{"id":16175,"date":"2023-02-11T22:30:05","date_gmt":"2023-02-11T20:30:05","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=16175"},"modified":"2023-11-06T14:03:22","modified_gmt":"2023-11-06T12:03:22","slug":"osoblyvosti-vykorystannya-paralelnyh-obchyslen-v-paketi-prykladnyh-program-mirela","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=16175","title":{"rendered":"\u041e\u0441\u043e\u0431\u043b\u0438\u0432\u043e\u0441\u0442\u0456 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u043d\u043d\u044f \u043f\u0430\u0440\u0430\u043b\u0435\u043b\u044c\u043d\u0438\u0445 \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u044c \u0432 \u043f\u0430\u043a\u0435\u0442\u0456 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u0438\u0445 \u043f\u0440\u043e\u0433\u0440\u0430\u043c \u00ab\u041c\u0456\u0440\u0435\u043b\u0430+\u00bb"},"content":{"rendered":"

<\/p>\n

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FEATURES OF THE USE OF PARALLEL CALCULATIONS IN THE PACKAGE OF APPLICATION PROGRAMS \u00abMIRELA+\u00bb<\/p>\n

\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 60-64. \u041d\u043e\u043c\u0435\u0440: \u2116<\/strong>6<\/strong>.\u0442.2, 2022 (315)\u00a0<\/strong> \"\"<\/a>
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2022-315-6(2)-60-64<\/a>
\n\u0410<\/strong>\u0432\u0442\u043e\u0440\u0438<\/strong>: <\/strong>
\n\u0421\u0435\u0440\u0433\u0456\u0439 \u0413\u041e\u041c\u0415\u041d\u042e\u041a
\n\u0417\u0430\u043f\u043e\u0440\u0456\u0437\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442
\nhttps:\/\/orcid.org\/0000-0001-7340-5947<\/a>
\ne-mail: gserega71@gmail.com
\n\u0412\u043b\u0430\u0434\u0438\u0441\u043b\u0430\u0432 \u041a\u041e\u0417\u0423\u0411
\n\u041b\u0443\u0433\u0430\u043d\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0422\u0430\u0440\u0430\u0441\u0430 \u0428\u0435\u0432\u0447\u0435\u043d\u043a\u0430
\nhttps:\/\/orcid.org\/0000-0003-2710-7206<\/a>
\ne-mail: v.y.kozub@gmail.com<\/a>
\nSerhii HOMENIUK
\nZaporizhzhia National University
\nVladyslav KOZUB
\nLuhansk Taras Shevchenko National University<\/p>\n

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\u0420\u043e\u0437\u0440\u043e\u0431\u043b\u0435\u043d\u043e \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0438 \u043f\u0430\u0440\u0430\u043b\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0443\u0432\u0430\u043d\u043d\u044f \u0434\u043b\u044f \u043f\u043e\u0431\u0443\u0434\u043e\u0432\u0438 \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u0443\u0432\u0430\u043b\u044c\u043d\u0438\u0445 \u0440\u0456\u0432\u043d\u044f\u043d\u044c \u043f\u0430\u043a\u0435\u0442\u0443 \u043f\u0440\u043e\u0433\u0440\u0430\u043c \u00ab\u041c\u0406\u0420\u0415\u041b\u0410+\u00bb. \u041e\u0442\u0440\u0438\u043c\u0430\u043d\u043e \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u043a\u0438 \u0434\u043b\u044f \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u043e\u0432\u0438\u0445 \u0441\u0456\u0442\u043e\u043a \u0440\u0456\u0437\u043d\u0438\u0445 \u0440\u043e\u0437\u043c\u0456\u0440\u0456\u0432. \u0414\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043e \u0432\u043f\u043b\u0438\u0432 \u043f\u0430\u0440\u0430\u043b\u0435\u043b\u0456\u0437\u0430\u0446\u0456\u0457 \u043d\u0430 \u0447\u0430\u0441 \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u0443.
\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430<\/strong>: \u0441\u043a\u0456\u043d\u0447\u0435\u043d\u043d\u0438\u0439 \u0435\u043b\u0435\u043c\u0435\u043d\u0442, \u043f\u0430\u0440\u0430\u043b\u0435\u043b\u044c\u043d\u0456 \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044f, OpenMP, \u043c\u0430\u0442\u0440\u0438\u0446\u044f \u0436\u043e\u0440\u0441\u0442\u043a\u043e\u0441\u0442\u0456, \u043c\u0430\u0442\u0440\u0438\u0446\u044f \u0442\u0435\u043f\u043b\u043e\u043f\u0440\u043e\u0432\u0456\u0434\u043d\u043e\u0441\u0442\u0456.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u00a0\u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

