No abstract

Solving multiphysical problems is a challenging task in computational engineering both in regard to accuracy and efficiency. Finite element methods (FEM) – while very popular and well established for standard problems – are less straightforward for problems involving interfaces moving due to the influence of external fields. Such problems are characterized by additional challenges, such as mesh dynamics, re‐meshing and possible unboundedness of the external field. The boundary element method (BEM) can help to overcome these challenges. In the BEM formulation, the problem is solved solely from the boundary of the domain. This property – in conjunction with finite element shell and membrane formulations – leads to a very interesting coupled method, requiring only the surface discretization to solve multiphysical interface problems. To show the underling idea of the formulation, the electro‐mechanical interaction between two charged shells is considered as an example.

The boundary element method (BEM) is able to solve partial differential equations without volumetric discretization and integration. Therefore, the BEM is able to reduce the compuational as well as the meshing effort compared to volumetric methods like classical finite elements. In this work, a conventional and a nonsingular BEM formulation for Stokes flow are presented and investigated in three-dimensions, considering rotating spheres within a viscous fluid.