Nonlinear Monolithic Two-Level Schwarz Methods for the Navier-Stokes Equations (2409.03041v1)
Abstract: Nonlinear domain decomposition methods became popular in recent years since they can improve the nonlinear convergence behavior of Newton's method significantly for many complex problems. In this article, a nonlinear two-level Schwarz approach is considered and, for the first time, equipped with monolithic GDSW (Generalized Dryja-Smith-Widlund) coarse basis functions for the Navier-Stokes equations. Results for lid-driven cavity problems with high Reynolds numbers are presented and compared with classical global Newton's method equipped with a linear Schwarz preconditioner. Different options, for example, local pressure corrections on the subdomain and recycling of coarse basis functions are discussed in the nonlinear Schwarz approach for the first time.
- SIAM J. Sci. Comput. 24(1), 183–200 (2002). DOI 10.1137/S106482750037620X. URL https://doi.org/10.1137/S106482750037620X
- pp. 1463–1470 (2002). DOI 10.1002/fld.404. URL https://doi.org/10.1002/fld.404. LMS Workshop on Domain Decomposition Methods in Fluid Mechanics (London, 2001)
- SIAM Journal on Numerical Analysis 46(4), 2153–2168 (2008). DOI 10.1137/070685841. URL https://doi.org/10.1137/070685841
- SIAM Journal on Scientific Computing 39(4), A1466–A1488 (2017). DOI 10.1137/17M1114272. URL https://doi.org/10.1137/17M1114272
- SIAM J. Sci. Comput. 38(6), A3357–A3380 (2016). DOI 10.1137/15M102887X. URL https://doi.org/10.1137/15M102887X
- SIAM J. Optim. 4(2), 393–422 (1994). DOI 10.1137/0804022. URL https://doi.org/10.1137/0804022
- SIAM J. Sci. Comput. 41(4), C291–C316 (2019). DOI 10.1137/18M1184047. URL https://doi.org/10.1137/18M1184047
- Internat. J. Numer. Methods Engrg. 121(6), 1101–1119 (2020). DOI 10.1002/nme.6258. URL https://doi.org/10.1002/nme.6258
- SIAM J. Sci. Comput. 45(3), S152–S172 (2023). DOI 10.1137/21M1433605. URL https://doi.org/10.1137/21M1433605
- SIAM J. Sci. Comput. 42(4), A2461–A2488 (2020). DOI 10.1137/19M1276972. URL https://doi.org/10.1137/19M1276972
- SIAM J. Sci. Comput. 36(2), A737–A765 (2014). DOI 10.1137/130920563. URL https://doi.org/10.1137/130920563
- Vietnam J. Math. 50(4), 1053–1079 (2022). DOI 10.1007/s10013-022-00567-2. URL https://doi.org/10.1007/s10013-022-00567-2
- In: Domain Decomposition Methods in Science and Engineering XXVII, Lect. Notes Comput. Sci. Eng., vol. 149, pp. 479–486. Springer, Cham (2024). DOI 10.1007/978-3-031-50769-4“˙57. URL https://doi.org/10.1007/978-3-031-50769-4\_57
- Comput. Methods Appl. Mech. Engrg. 403, Paper No. 115733, 31 (2023). DOI 10.1016/j.cma.2022.115733. URL https://doi.org/10.1016/j.cma.2022.115733
- J. Comput. Phys. 496, Paper No. 112548, 22 (2024). DOI 10.1016/j.jcp.2023.112548. URL https://doi.org/10.1016/j.jcp.2023.112548
- SIAM J. Sci. Comput. 37(3), A1388–A1409 (2015). DOI 10.1137/140970379. URL https://doi.org/10.1137/140970379
- Mathematics 9(24) (2021). DOI 10.3390/math9243165. URL https://www.mdpi.com/2227-7390/9/24/3165
- International Journal for Multiscale Computational Engineering 6(3), 251–262 (2008)
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.