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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:
74S05Finite element methods in solid mechanics
74S15Boundary element methods in solid mechanics
74B99Elastic materials
74H99Dynamical problems in solid mechanics
65N55Multigrid methods; domain decomposition (BVP of PDE)