A fully symmetric multi-zone Galerkin boundary element method

This paper examines the e¦cient integration of a Symmetric Galerkin Boundary Element Analysis (SGBEA) method with multi-zone resulting in a fully symmetric Galerkin multi-zone formulation. In a previous approach, a Galerkin multi-zone method was developed where the interfacial nodes are assigned degrees of freedom globally so that the displacement and traction continuity across the zonal interfaces are addressed directly. However, the method was only block symmetric. In the present paper, two new approaches are derived. In the Þrst approach, the degrees of freedom for a particular zone are assigned locally, independent of the other zones. The usual linear set of equations, from the symmetric Galerkin approach, are augmented with an additional set of equations generated by the Galerkin form of hypersingular boundary integrals along the interfaces. Zonal continuity is imposed externally through LagrangeÕs constraints. This approach is also only block symmetric. The second approach derived from the Þrst, uses the continuity constraints at the zonal assembly level to achieve full symmetry. These methods are compared to collocation multi-zone and an earlier formulation, on two elasticity problems from the literature. It was found that the second method is much faster than the collocation method for medium to large scale problems, primarily due to its complete symmetry. It is also observed that these methods spend marginally more time on integration than the previous Galerkin multi-zone method but are better suited to parallel processing. Copyright