large sparse matrix problems arising from finite element discretizations, the convergence of these methods deteriorates with increasing mesh density and increasing frequency of analysis. In such cases effective preconditioning becomes essential in order to accelerate iterative convergence. In the second part, we investigate a multilevel preconditioning approach that is based on the h-version of the hierarchical finite element method.
Consider the coupled system illustrated in Figure 9.1, consisting of the computational domain , composed of a fluid domain Ωf, and structural domain Ωs. The fluid boundary is divided into the fluid-structure interface boundary Гi and the artificial boundary . The structural boundary is composed of the fluid-structure interface boundary Гi and a traction boundary Gs. The infinite domain outside the artificial boundary is denoted by . The temporal interval of interest is and the number of spatial dimensions is d.
The structure is governed by the equations of elastodynamics, while the fluid equations are derived under the usual linear acoustic assumptions of an inviscid, compressible fluid with small disturbance. The strong form of the fluid-structure initial boundary-value problem is given by:
Find , and , such that