Abstract
The paper is aimed to develop and investigate efficient parallel algorithms for solving heat-transfer equations in a three-dimensional domain. Applying the alternating-direction finite-difference scheme, the problem is reduced to solving multiple SLAEs with tridiagonal matrices. In this work, several approaches to computing the coefficients of these systems are implemented. To solve the systems, the sweep method is used. Parallel algorithms are implemented for multicore processors using OpenMP technology. The results of numerical experiments and the evaluation of the algorithms efficiency are presented. A comparison of the computing times shows that the new implementation is up to two times faster than the earlier one.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Samarsky, A.A., Vabishchevich, P.N.: Computational Heat Transfer, vol. 2, The Finite Difference Methodology. Wiley, Chichester (1995)
Romanovsky, V.E., Smith, S.L., Christiansen, H.H.: Permafrost thermal state in the polar Northern 430 Hemisphere during the International Polar Year 2007–2009: a synthesis. Permafr. Periglac. Proces. 21, 106–116 (2010). https://doi.org/10.1002/ppp.689
Gornov, V.F., Stepanov, S.P., Vasilyeva, M.V., Vasilyev, V.I.: Mathematical modeling of heat transfer problems in the permafrost. AIP Conf. Proc. 1629, 424–431 (2014). https://doi.org/10.1063/1.4902304
Stepanov, S.P., Sirditov, I.K., Vabishchevich, P.N., Vasilyeva, M.V., Vasilyev, V.I., Tceeva, A.N.: Numerical simulation of heat transfer of the pile foundations with permafrost. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) Numerical Analysis and Its Applications. NAA 2016. LNCS, vol. 10187, pp. 625–632. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57099-0_71
Kong, X, Doré, G, Calmels, F.: Thermal modeling of heat balance through embankments in permafrost regions. Cold Reg. Sci. Technol. 158, 117–127 (2019). https://doi.org/10.1016/j.coldregions.2018.11.013
Vaganova, N.A., Filimonov, M.Y.: Computer simulation of nonstationary thermal fields in design and operation of northern oil and gas fields. AIP Conf. Proc. 1690, 020016 (2015). https://doi.org/10.1063/1.4936694
Filimonov, M., Vaganova, N.: Permafrost thawing from different technical systems in arctic regions. IOP Conf. Ser. Earth Environ. Sci. 72, 012006 (2017). https://doi.org/10.1088/1755-1315/72/1/012006
Voevodin, V. V., Antonov S. A., Dongarra, J.: AlgoWiki: an open encyclopedia of parallel algorithmic features. Supercomput. Front. Innov. 2(1), 4–18 (2015). https://doi.org/10.14529/jsfi150101
Ortega, J. M.: Introduction to Parallel and Vector Solution of Linear Systems. Springer Science & Business Media, New York (2013). https://doi.org/10.1007/978-1-4899-2112-3
Rodrigue, G. (Ed.): Parallel Computations, vol. 1. Elsevier, Amsterdam (2014)
Chandra, R., Dagum, L., Kohr, D., Menon, R., Maydan, D., McDonald, J.: Parallel Programming in OpenMP. Morgan Kaufmann, Burlington (2001)
Pavlova, N.V., Vabishchevich, P.N., Vasilyeva, M.V.: Mathematical modeling of thermal stabilization of vertical wells on high performance computing systems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2013. LNCS, vol. 8353, pp. 636–643. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43880-0_73
Pepper, D. W., Lombardo, J. M.: High-Performance Computing for Fluid Flow and Heat Transfer. Advances in Numerical Heat Transfer, vol. 2. Routledge, Milton Park (2018)
Orgogozo, L., et al.: Water and energy transfer modeling in a permafrost-dominated, forested catchment of central Siberia: the key role of rooting depth. Permafr. Periglac. Process. 30(2), 75–89 (2019). https://doi.org/10.1002/ppp.1995
Akimova, E.N., Filimonov, M.Y., Misilov, V.E., Vaganova, N.A.: Application of high performance computations for modeling thermal fields near the wellheads. In: Sokolinsky, L., Zymbler, M. (eds.) PCT 2020. CCIS, vol. 1263, pp. 266–278. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-55326-5_19
Samarskii, A.A., Nikolaev, E.S.: Methods of Solving Finite-Difference Equations. Moscow (1978). (in Russian)
Vaganova, N., Filimonov, M.: Parallel splitting and decomposition method for computations of heat distribution in permafrost. In: CEUR Workshop Proceedings, vol. 1513, pp. 42–49 (2015)
Akimova, E.N., Filimonov, M.Y., Misilov, V.E., Vaganova, N.A.: Simulation of thermal processes in permafrost: parallel implementation on multicore CPU. In: CEUR Workshop Proceedings, vol. 2274, pp. 1–9 (2018)
Intel Corporation: Introduction to the SIMD Data Layout Templates. https://www.intel.com/content/www/us/en/develop/documentation/cpp-compiler-developer-guide-and-reference/top/compiler-reference/libraries/introduction-to-the-simd-data-layout-templates.html. Accessed 14 Feb 2022
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Akimova, E.N., Misilov, V.E. (2022). Simulation of Nonstationary Thermal Fields in Permafrost Using Multicore Processors. In: Sokolinsky, L., Zymbler, M. (eds) Parallel Computational Technologies. PCT 2022. Communications in Computer and Information Science, vol 1618. Springer, Cham. https://doi.org/10.1007/978-3-031-11623-0_21
Download citation
DOI: https://doi.org/10.1007/978-3-031-11623-0_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-11622-3
Online ISBN: 978-3-031-11623-0
eBook Packages: Computer ScienceComputer Science (R0)