Mixed-dimensional, symmetric coupling of FEM and BEM
With the Symmetric Galerkin Boundary Element Method (SGBEM), FEM-like stiffness matrices can be produced which are suitable for coupling the Boundary Element Method (BEM) and the Finite Element Method (FEM). Here, we focus on the mixed-dimensional coupling in linear elasticity, i.e. three-dimensional BEM-domains will be coupled with two-dimensional finite shell elements. After briefly recalling the basics of the SGBEM, a direct kinematic coupling scheme will be presented, where the BE-domain is treated as a finite macro element. When assembling the stiffness matrix, the different kinematic degrees of freedom at the interface of both formulations require special attention. The accuracy of the method used is demonstrated by a numerical example.
symmetric coupling coupling boundary element method finite element method mixed-dimensional coupling shell elements symmetric-galerkin approximation