Electronic Scientific Journal
 
Diagnostics, Resource and Mechanics 
         of materials and structures
Рус/Eng  

 

advanced search

IssuesAbout the JournalAuthorContactsNewsRegistration

All Issues

All Issues
 
2024 Issue 5
 
2024 Issue 4
 
2024 Issue 3
 
2024 Issue 2
 
2024 Issue 1
 
2023 Issue 6
 
2023 Issue 5
 
2023 Issue 4
 
2023 Issue 3
 
2023 Issue 2
 
2023 Issue 1
 
2022 Issue 6
 
2022 Issue 5
 
2022 Issue 4
 
2022 Issue 3
 
2022 Issue 2
 
2022 Issue 1
 
2021 Issue 6
 
2021 Issue 5
 
2021 Issue 4
 
2021 Issue 3
 
2021 Issue 2
 
2021 Issue 1
 
2020 Issue 6
 
2020 Issue 5
 
2020 Issue 4
 
2020 Issue 3
 
2020 Issue 2
 
2020 Issue 1
 
2019 Issue 6
 
2019 Issue 5
 
2019 Issue 4
 
2019 Issue 3
 
2019 Issue 2
 
2019 Issue 1
 
2018 Issue 6
 
2018 Issue 5
 
2018 Issue 4
 
2018 Issue 3
 
2018 Issue 2
 
2018 Issue 1
 
2017 Issue 6
 
2017 Issue 5
 
2017 Issue 4
 
2017 Issue 3
 
2017 Issue 2
 
2017 Issue 1
 
2016 Issue 6
 
2016 Issue 5
 
2016 Issue 4
 
2016 Issue 3
 
2016 Issue 2
 
2016 Issue 1
 
2015 Issue 6
 
2015 Issue 5
 
2015 Issue 4
 
2015 Issue 3
 
2015 Issue 2
 
2015 Issue 1

 

 

 

 

 

L. F. Spevak, O. A. Nefedova

PARALLEL TECHNOLOGY FOR SOLVING NONSTATIONARY HEAT CONDUCTION PROBLEMS IN AXISYMMETRIC DOMAINS

DOI: 10.17804/2410-9908.2021.6.60-71

The paper develops a parallel algorithm and program for solving nonstationary heat conduction and diffusion problems in axisymmetric domains with axisymmetric boundary conditions. The numerical solution is based on the boundary element method. In order to optimize and enhance the effectiveness of the computer implementation of the algorithm, the computations are parallelized and the OpenMP application program interface is used. The program is tested by comparing the calculation results with the data of known exact solutions. The calculations confirm the correctness of the numerical solutions and the possibility of full scaling at different numbers of boundary elements according to the number of cores/processors available. The program is applicable to solving axisymmetric heat conduction and diffusion problems and, as a component of a software system, to solving nonlinear problems.

Acknowledgments: The work was performed under a state assignment, state registration number AAAA-A18-118020790140-5.

Keywords: axisymmetric heat conduction problem, boundary element method, parallel computations, OpenMP

References:

