Abstract
According to the principles of multiphysical, multiscale simulation of phenomena and processes which take place during the electric current treatment of liquid metals, the need to create an adjustable and concise geometrical platform for the big database computing of mathematical models and simulations is justified. In this article, a geometrical platform was developed based on approximation of boundary contours using arcs for application of the integral equations method and matrix transformations. This method achieves regular procedures using multidimensional scale matrices for big data transfer and computing. The efficiency of this method was verified by computer simulation and used for different model contours, which are parts of real contours. The obtained results showed that the numerical algorithm was highly accurate based on the presented geometrical platform of big database computing and that it possesses a potential ability for use in the organization of computational processes regarding the modeling and simulation of electromagnetic, thermal, hydrodynamic, wave, and mechanical fields (as a practical case in metal melts treated by electric current). The efficiency of this developed approach for big data matrices computing and equation system formation was displayed, as the number of numerical procedures, as well as the time taken to perform them, were much smaller when compared to the finite element method used for the same model contours.
Highlights
The study of complex processes and phenomena by mathematical modeling is a natural way to improve and enhance the efficiency of technical methods and technologies
Mathematical models are often used alongside data obtained from nature experiments, and physical model construction is firmly established in the practice of engineering design
The only way to identify the influence of setting exposures on controlled parameters, intermediate data, and final results is by using a computational method that utilizes generalized data of empirical dependencies or numerical simulations based on existing theories of the corresponding phenomena
Summary
The study of complex processes and phenomena by mathematical modeling is a natural way to improve and enhance the efficiency of technical methods and technologies. There are technical spheres where the experimental study of the internal content of current processes and real measurements of local physical parameters of reagents or interacting media are not currently possible. In these cases, the only way to identify the influence of setting exposures on controlled parameters, intermediate data, and final results is by using a computational method that utilizes generalized data of empirical dependencies or numerical simulations based on existing theories of the corresponding phenomena
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