Subject:  Numerical Simulation of FluidStructure Interaction Problems on Hybrid Meshes with Algebraic Multigrid Methods 
Author:  Dipl.Math. Huidong Yang 
Supervision:  A.Univ.Prof. Dipl.Ing. Dr. Walter Zulehner O.Univ.Prof. Dipl.Ing. Dr. Ulrich Langer 
External referee:  Prof. Dr. Peter Bastian (Universität Heidelberg) 
Fluidstructure interaction problems arise in many application fields such as flows around elastic structures or blood flow problems in arteries. One method for solving such a problem is based on a reduction to an equation at the interface, involving the socalled SteklovPoincare operators. This interface equation is solved by a Newton iteration for which directional derivatives with respect to the interface perturbation have to be evaluated appropriately. One step of the Newton iteration requires the solution of several decoupled linear subproblems in the structure and the fluid domains. These subproblems are spatially discretized by a finite element method on hybrid meshes containing different types of elements. For the time discretization implicit first order methods are used. The discretized equations are solved by algebraic multigrid methods for which a stabilized coarsening hierarchy is constructed in a proper way. We developed a draft implementation of a gridenabled solver for this fluidstructure interaction problem. A recently designed Client/Server model under the grid environment is used. The interface equation is solved on the server grid node, while the fluid and the structure subproblems are solved independently on client grid nodes. 
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