On the formulation and local implementation of a variationally coupled finite element-boundary element method

The formulation and local implementation of a variationally coupled finite element-boundary element method are presented. In the formulation, a variational statement is obtained which does not involve a singular domain integration over a region in the finite element domain. This permits the use of standard techniques in finite elements and boundary elements to obtain the discretized equations. The numerical implementation is approached from a displacement based finite element point of view. Special finite elements contiguous to the interface between the boundary element and finite element domains, and boundary elements on the external boundary of the boundary element domain are introduced. Through a novel local node numbering scheme for each of these elements, the stiffness contribution of the boundary element domain is incorporated into the local stiffness matrices of these elements. In this manner, the coupled method can be implemented by adding element subroutines to an existing finite element code without making any changes to the main program. It is shown that the method implemented in this way passes a patch test devised for coupled procedures, and the utility of the methods for problems in micromechanics is demonstrated through an example.