approaches for building mathematical models of geometrical objects. The purpose of the research is to develop methods and approaches to formalize the description of mathematical models geometric objects on the basis of the theory of R-functions and the construction of the relevant discrete models on the basis of triangular finite elements. Research methods are based on methods of mathematical analysis, analytical geometry, mathematical modeling, computational mathematics, systems analysis. The theory of R-functions is used for description of the mathematical models of complex geometrical objects. First were proposed methods for mesh optimization on the basis of differential characteristics of the boundary of geometrical object which defined by R-function. Results of the research are implemented in learning process of Zaporizhzhya National University, Department of Mathematics. Industries: computer graphics, mechanical engineering, aircraft, construction.