ВІЗУАЛІЗАЦІЯ R-ФУНКЦІЙ В ПАРАЛЕЛЬНИХ ОБЧИСЛЮВАЛЬНИХ СИСТЕМАХ ЗІ СПІЛЬНОЮ ПАМ’ЯТТЮ

Abstract

The use of numerical methods for solving boundary value problems requires the creation of discrete models of geometric regions of complex shape. The automatic generation of mesh can be divided into two independent problems: creating a formal description of the initial geometric region and building its discrete model based on this description. The most difficult is precisely the first problem. A universal way of formally describing geometric regions of arbitrary shape is to use R-functions, which allow using logical operations of inversion, conjunction, and disjunction over elementary mathematical relations to construct implicit functions that uniquely describe the boundary of an arbitrary geometric object.
This paper proposes a parallel algorithm for constructing and visualizing implicit R-functions in shared-memory computing systems. The algorithm was implemented using the C++ Standard library (C++11 version). The software was implemented and a number of computational experiments were carried out, which showed the effectiveness of the proposed algorithm on computers with various types of processors.