On the formulation and local implementation of a variationally coupled finite element-boundary element method (Q1309657)

Finite element (FE) and boundary element (BE) formulations were unified to facilitate their application in practice. Both approaches have advantages in different areas, and their coupling is particularly attractive e.g. for solving problems of fracture mechanics, geomechanics, and micromechanics. In such cases, boundary elements can be applied to model the infinite domain while the finite element approach enables to consider nonlinearities of the material. Coupling of the two methods is usually done at the level of the discretized equations or at the variational level. In the paper, the variational statement which is employed to obtain the discretized equations has a simpler form than it is given by other authors. It is not necessary to define the exact form of the test functions. Thus the authors can avoid the issue of singular integration over a region in the finite element domain. Standard techniques in boundary elements and finite elements are used to evaluate the resulting integrals over the FE domain and the external boundary of the BE domain. Special finite elements contiguous to the interface between the BE and FE domains, and boundary elements on the external boundary of the BE domain are introduced. The stiffness of the BE domain is incorporated to the local stiffness matrices of these elements. In this manner, the coupled method can be implemented by adding new element subroutines to an existing finite element code without changing the main program. Two examples prove the precision of the presented approach. The FEM is not accurate by itself. However, the method coupled with BEM gives astonishing accuracy of results compared with exact or theoretical values. One can be convinced that the proposed coupling can enhance the accuracy of the approximate method. The paper, besides the theoretical base, gives the numerical algorithm with explanations. It can be helpful for individual applications.