# Numerical simulation of ﬂuid-structure interaction problems on hybrid meshes with algebraic multigrid methods

## Dr. Huidong Yang

**May 26, 2009, 2:15 p.m. MZ 005B**

Fluid-structure interaction problems arise in many application ﬁelds such as ﬂows around elastic structures or blood ﬂow problems in arteries. The method presented in this paper for solving such a problem is based on a reduction to an equation at the interface, involving the so-called Steklov-Poincaré operators.

This interface equation is solved by a Newton-like iteration for which directional derivatives involving shape derivatives with respect to the interface perturbation have to be evaluated appropriately.

One step of the Newton-like iteration requires the solution of several decoupled linear sub-problems in the structure and the ﬂuid domains. These sub-problems are spatially discretized by a ﬁnite element method on hybrid meshes. For the time discretization the implicit Euler method is used. The discretized equations are solved by algebraic multigrid methods.

This is a joint work with Prof. Zulehner.