Multilevel BDDC for incompressible Navier-Stokes equations

0535448 - MÚ 2021 RIV US eng J - Journal Article
Hanek, Martin - Šístek, Jakub - Burda, P.
Multilevel BDDC for incompressible Navier-Stokes equations.
SIAM Journal on Scientific Computing. Roč. 42, č. 6 (2020), C359-C383. ISSN 1064-8275. E-ISSN 1095-7197
R&D Projects: GA ČR(CZ) GA18-09628S
Institutional support: RVO:67985840
Keywords : multilevel BDDC * domain decomposition * finite element method * Navier-Stokes equations
OECD category: Applied mathematics
Impact factor: 2.373, year: 2020
Method of publishing: Open access
https://doi.org/10.1137/19M1276479

We present an approach to the numerical solution of steady Navier–Stokes equations. Approximation by the finite element method (FEM) leads to a nonlinear saddle-point system. The system is linearized by the Picard iteration, which leads to a sequence of linear saddle-point systems with nonsymmetric matrices. In this paper, we study the application of Balancing Domain Decomposition based on Constraints (BDDC) to these systems. In particular, we formulate the multilevel BDDC method and explore its applicability for the benchmark problem of lid-driven cavity. Another contribution of the paper is describing the development and application of our BDDC solver to real-world problems of oil flow in hydrostatic bearings.
Permanent Link: http://hdl.handle.net/11104/0313462