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Title of the article PARALLELIZING OF COMPUTATIONS ON A GRAPHICS PROCESSING UNIT FOR ACCELERATING BOUNDARY ELEMENT CALCULATIONS IN MECHANICS
Authors

SHERBAKOV Sergei S., D. Sc. in Phys. and Math., Prof., Chief Researcher of the Laboratory of Wear and Fatigue Pamage Mechanics of the Republican Computer Center of Mechanical Engineering, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus; Professor of the Department of Theoretical and Applied Mechanics, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

POLESTCHUK Mikhail M., Junior Researcher of the Research Laboratory of Applied Mechanics, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

MARMYSH Dzianis E., Ph. D. in Phys. and Math., Assoc. Prof., Associate Professor of the Department of Theoretical and Applied Mechanics, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section MECHANICS OF DEFORMED SOLIDS
Year 2024
Issue 1(66)
Pages 80–85
Type of article RAR
Index UDK 539.3:519.6+519.85
DOI https://doi.org/10.46864/1995-0470-2024-1-66-80-85
Abstract In solving problems of computer modeling using various methods, accuracy and computational efficiency questions always arise. This study explores the application of two modifications of the boundary element method to solve the problem of potential distribution within a closed two-dimensional domain with a uniform potential distribution on its boundary. The first modification involves using three nonlinear shape functions instead of one. The second modification applies the Galerkin method to the boundary element approach with three nonlinear shape functions. The essence of this modification lies in the fact that the system of equations is formulated in integral form over the entire boundary element, rather than at collocation points. In addition to this, the paper describes and investigates the advantages and disadvantages of the smoothing modification applied to these approaches. Since the influence matrix consists of independently computable elements, parallelization of calculations using NVIDIA CUDA technology has been proposed to enhance computational efficiency, significantly accelerating the calculation of interaction matrix. The choice of this technology is advantageous due to the prevalence of NVIDIA graphics accelerators in almost every personal computer or laptop, as well as it is easy to use. The study presents an approach to the application of this technology and demonstrates the results, showing the acceleration of parallelized calculations which show the dependence on the number of boundary elements. A comparison of the efficiency of the selected technology when applied to two methods, collocation and Galerkin, is also presented, indicating a significant speedup of up to 22 times by computing the influence matrix of the boundary elements.
Keywords boundary element method, nonlinear shape functions, potential distribution, NVIDIA CUDA, collocation method, Galerkin method, algorithm parallelization, numerical modeling, computational acceleration, interaction matrix
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