A symmetric Galerkin multi-zone boundary element formulation

Abstract

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 benefits of both techniques resulting in a Galerkin multi‐zone method, that is overall unsymmetric but contains a significant 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. © 1997 John Wiley & Sons, Ltd.

Frictionless contact-detachment analysis: iterative linear complementarity and quadratic programming approaches

“…We want to obtain the length of the boundary which has modified its status (in contact or detached) and, for each body, the elastic response to the external actions in terms of displacements u 2 on 2 and reactive forces f 1 on 1 , but also in terms of the displacements u 0v and tractions t 0v (the latter vector null by definition) on the virtual boundary 0v , displacements u 0r and tractions t 0r at the real boundary 0r and in terms of stresses σ in the domain of each body by using the mixed variable multidomain SGBEM approach [16][17][18][19][20][21][22].…”

“…In this paper a strategy is shown for the solution to the coupled contact-detachment problem using the mixed 123 variable multidomain SGBEM approach. The idea is based on the classical subdivision of the domain into substructures introduced in the SGBEM by some authors [15][16][17][18][19][20][21][22], where a mixed variable approach is utilized.…”

A multi-domain boundary element formulation for acoustic frequency sensitivity analysis

“…Using a multi-domain method [28][29][30][31][32][33][34][35][36][37][38][39], also known by the names of sub-domain technique, multi-region, poly-region or domain decomposition [29], the system matrix becomes sparse and thus, the necessary amount of memory can be considerably decreased. The basic idea is to divide the vibrating structure into smaller domain elements connected by hypothetical interface planes.…”

Boundary discretization based on the residual energy using the SGBEM

“…Indeed, Gray and Paulino (1997) used this strategy for potential problems showing an example regarding the heat transfer. Afterwards, Layton et al (1997) and Ganguly et al (1999) proposed a solution regarding an elastic system made by two zones, by inserting in the analysis problem all the boundary mixed unknowns. Finally, Panzeca and Salerno (2000) and Panzeca et al (2002a,b) performed a domain subdivision into substructures, called bem-elements, considering only the interfaces unknowns in the analysis process.…”