Комп’ютерні технології швидкого обчислення математичних моделей

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Комп’ютерні технології швидкого обчислення математичних моделей

Journal Title: Математичне моделювання - Year 2017, Vol 1, Issue 2

Abstract

COMPUTATIONAL TECHNOLOGIES FOR THE CALCULATION OF MATHEMATICAL MODELS Krasnikov K.S. Abstract The author focus on the problem of increasing of computational efficiency of three-dimensional mathematical model that was developed earlier. One of the pecularities of compound math models is the requirement of a large number of arithmetic operations and the calculation of large data arrays, which affects the time of calculation, which can last for a several days without acceleration. Due to the development of computer technology, today there are methods to significantly increase the speed of computing by using parallel technologies in the program code. The purpose of the work is to increase the speed of computations in a computer program with increasing number of cores using modern programming concepts and achivements in processor industry. It is considired four levels of paralelism in a computer program. It is suggested to use the second level of the mentioned parallelization of computations for the solution of the system of linear algebraic equations for the dynamics of the solids system: each number in the row of the matrix is multiplied by the corresponding number in the vector of values and the result is added. Instead of consistently completing the addition and product, it is recommended to use the appropriate processor instruction. An arithmetic addition operation is usually performed sequentially, but this sequence can be parsed for acceleration if the set of numbers for a sum is sufficiently large. The third level is proposed to be used in the calculation of hydrodynamics, by dividing the calculated area into parts, each of which is calculated independently at each stage of the mathematical model. The fourth level approaches the delimitation of the calculation of the mathematical model of the physical process being investigated and the calculations associated with obtaining the 3D image of the results obtained if they are combined into a single computer program. As a result of the parallelization of computer program, it has accelerated by around 1.5 times. The image processing task is very well suited for parallelizing because almost 100% of the calculations are distributed between processors. In result acceleration corresponds to an increase in the number of streams involved. Future investigation will be devoted to computing using general purpose GPU. References [1] Krasnikov, K.S. (2015). The mathematical model of three-dimensional motion of cored wire in molten steel during inert gas blowing on furnace-ladle. Journal «Visnyk of Kherson National Technical University», Kherson, № 3, pp. 378-383. [2] Culler, D. (1998). Parallel computer architecture: a hardware / software approach / David Culler, Jaswinder Pal Singh, Anoop Gupta // Morgan Caufmann Publishers, 1998. — pp. 1056 [3] Quinn, M. J. Parallel programming in C with MPI and OpenMP // McGraw-Hill Education, 2003. — pp. 527. [4] Amdahl, G. (April 1967) «The validity of the single processor approach to achieving large-scale computing capabilities». In Proceedings of AFIPS Spring Joint Computer Conference, Atlantic City, N.J., AFIPS Press, 1967. — pp. 483-85. [5] McCool, M. D., Robison, A. D., Reinders James (2012). "2.5 Performance Theory". Structured Parallel Programming: Patterns for Efficient Computation. Elsevier, 2012. — pp. 61–62. ISBN 978-0-12-415993-8. [6] http://www.intuit.ru/studies/courses/10554/1092/lecture/27095

Authors and Affiliations

К. С. Красніков

EP ID EP276900
DOI -
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