| Summary: | The interaction problem of incompressible fluid and incompressible elastic material in the so-called Arbitrary Lagrangian-Eulerian formulation is be- ing studied in this thesis. After giving an overview of the essential principles of continuum mechanics in the moving domains, the fluid-structure interaction model is defined. Next, appropriate numerical scheme in three-dimensional space, based on finite element method, is presented and suitable numerical implementation is proposed. The properties of the presented numerical method are demonstrated on the number of numerical examples. The simplest approach, decoupling the problem into the fluid and solid parts and treating the interaction between them as an external boundary condition, is later revised by introducing the single continuum formulation. The interaction is then seen as an internal boundary, which does not require any special treatment. The proposed method allows to model the large deformations of an incom- pressible Neo-Hookean material, a flow of an incompressible power-law fluid and a mutual material interaction. The quasi-Newton method is used to solve with the original non-linear problem, while a direct solver is the tool that deals with the resulting linearized form. The numerical implementation takes advantage of parallel programming...
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