[Un algorithme exact de Newton par blocs pour la résolution de problèmes d'interaction fluide–structure]
Dans cette Note, nous nous intéressons à une méthode à partitions de type Newton pour la résolution de systèmes couplés non-linéaires intervenant dans l'approximation numérique des problèmes d'interaction fluide–structure. Cet algorithme utilise, de manière fondamentale, l'évaluation exacte des jacobiens construits à partir des sous-problèmes fluide–structure linéarisés dont nous fournissons la structure exacte.
In this Note, we introduce a partitioned Newton based method for solving nonlinear coupled systems arising in the numerical approximation of fluid–structure interaction problems. The originality of this Schur–Newton algorithm lies in the exact Jacobians evaluation involving the fluid–structure linearized subsystems which are here fully developed.
Accepté le :
Publié le :
Miguel Ángel Fernández 1 ; Marwan Moubachir 2
@article{CRMATH_2003__336_8_681_0,
author = {Miguel \'Angel Fern\'andez and Marwan Moubachir},
title = {An exact {Block{\textendash}Newton} algorithm for solving fluid{\textendash}structure interaction problems},
journal = {Comptes Rendus. Math\'ematique},
pages = {681--686},
publisher = {Elsevier},
volume = {336},
number = {8},
year = {2003},
doi = {10.1016/S1631-073X(03)00151-1},
language = {en},
}
TY - JOUR AU - Miguel Ángel Fernández AU - Marwan Moubachir TI - An exact Block–Newton algorithm for solving fluid–structure interaction problems JO - Comptes Rendus. Mathématique PY - 2003 SP - 681 EP - 686 VL - 336 IS - 8 PB - Elsevier DO - 10.1016/S1631-073X(03)00151-1 LA - en ID - CRMATH_2003__336_8_681_0 ER -
Miguel Ángel Fernández; Marwan Moubachir. An exact Block–Newton algorithm for solving fluid–structure interaction problems. Comptes Rendus. Mathématique, Volume 336 (2003) no. 8, pp. 681-686. doi : 10.1016/S1631-073X(03)00151-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00151-1/
[1] Sensitivity analysis for an incompressible aeroelastic system, Math. Models Methods Appl. Sci., Volume 12 (2002) no. 8, pp. 1109-1130
[2] Fluid structure interaction with large structural displacements, Comput. Methods Appl. Mech. Engrg., Volume 190 (2001) no. 24–25, pp. 3039-3067
[3] Numerical efficiency of different partitioned methods for fluid–structure interaction, Z. Angew. Math. Mech., Volume 80 (2000) no. 2, pp. 557-558
- Global uniform stabilization to nontrivial equilibrium of a nonlinear fluid viscoelastic-structure interaction, Applicable Analysis, Volume 97 (2018) no. 10, pp. 1797-1813 | DOI:10.1080/00036811.2017.1341975 | Zbl:1395.35021
- Feedback stabilization of a linear hydro-elastic system, Discrete and Continuous Dynamical Systems. Series B, Volume 23 (2018) no. 3, pp. 1107-1132 | DOI:10.3934/dcdsb.2018144 | Zbl:1395.74028
- Linearized hydro-elasticity: a numerical study, Evolution Equations and Control Theory, Volume 5 (2016) no. 4, pp. 533-559 | DOI:10.3934/eect.2016018 | Zbl:1351.74022
- Uniform stabilization to equilibrium of a nonlinear fluid-structure interaction model, Nonlinear Analysis. Real World Applications, Volume 25 (2015), pp. 51-63 | DOI:10.1016/j.nonrwa.2015.02.006 | Zbl:1327.35322
- Well-posedness analysis for a linearization of a fluid-elasticity interaction, SIAM Journal on Mathematical Analysis, Volume 47 (2015) no. 3, pp. 1958-2000 | DOI:10.1137/140970689 | Zbl:1321.74020
- Method of Successive Approximations for a Fluid Structure Interaction Problem, Applied Mathematics, Volume 05 (2014) no. 15, p. 2299 | DOI:10.4236/am.2014.515223
- Mathematical and numerical analysis of some FSI problems, Fluid-structure interaction and biomedical applications, Basel: Birkhäuser/Springer, 2014, pp. 1-77 | DOI:10.1007/978-3-0348-0822-4_1 | Zbl:1365.74066
- Immersed boundary methods for simulating fluid–structure interaction, Progress in Aerospace Sciences, Volume 65 (2014), p. 1 | DOI:10.1016/j.paerosci.2013.09.003
- Solutions to a fluid-structure interaction free boundary problem, Discrete Continuous Dynamical Systems - A, Volume 32 (2012) no. 4, p. 1355 | DOI:10.3934/dcds.2012.32.1355
- Well-posedness for the compressible Navier–Stokes–Lamé system with a free interface, Nonlinearity, Volume 25 (2012) no. 11, p. 3111 | DOI:10.1088/0951-7715/25/11/3111
- Finite element approach to immersed boundary method with different fluid and solid densities, M
- Asymptotic stability of finite energy in Navier Stokes-elastic wave interaction, Semigroup Forum, Volume 82 (2011) no. 1, pp. 61-82 | DOI:10.1007/s00233-010-9281-7 | Zbl:1210.35179
- , 49th IEEE Conference on Decision and Control (CDC) (2010), p. 7057 | DOI:10.1109/cdc.2010.5717717
- Performance of partitioned procedures in fluid–structure interaction, Computers Structures, Volume 88 (2010) no. 7-8, p. 446 | DOI:10.1016/j.compstruc.2009.12.006
- Stabilization of explicit coupling in fluid-structure interaction involving fluid incompressibility, Computer Methods in Applied Mechanics and Engineering, Volume 198 (2009) no. 5-8, pp. 766-784 | DOI:10.1016/j.cma.2008.10.012 | Zbl:1229.76045
- Optimal Feedback Synthesis for Bolza Control Problem Arising in Linearized Fluid Structure Interaction, Optimal Control of Coupled Systems of Partial Differential Equations, Volume 158 (2009), p. 171 | DOI:10.1007/978-3-7643-8923-9_10
- Riccati theory and singular estimates for a Bolza control problem arising in linearized fluid-structure interaction, Systems Control Letters, Volume 58 (2009) no. 7, pp. 499-509 | DOI:10.1016/j.sysconle.2009.02.010 | Zbl:1166.49036
- , 2008 47th IEEE Conference on Decision and Control (2008), p. 203 | DOI:10.1109/cdc.2008.4738966
- A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid, International Journal for Numerical Methods in Engineering, Volume 69 (2007) no. 4, pp. 794-821 | DOI:10.1002/nme.1792 | Zbl:1194.74393
- A semi-implicit approach for fluid-structure interaction based on an algebraic fractional step method, M
- A Newton method using exact jacobians for solving fluid–structure coupling, Computers Structures, Volume 83 (2005) no. 2-3, p. 127 | DOI:10.1016/j.compstruc.2004.04.021
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