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Zbl 0891.73070
Schnack, E.; Szikrai, Sz.; Türke, K.
Non-overlapping domain decomposition with BEM and FEM. (English)
[A] 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). ISBN 0-471-96270-8

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 2000:: *74S05 Finite element methods
74S15 Boundary element methods
74B99 Elasitc materials
74H99 Dynamical problems
65N55 Multigrid methods; domain decomposition (BVP of PDE)

Keywords: iterative procedure; mixed variational formulation; non-conforming grids; Neumann series; stress concentration problems; macro-elements

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Zentralblatt MATH Berlin [Germany]