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On the parameter in augmented Lagrangian preconditioning for isogeometric discretizations of the Navier-Stokes equations

Jiří Egermaier;  Hana Horníková — 2022

Applications of Mathematics

In this paper, we deal with the optimal choice of the parameter γ for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using the B-spline based isogeometric analysis approach. We are interested in the dependence of the convergence on the parameter γ for various problem parameters (Reynolds number, mesh refinement) and especially for...

Gradient-free and gradient-based methods for shape optimization of water turbine blade

Bastl, Bohumír;  Brandner, Marek;  Egermaier, Jiří;  Horníková, Hana;  Michálková, Kristýna;  Turnerová, Eva — 2019

Programs and Algorithms of Numerical Mathematics

The purpose of our work is to develop an automatic shape optimization tool for runner wheel blades in reaction water turbines, especially in Kaplan turbines. The fluid flow is simulated using an in-house incompressible turbulent flow solver based on recently introduced isogeometric analysis (see e.g. J. A. Cotrell et al.: Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, 2009). The proposed automatic shape optimization approach is based on a so-called hybrid optimization which combines...

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