A quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows
ESAIM: Mathematical Modelling and Numerical Analysis , Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 631-647.

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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 : 10.1051/m2an:2003049
Classification : 65M60, 74K25, 76D05, 76Z05
Mots-clés : fluid-structure interaction, quasi-Newton algorithm, added mass effect, blood flows 
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     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 },
     pages = {631--647},
     publisher = {EDP-Sciences},
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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 , Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 631-647. doi : 10.1051/m2an:2003049. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003049/

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