In this work, we address the numerical solution of fluid-structure
interaction problems. This issue is particularly difficulty to tackle
when the fluid and the solid densities are of the same order, for
instance as it happens in hemodynamic applications, since fully
implicit coupling schemes are required to ensure stability of the
resulting method. Thus, at each time step, we have to solve a highly
non-linear coupled system, since the fluid domain depends on the
unknown displacement of the structure. Standard strategies for solving
this non-linear problems, are fixed point based methods such as
Block-Gauss-Seidel (BGS) iterations. Unfortunately, these methods are
very CPU time consuming and usually show slow convergence. We propose
a modified fixed-point algorithm which combines the standard BGS
iterations with a transpiration formulation. Numerical experiments
show the great improvement in computing time with respect to the
standard BGS method.