The article examines approaches to the optimization of structural calculations, which require a comprehensive analysis of deformation processes under the action of operational loads. The finite element method is usually used to solve such problems. Modeling of structures taking into account stress concentrators requires the use of large-sized calculation grids. In real operating conditions, most structural elements are under the influence of mechanical and thermal loads. The package of application programs \u00abMIRELA+\u00bb is intended for solving problems of thermoelasticity of structures made of weakly compressible elastomers and composites with an elastomeric matrix. One of the stages of solving problems of thermoelasticity is the formation of stiffness matrices taking into account weak compressibility and thermal conductivity of finite elements. When forming the stiffness and thermal conductivity matrices, it is necessary to perform integration over the area of \u200b\u200bthe finite element. For elements of the same type, calculations are used according to the same procedure, and the number of such calculations determines the time to solve the problem. In the traditional approach, these calculations are performed sequentially. In the case of large grid sizes, the number and time of calculations increase, which requires optimization of calculations using parallel calculation algorithms. Using the OpenMP library, a parallel algorithm for forming the matrix of solving equations was built. The calculation of terms according to the quadrature scheme is included in the parallel area of \u200b\u200bthe algorithm. Filling of the stiffness matrix of the finite element takes place in the sequential region. The execution time of parallel calculations is determined by the slowest subtask. Using the moment scheme of finite elements, displacement and deformation are approximated by the same polynomials, which simplifies the calculation of integrals. Parallel programming algorithms for constructing solving equations of the “MIRELA+” program package have been developed. Solutions for calculation grids of different sizes have been obtained. The effect of parallelization on the calculation time was studied.
\nKeywords:<\/strong> finite element, parallel computing, OpenMP, stiffness matrix, thermal conductivity matrix.<\/p>\n

\u041b\u0456\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430<\/strong><\/p>\n

