|Title||Analysis of the computing power of the interlineational finite element method of solution of the non-stationary heat conduction problem|
|Publication Type||Journal Article|
|Year of Publication||2014|
|Authors||Sergienko, IV, Lytvyn, OM, Lobanova, LS, Zaluzhna, GV|
|Abbreviated Key Title||Dopov. Nac. akad. nauk Ukr.|
|Section||Information Science and Cybernetics|
Some aspects of a numerical implementation of the interlineational finite element method solution of the non-stationary heat conduction problem for planar domains with complex shapes are considered.It is proposed to test this method, by using exact solutions, for which the method of construction is proposed by the authors. The interlineational finite element method allows us to reduce the non-stationary heat conduction problem to the Cauchy problem for a system of ordinary differential equations of lower order than in the classical finite element method.
|Keywords||heat conduction, interlineational method, non-stationary problem|
1. Sergienko I. V., Lytvyn O. M. Dop. AN UkrSSR. Ser. A, 1990, No. 10: 69–73 (in Ukrainian).
2. Sergienko I. V., Lytvyn O. M., Drobot E. I. Dopov. Nac. akad. nauk Ukr., 2000, No. 2: 67–73 (in Ukrainian).
3. Current problems of stress concentration. Proceedings of the international scientific conference dedicated to the 75th anniversary of NAS academician A. S. Kosmodamiansky. Donetsk: DonGU, 1998: 417 (in Russian).
4. Babuska I. Computing, 1970, 6, No. 3: 264–273. https://doi.org/10.1007/BF02238811
5. Lytvyn O. M. Interlineation of the functions and some of its applications. Kharkiv: Osnova, 2002 (in Ukrainian).
6. Rvachev V. L. Theory of R-functions and some of its applications. Kyiv: Nauk. dumka, 1982 (in Russian).
7. Lytvyn O. M., Lobanova L. S., Zaluzhna G. V. The solution of non-stationary heat conductivity problem for interlineation plate by finite elements. Proceedings of the International Symposium “Issues Calculation Optimization (Poo-XXXV)”. – Kyiv: V. M. Glushkov Institute of Cybernetics of NAS of Ukraine, 2009: 14–19.
8. Lytvyn O. M., Lobanova L. S., Zaluzhna G. V. Matemat. ta kompiuterne modeliuvannia. Ser. Fiz.-mat. nauky, 2010, Iss. 4: 132–138 (in Ukrainian).
9. Lytvyn O. M., Lobanova L. S., Zaluzhna G. V. Iskusstvennyi intelekt, 2012, No. 1: 219–228 (in Ukrainian).
10. Lytvyn O. M., Lobanova L. S., Zaluzhna G. V. Upravliaiushchie systemy i mashyny, 2012, No. 4: 11–19 (in Russian).