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Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms

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  • Jaroslav Haslinger

    (Faculty of Mechanical Engineering, VŠB-TUO, 17. Listopadu 2172/15, 708 00 Ostrava-Poruba, Czech Republic
    IT4Innovations, VŠB-TUO, Studentská 6231/1B, 708 00 Ostrava-Poruba, Czech Republic
    These authors contributed equally to this work.)

  • Radek Kučera

    (Faculty of Mechanical Engineering, VŠB-TUO, 17. Listopadu 2172/15, 708 00 Ostrava-Poruba, Czech Republic
    IT4Innovations, VŠB-TUO, Studentská 6231/1B, 708 00 Ostrava-Poruba, Czech Republic
    These authors contributed equally to this work.)

  • Kristina Motyčková

    (IT4Innovations, VŠB-TUO, Studentská 6231/1B, 708 00 Ostrava-Poruba, Czech Republic
    These authors contributed equally to this work.)

  • Václav Šátek

    (IT4Innovations, VŠB-TUO, Studentská 6231/1B, 708 00 Ostrava-Poruba, Czech Republic
    Faculty of Information Technology, Brno University of Technology, Božetěchova 1/2, 612 66 Brno, Czech Republic
    These authors contributed equally to this work.)

Abstract

The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth. It is solved by the path-following variant of the interior point method, and by the active-set implementation of the semi-smooth Newton method. Inner linear systems are solved by the preconditioned conjugate gradient method. Numerical experiments illustrate scalability of the algorithms. The novelty of this work consists in applying dual strategies for solving the problem.

Suggested Citation

  • Jaroslav Haslinger & Radek Kučera & Kristina Motyčková & Václav Šátek, 2021. "Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms," Mathematics, MDPI, vol. 9(22), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2906-:d:679752
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    References listed on IDEAS

    as
    1. Kučera, Radek & Haslinger, Jaroslav & Šátek, Václav & Jarošová, Marta, 2018. "Efficient methods for solving the Stokes problem with slip boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 145(C), pages 114-124.
    2. Radek Kučera & Kristina Motyčková & Alexandros Markopoulos, 2015. "The R-linear convergence rate of an algorithm arising from the semi-smooth Newton method applied to 2D contact problems with friction," Computational Optimization and Applications, Springer, vol. 61(2), pages 437-461, June.
    3. Haslinger, Jaroslav & Kučera, Radek & Sassi, Taoufik & Šátek, Václav, 2021. "Dual strategies for solving the Stokes problem with stick–slip boundary conditions in 3D," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 189(C), pages 191-206.
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    Cited by:

    1. Haslinger, Jaroslav & Mäkinen, Raino A.E., 2024. "Shape optimization for the Stokes system with threshold leak boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 180-196.

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