Preconditioning in the path-following algorithm for the stokes flow with stick-slip conditions

• Autorzy: Jarošová M. , Kucera R. , Šátek V.

Warianty tytułu

CS

Předpodmínění algoritmu sledování cesty pro stokesovo proudění se skluzovou podmínkou

• Języki publikacji: EN

Abstrakty

EN

The Stokes problem with the stick-slip boundary condition is solved by the mixed finite element method combined with the TFETI method. An interior point method for the minimization subject to box and equality constraints is used. The preconditioned projected conjugate gradient method solves the inner linear systems. The preconditioners are tested experimentally. The aim of our research is to develop efficient solvers for modelling of a flow over hydrophobic walls that exhibits applications in engineering areas including biomedical modelling or transport of fluid.

CS

Stokesova úloha se skluzovou podmínkou je rešena smíšenou metodou konecných prvku kombinovanou s TFETI metodou. Výpocet rešení se provádí metodou vnitrních bodu urcenou k minimalizaci s oboustraným omezením a rovnostní vazbou. Predpodmínená projektovaná metoda sdružených gradientu se používá pro rešení vnitrních lineárních soustav. Úcinost predpodminovacu se testuje experimentálne. Cílem výzkumu je vyvinout efektivní rešice pro modelování proudení po hydrofobních stenách, což nachází uplatnení v inženýrských oblastech zahrnujících modelování v biomedicíne nebo pri prenosu tekutin.

Słowa kluczowe

EN

Stokes problem; stick-slip condition; interior point method; TFETI method

PL

zagadnienie Stokesa; stan stick-slip; metoda punktu wewnętrznego; metoda TFETI

• Wydawca: STE GROUP
• Czasopismo: Systemy Wspomagania w Inżynierii Produkcji
• Rocznik: 2017
• Tom: Vol. 6, iss. 4
• Strony: 274--285
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Jarošová M.

• VŠB - Technical University of Ostrava, IT4Innovations, 17. listopadu 15/2172, 708 33, Ostrava, Czech Republic, tel.: [phone]

autor

Kucera R.

• VŠB - Technical University of Ostrava, Department of Mathematics and Descriptive Geometry, 17. listopadu 15/2172, 708 33, Ostrava, Czech Republic, tel.: [phone]

autor

Šátek V.

• VŠB - Technical University of Ostrava, IT4Innovations, 17. listopadu 15/2172, 708 33, Ostrava, Czech Republic, tel.: [phone]

Bibliografia

• 1. C. L. M. H. Navier. “Mémoire sur les lois du movement des fluides”, Mém. de l Acad. R. Sci. Paris, 1823, 6: 389416.
• 2. I. J. Rao, K. Rajagopal. “The effect of the slip boundary condition on the flow of fluids in a channel”, Acta Mechanica, Vol. 135(3), 1999, p. 113-126.
• 3. M. Ayadi, L. Baffico, M. K. Gdoura, T. Sassi. “Error estimates for Stokes problem with Tresca friction conditions”, ESAIM: Math. Model. Numer. Anal., Vol. 48(5), 2014, p. 1413-1429.
• 4. D. Arnold, F. Brezzi, M. Fortin. “A stable finite element for the stokes equations”, Calcolo, 21(4), 1984, p. 337-344.
• 5. J. Koko. “Vectorized Matlab codes for the Stokes problem with P1-bubble/P1 finite element”, 2012, http://www.isima.fr/˜ jkoko/Codes/StokesP1BubbleP1.pdf [online].
• 6. Z. Dostál, D. Horák, R. Kucera. “Total FETI - an easier implementable variant of the FETI method for numerical solution of elliptic PDE”, Commun. Numer. Methods Eng., Vol. 22(12), 2006, p. 1155-1162.
• 7. R. Kucera, J. Machalová, H. Netuka, P. Žencák. “An interior point algorithm for the minimization arising from 3D contact problems with friction”, Optim. Methods Softw., 6(28), 2013, p. 1195-1217.
• 8. R. Kucera, V. Šátek, M. Jarošová. “Path-following interior point method for QPP with box and equality constraints: theory and applications”, in preparation 2017.
• 9. R. Kucera, J. Haslinger, V. Šátek, M. Jarošová. “Efficient methods for solving the Stokes problem with slip boundary conditions”, Math. Comput. Simul., http://dx.doi.org/10.1016/j.matcom.2016.05.012.
• 10. M. Jarošová, R. Kucera, V. Šátek. “A new variant of the path-following algorithm for the parallel solving of the Stokes problem with friction”, in P. Iványi, B. H. V. Topping (Editors), Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering. Civil-Comp Press, Paper 11, Stirlingshire, UK, 2015.
• 11. R. Kucera, T. Kozubek, A. Markopoulos. “On large-scale generalized inverses in solving two-by-two block linear systems”, Linear Algebra Appl., 438(7), 2013, p. 3011-3029.