Preconditioning in the Path-Following Algorithm for the Stokes Flow with Stick-Slip Conditions

• Autorzy: Marta Jarošová , Radek Kučera , Václav Šátek
• 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. (original abstract)

Słowa kluczowe

PL

Algorytmy; Inżynieria materiałowa

EN

Algorithms; Materials engineering

• Czasopismo: Systems Supporting Production Engineering
• Rocznik: 2017
• Numer: 6(4) Cross-Border Exchange of Experience in Production Engineering Using Principles of Mathematics
• Strony: 274-285

Twórcy

autor

Marta Jarošová

• VŠB - Technical University of Ostrava, Czech Republic

autor

Radek Kučera

• VŠB - Technical University of Ostrava, Czech Republic

autor

Václav Šátek

• VŠB - Technical University of Ostrava, Czech Republic

Bibliografia

• C. L. M. H. Navier. "Mémoire sur les lois du movement des fluides", Mém. de l Acad. R. Sci. Paris, 1823, 6: 389416.
• 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.
• 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.
• D. Arnold, F. Brezzi, M. Fortin. "A stable finite element for the stokes equations", Calcolo, 21(4), 1984, p. 337-344.
• 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].
• 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.
• 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.
• R. Kucera, V. Šátek, M. Jarošová. "Path-following interior point method for QPP with box and equality constraints: theory and applications", in preparation 2017.
• 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.
• 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.
• 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.