    \n
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  2. Ju S.H. An Out-of-Core Eigen-Solver with OpenMP Parallel Scheme for Large Spare Damped System [\u0415\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438\u0439 \u0440\u0435\u0441\u0443\u0440\u0441] \/ S.H.\u00a0Ju, H.H. Hsu \/\/ J.Computational Methods \u2013 2019. \u2013 Vol. 16. No 7. \u2013 \u0420\u0435\u0436\u0438\u043c \u0434\u043e\u0441\u0442\u0443\u043f\u0443\u00a0: https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219876219500385.<\/li>\n
  3. \u0416\u0434\u0430\u043d\u043e\u0432\u00a0\u0410.\u0418. \u041e\u0431 \u043e\u0434\u043d\u043e\u0439 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0431\u043b\u043e\u0447\u043d\u043e\u0433\u043e \u043c\u0435\u0442\u043e\u0434\u0430 \u0413\u0430\u0443\u0441\u0441\u0430-\u0417\u0435\u0439\u0434\u0435\u043b\u044f \/ \u0410.\u0418.\u00a0\u0416\u0434\u0430\u043d\u043e\u0432, \u0415.\u042e.\u00a0\u0411\u043e\u0433\u0434\u0430\u043d\u043e\u0432\u0430 \/\/ \u0412\u0435\u0441\u0442\u043d. \u0421\u0430\u043c.\u0433\u043e\u0441. \u0442\u0435\u0445.\u0443\u043d-\u0442\u0430. \u0421\u0435\u0440. \u0424\u0438\u0437.-\u043c\u0430\u0442. \u043d\u0430\u0443\u043a\u0438. \u2013 2016. \u2013 \u0422.20, \u21164. \u2013 \u0421. 730 \u2013 738.<\/li>\n
  4. Leonardo Nunes da Silva. Performance of hybrid openMP\/MPI parallel programming application of finite element method\u00a0[\u0415\u043b\u0435\u043a\u0442\u0440\u043e\u043d\u043d\u0438\u0439 \u0440\u0435\u0441\u0443\u0440\u0441] \/ Leonardo Nunes da Silva, Fl\u00e1via Romano Villa Verde, Gerson Henrique Pfitscher \/\/ Proc. COBEM 2007 19th International Congress of Mechanical Engineering, \u2013 November 5-9, 2007. \u2013 \u0420\u0435\u0436\u0438\u043c \u0434\u043e\u0441\u0442\u0443\u043f\u0443 : https:\/\/www.abcm.org.br\/anais\/cobem\/2007\/pdf\/COBEM2007-1463.pdf<\/li>\n
  5. Yamaguchi T. Performance Evaluation of 3-D Hybrid Parallel Finite Element Method by MPI\/OpenMP\u00a0\/ T. Yamaguchi, Y.\u00a0Kawase, A.\u00a0Nagase, S. Ishimura \/\/ J. Japan Society of Applied Electromagnetics and Mechanics. \u2013 2019. \u2013 Vol.27. No.1. \u2013 85-90.<\/li>\n
  6. Wozniak\u00a0M. Comparison of multi-frontal and alternating direction parallel hybrid memory iGRM direct solver for non-stationary simulations \/ M.\u00a0Wozniak, A.\u00a0Bukowska \/\/ Computer Science. \u2013 2020. \u2013 21(4). \u2013 P. 419-439.<\/li>\n
  7. Bo\u0161ansk\u00fd M. Parallelization of assembly operation in finite element method \/ M.\u00a0Bo\u0161ansk\u00fd, B.\u00a0Patz\u00e1k \/\/ Acta Polytechnica. \u2013 2020. \u2013 60(1). \u2013 P.25\u201337.<\/li>\n
  8. Amorim L. GPU Finite Element Method Computation Strategy Without Mesh Coloring \/ L.\u00a0Amorim, T.\u00a0Goveia, R.\u00a0Mesquita, I.\u00a0Baratta \/\/ J. Microwaves, Optoelectronics and Electromagnetic Applications. \u2013 2020. \u2013 19. No.2. \u2013 P. 252-264.<\/li>\n
  9. Atallah\u00a0A.M., Younes\u00a0A.B. Parallel Evaluation of Chebyshev Approximations\u00a0:Applications in Astrodynamics \/ A.M.\u00a0Atallah, A.B.\u00a0Younes \/\/ J. Astro-nautical Science. \u2013 2022. \u2013 Vol. 69. \u2013 \u0420.\u00a0692\u2013717.<\/li>\n
  10. Utpal Kiran. GPU-warp based finite element matrices generation and assembly using coloring method \/ Utpal Kiran, Deepak Sharma, Sachin Singh Gautam \/\/ Journal of Computation Design and Engineering, \u2013 2019. \u2013 No \u2013 P. 705-718.<\/li>\n
  11. Atallah A.M. Parallel Evaluation of Chebyshev Approximations\u00a0\/ A.M Atallah., A.B.\u00a0Younes\u00a0\/\/ Applications in Astrodynamics J. Astro-nautical Science. \u2013 \u2013 Vol. 69. \u2013 \u0420\u0440. 692\u2013717.<\/li>\n
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  13. \u041c\u0435\u0442\u043e\u0434 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u0432 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u043c \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u0435 \u00ab\u041c\u0406\u0420\u0415\u041b\u0410+\u00bb \/ \u0412.\u0412.\u00a0\u041a\u0438\u0440\u0438\u0447\u0435\u0432\u0441\u043a\u0438\u0439, \u0411.\u041c.\u00a0\u0414\u043e\u0445\u043d\u044f\u043a, \u042e.\u0413. \u041a\u043e\u0437\u0443\u0431 \u0438 \u0434\u0440. ; \u043f\u043e\u0434 \u043e\u0431\u0449. \u0440\u0435\u0434. \u0412.\u0412. \u041a\u0438\u0440\u0438\u0447\u0435\u0432\u0441\u043a\u043e\u0433\u043e. \u2013 \u041a.: \u041d\u0430\u0443\u043a. \u0434\u0443\u043c\u043a\u0430. \u2013 2005. \u2013 403 \u0441.<\/li>\n
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