Abstract
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 elastostatics. A mixed variational formulation on the coupling interfaces leads to the use of nonconforming grids for each substructure (cf. Schnack ). 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 operator concerning symmetry and definiteness can be controlled automatically within an adaptive algorithm. 1 Domain decomposition with non-overlapping substructures We consider a bounded, isotropic interior domain 0 = O U F in RTM, (m = 2,3), with a Lipschitz boundary F = <9Q. The boundary value problem is defined by the Navier equation without body forces + % = 0 or A*w = 0 for wf with given displacements on the Dirichlet boundary I and given tractions on the Neumann boundary I\: «(£) = «*(£) for f e i = r r, (2) = n «(£) = **(£) former, . (3) Transactions on Modelling and Simulation vol 12, © 1996 WIT Press, www.witpress.com, ISSN 1743-355X 204 Boundary Elements Tl denotes the traction operator. For the domain decomposition we divide O into p non-overlapping subdomains Oj (i — 1, . . . ,p) according to n = n^ung ; n^ = u^ ; %= U ^ (4 i=l i=q+l with The coupling boundary (interface) is defined by , = |J r, with r, = % . (5)
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