Coupling of BEM subdomains – BETI applied to collocation BEM with mixed basis functions

Abstract

This work is about the coupling of subdomains for elasticity problems using the boundary element tearing and interconnecting method (BETI). BETI is a substructuring technique which is able to solve large problems involving subdomains efficiently, because its formulation is ideally suited for parallel computation. In contrast to the original formulation of BETI, where the symmetric Galerkin boundary element method (SGBEM) is applied, here the traditional collocation BEM is used. As will be shown the solution algorithm is applied in a very similar way as in the original version. Special attention will be paid to the distribution of tractions along interfaces of BEM subdomains. Especially if the coupling interface is not smooth but has corners and edges erroneous traction results can be obtained by using the non-symmetric approximation of the Dirichlet-to-Neumann map. For a sequential calculation involving several load steps this leads to unacceptable results if a classical continuous approximation of the physical fields is used. Therefore discontinuous basis functions for the displacement and traction field are introduced. As will be shown in this work the quality of results can be improved drastically by this technique.