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.