Тулупова, Л.О.

Воронцова, І.В.

Discrete geometric modeling aims at the discrete representation and definition of geometric images (any engineering objects, processes or phenomena). Solving most engineering problems requires the construction and analysis of geometric models, processes, phenomena in discrete form. The main requirements for such models - adequacy, clarity, simplicity, accuracy. The created models with the set accuracy should reflect all characteristic features of objects and at the same time be as much as possible accessible at researches. Discrete geometric interpretation of numerical methods, in particular the finite difference method, is closely related to specific applications, gives numerical methods clarity and makes them an effective tool for designing geometric objects. The implementation of the process of discrete geometric modeling involves, in particular, the development of effective algorithms for the transition from a discrete image to its continuous counterpart and vice versa because the most significant theoretical and applied results of modeling techniques are obtained for continuous forms of input data. the requirements of the applied problems, forms of presentation, processing and analysis of data on a PC are discrete. Involvement of the geometric apparatus of superpositions allows to perform such transitions by simple methods. The use of the geometric apparatus of superpositions in combination with the classical method of finite differences, allows to significantly increase the efficiency and expand the possibilities of the process of discrete modeling of geometric images (GO). In particular, to investigate the possibility of using not only parabolic, but also any other functional dependencies as interpolants. On the example of the exponential function it is shown that the obtained formulas for calculating the values of the superposition coefficients of the given three nodal points for the selected calculation schemes allow to solve the problems of continuous discrete interpolation and extrapolation by numerical sequences of any one-dimensional functional dependences. ordinates of nodal points) without time-consuming operations of addition and solution of large systems of linear equations. Keywords: discrete modeling, geometric images, finite difference method, geometric apparatus of superpositions, exponential functions.

геометричні образи

метод скінчених різниць

геометричний апарат суперпозицій

показникові функції