A symmetric Galerkin multi-zone boundary element formulation

The recent development of the symmetric Galerkin approach to boundary element analysis (BEA) has been demonstrated to be superior to the collocation method for medium to large problems. This fact has been shown in both heat conduction and elasticity. Accounts of collocation multi-zone analysis techniques have also been prevalent in the literature, dealing with multiple boundary integral relations associated with portions of overall objects. This technique results in overall system matrices with a blocked, sparse, but unsymmetric character. It has been shown that multi-zone techniques can produce smaller solution times than a single zone analysis for large problems. These techniques are useful for multi-material problems as well. This paper presents an approach for combining the beneÞts of both techniques resulting in a Galerkin multi-zone method, that is overall unsymmetric but contains a signiÞcant amount of block symmetry. A condensation technique in the multi-zone solver is shown to exploit the symmetry of the Galerkin formulation as well as the blocked sparsity of the multi-zone technique. This method is compared to collocation multi-zone on two elasticity problems from the literature. It is concluded that an appropriate implementation of the symmetric Galerkin multi-zone BEA indeed has the potential to be superior to the collocation based multi-zone BEA, for medium to large-scale elasticity problems