Different Methodologies for Coupled BEM and FEM with Implementation on Parallel Computers

The boundary element method (BEM) and the finite element method (FEM) may be computationally expensive if complex problems are to be solved, thus there is the need of implementing them on fast computer architectures, especially parallel computers. Because BEM and FEM are complementary to each other, the coupling of these methods is widely used. In this paper, a parallel FE-BE-code and its implementation on a distributed memory system (Parsytec MultiCluster2) is described. As model problems, we assume linear elasticity for the boundary element method and elastoplasticity for the finite element method. The efficiency of our implementation is shown by various test examples. Two coupling methods are proposed. First, we show by numerical examples that a multiplicative Schwarz method for coupling BEM with FEM is very well suited for parallel implementation. Furthermore, we treat a symmetric coupling of Galerkin-Bem and mixed finite elements of Raviart-Thomas type leading to improved stress approximation.