  1. Fedotov V.P., Spevak L.F., Nefedova O.A. Parallel algorithms for strength analysis of hydrogenated structures. Programmnye produkty i sistemy, 2012, vol. 99, No. 3, pp. 235–239. (In Russian).
  2. Fedotov V.P., Spevak L.F., Nefedova O.A. A software package designed to solve problems of the potential theory by the boundary element method Programmnye produkty i sistemy, 2014, vol. 108, No. 4, pp. 178–183. DOI: 10.15827/0236-235X.108.178-182. (In Russian).
  3. Fedotov V.P., Spevak L.F. Analytical integration of kernel functions for solving elasticity problems and potential theory by the method of boundary elements. Matematicheskoe modelirovanie, 2007, vol. 19, No. 2, pp. 87–104. (In Russian).
  4. Fedotov V.P., Spevak L.F. One approach to the derivation of exact integration formulae in the boundary element method. Engineering Analysis with Boundary Elements, 2008, vol. 32, No. 10, pp. 883–888. DOI: 10.1016/j.enganabound.2008.03.001.
  5. Fedotov V.P., Spevak L.F., Nefedova O.A. Моделирование процессов упругопластического деформирования модифицированным методом граничных элементов. Programmnye produkty i sistemy, 2013, vol. 4, No. 4, pp. 253–257. (In Russian).
  6. Spevak L.F., Nefedova O.A. Solving a two-dimensional nonlinear heat conduction equation with degeneration by the boundary element method with the application of the dual reciprocity method. AIP Conference Proceedings, 2016, vol. 1785, 040077. DOI: 10.1063/1.4967134.
  7. Spevak L.F., Nefedova O.A. Solving a two-dimensional nonlinear heat conduction equation with nonzero boundary conditions by the boundary element method. AIP Conference Proceedings, 2017, vol. 1915, 040055. DOI: 10.1063/1.5017403.
  8. Kazakov A.L., Nefedova O.A., Spevak L.F. Solution of the Problem of Initiating the Heat Wave for a Nonlinear Heat Conduction Equation Using the Boundary Element Method. Computational Mathematics and Mathematical Physics, 2019, vol. 59, iss. 6, pp. 1015–1029. DOI: 10.1134/S0965542519060083.
  9. Kazakov A., Spevak L., Nefedova O., Lempert A. On the Analytical and Numerical Study of a Two-Dimensional Nonlinear Heat Equation with a Source Term. Symmetry-Basel, 2020, vol. 12, iss. 6, article 921. DOI: 10.3390/sym12060921.
  10. Kazakov A.L., Spevak L.F., Nefedova O.A. A Numerical Solution to the Two-Dimensional Nonlinear Degenerate Heat Conduction Equation with a Source. AIP Conference Proceedings, 2020, vol. 2315, 040018. DOI: 10.1063/5.0036718.
  11. Spevak L.F., Nefedova O.A. Parallel technology for solving the poisson equation in axisymmetric domains by the boundary element method. AIP Conference Proceedings, 2018, vol. 2053, 030070. DOI: 10.1063/1.5084431.
  12. Nefedova O.A., Spevak L.F. Parallel Technology for Solving Axisymmetric Problems of the Theory of Elasticity by the Boundary Element Method. AIP Conference Proceedings, 2020, vol. 2315, 020030. DOI: 10.1063/5.0037021.
  13. Rizzo F.J., Shippy D.J. A method of solution for certain problems of transient heat conduction. AIAA J., 1970, vol. 8, pp. 2004–2009. DOI:10.2514/3.6038.
  14. Shaw R.P. An integral equation approach to diffusion. International Journal of Heat and Mass Transfer, 1974, vol. 17 (6), pp. 693–699. DOI: 10.1016/0017-9310(74)90202-6.
  15. Brebbia C.A., Walker S. Boundary Element Techniques in Engineering, Newnes–Butterworths, London, 1980. ISBN: 9781483102566.
  16. Wrobel L.C., Brebbia C.A. A formulation of the boundary element method for axisymmetric transient heat conduction. International Journal of Heat and Mass Transfer, 1981, vol. 24, pp. 843–850. DOI: 10.1016/S0017-9310(81)80007-5.
  17. Zhu S.P. Time-dependent reaction diffusion problems and the LTDRM approach. In: M. Goldberg, ed. Boundary Integral Methods: Numerical and Mathematical Aspects. Computational Mechanics Publications, Southampton, Boston, 1999, pp. 1–35.
  18. Sutradhar A, Paulino G.H, Gray L.J. Transient heat conduction in homogeneous and nonhomogeneous materials by the Laplace Transform Galerkin boundary element method. Engineering Analysis with Boundary Elements, vol. 26 (2), pp. 119–132. DOI: 10.1016/S0955-7997(01)00090-X.
  19. Brebbia C.A., Telles J.F.C., Wrobel L.C. Boundary Element Techniques, Springer-Verlag, Berlin, Neidelberg, New-York, Tokyo, 1984, 466 р. ISBN: 978-3-642-48862-7 (print), 978-3-642-48860-3 (online). DOI: 10.1007/978-3-642-48860-3.
  20. Abramowitz M., Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. In: M. Abramowitz, I. A. Stegun, eds. Dover Books on Advanced Mathematics, Dover Publications, New York, 1965.
  21. Kronrod A.S. Uzly i vesa kvadraturnykh formul [Nodes and weights of quadrature formulas]. Moscow, Nauka Publ., 1964, 143 p. (In Russian).
  22. Lifanov I.K. Metod singulyarnykh integralnykh uravnenii i chislennyi eksperiment [Singular integral equations method and numerical experiment]. Moscow, Yanus Publ.,1995, 520 p. ISBN 5-88929-003-7. (In Russian).
  23. GSL–GNU Scientific Library. Available at: http://www.gnu.org/software/gsl/ (accessed 07.04.2021).
  24. Boost C++ Libraries. Available at: http://www.boost.org/ (accessed 07.04.2021).
  25. What is OpenMP? PARALLEL.RU. Available at: https://parallel.ru/tech/tech_dev/openmp.html (accessed 11.05.2021).
  26. OpenMP. Available at: http://www.openmp.org/ (accessed 11.05.2021).
  27. Lykov A.V. Teoriya teploprovodnosti [Heat conduction theory]. Moscow, Vysshaya shkola Publ., 1967, 597 p. (In Russian).


PDF      

Article reference

Spevak L. F., Nefedova O. A. Parallel Technology for Solving Nonstationary Heat Conduction Problems in Axisymmetric Domains // Diagnostics, Resource and Mechanics of materials and structures. - 2021. - Iss. 5. - P. 60-71. -
DOI: 10.17804/2410-9908.2021.6.60-71. -
URL: http://eng.dream-journal.org/issues/content/article_349.html
(accessed: 12/02/2024).

 

impact factor
RSCI 0.42

 

MRDMS 2024
Google Scholar


NLR

 

Founder:  Institute of Engineering Science, Russian Academy of Sciences (Ural Branch)
Chief Editor:  S.V. Smirnov
When citing, it is obligatory that you refer to the Journal. Reproduction in electronic or other periodicals without permission of the Editorial Board is prohibited. The materials published in the Journal may be used only for non-profit purposes.
Contacts  
 
Home E-mail 0+
 

ISSN 2410-9908 Registration SMI Эл № ФС77-57355 dated March 24, 2014 © IMACH of RAS (UB) 2014-2024, www.imach.uran.ru