A quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 4, p. 631-647

We propose a quasi-Newton algorithm for solving fluid-structure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We present 2D and 3D fluid-structure simulations performed either with a simple 1D structure model or with shells in large displacements.

DOI : https://doi.org/10.1051/m2an:2003049
Classification:  65M60,  74K25,  76D05,  76Z05
Keywords: fluid-structure interaction, quasi-Newton algorithm, added mass effect, blood flows
@article{M2AN_2003__37_4_631_0,
author = {Gerbeau, Jean-Fr\'ed\'eric and Vidrascu, Marina},
title = {A quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {37},
number = {4},
year = {2003},
pages = {631-647},
doi = {10.1051/m2an:2003049},
zbl = {1070.74047},
mrnumber = {2018434},
language = {en},
url = {http://www.numdam.org/item/M2AN_2003__37_4_631_0}
}

Gerbeau, Jean-Frédéric; Vidrascu, Marina. A quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 4, pp. 631-647. doi : 10.1051/m2an:2003049. http://www.numdam.org/item/M2AN_2003__37_4_631_0/

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