Application of the finite element method for real-time modelling of physical processes using distributed computing

Abstract

This study investigated the application of the finite element method for modelling complex physical processes in real time. The aim of the research was to determine the effectiveness of this method when combined with distributed computing. An integrated model was developed, combining classical numerical analysis with modern distributed system technologies to ensure high accuracy and computational efficiency. It was established that the finite element method had traditionally been used for modelling heat transfer, deformations, and electromagnetic phenomena. However, modern requirements for monitoring and control created the need to adapt this method for distributed computing. Algorithms for the efficient distribution of computational tasks were developed, allowing data processing delays to be minimised. Experimental simulations showed that the use of distributed computing reduced calculation time by almost 14.5 times – 420 seconds on a single node to 29 seconds on 16 nodes – while maintaining a relative error of 2-4%. More than 50 test runs were conducted, confirming the system’s operational stability. The use of an adaptive integration step reduced computation time by 15% compared to a fixed step, demonstrating the effectiveness of load distribution optimisation. The obtained results confirmed the high potential of this method for solving real engineering problems, speed and accuracy of calculations were crucial. The proposed methodology was recommended for use in industrial processes, monitoring, and control systems, as it provided fast and accurate modelling of complex engineering tasks with high scalability.