Non-overlapping domain decomposition with BEM and FEM.

*(English)* Zbl 0891.73070
Whiteman, J. R. (ed.), The mathematics of finite elements and applications. Highlights 1996. Proceedings of the 9th conference, MAFELAP 1996, Uxbridge, GB, June 25–28, 1996, Chichester: Wiley. 145-154 (1997).

This paper presents a coupling algorithm of the finite element method and the boundary element method within a domain decomposition procedure for solving mixed boundary value problems in two- and three-dimensional elastostatics. A mixed variational formulation on the coupling interfaces leads to the use of non-conforming grids for each substructure. The local BEM problems are solved iteratively by expanding the boundary integral equation in a Neumann series. As a consequence, the properties of the coupling matrix concerning symmetry and definiteness can be controlled automatically within an adaptive algorithm. In particular, the proposed FE/BE technique handles stress concentration problems very efficiently, providing locally high resolution of the desired stress fields. The BE macro-elements can be incorporated into standard FEM codes.

##### MSC:

74S05 | Finite element methods in solid mechanics |

74S15 | Boundary element methods in solid mechanics |

74B99 | Elastic materials |

74H99 | Dynamical problems in solid mechanics |

65N55 | Multigrid methods; domain decomposition (BVP of PDE) |