Discrete models of geometric objects in parallel computing systems

The usage of powerful computer systems defines computational experiments as novel and significant research methods enabling to solve complex. Taking into account the fact that raditional analytical methods for visualizing mathematical models are of a determinative nature, there is still a need to apply modern mathematical theories which in their turn will enable to expand the possibilities of applied mathematical research. The object of the research is the process of developing functional design of complex geometric models. The subject of the research is the usage of parallel methods for constructing the surfaces of discrete models of some geometric objects. The methods of the research are: application of the apparatus of analytical geometry, mathematical analysis, the theory of R-functions, parallel architecture and numerical methods. The purpose of the research is to solve current scientific and technical problems, in particular to increase the efficiency in the design of the programme for building discrete models, which can be implemented in the finite element analysis of complex technical systems by means of using parallel architecture. The following tasks were set to achieve the goal: analysis and review of currently known methods and approaches related to the construction of discrete models in complex computing systems. Development of the appropriate method and visualization of mathematical models based on the functional approach. Modification of the "Marching Cubes" method. Implementation in parallel architectures resorting to modern technologies and programming libraries, such as OpenMP and MPI, and conducting test experimental calculations that prove the efficiency of the proposed algorithm. Considering the importance of geometric model accuracy for the safety of complex technical systems, the application of parallel methods for building discrete models can significantly impact the reliability and safety in the development and testing of high-tech products, particularly in fields such as rocket engineering. In the process of creating models used for designing rocket systems and other advanced technologies, it is crucial to achieve high precision, computational speed, and reliability of results. The developed parallel computation methods help reduce the risk of errors and optimize the design processes, which is vital for ensuring safety in this critical area.