Restriction matrices for SGBEM applications

Abstract

In the context of linear elasticity, we consider a symmetric boundary integral formulation associated with a mixed boundary value problem defined on a domain Ω⊂ℝ^m, m=2,3, with piecewise smooth boundary Γ. We assume that is mapped onto itself by a finite group of congruences having at least two distinct elements. The aim of this paper is to present a systematic technique for exploiting geometrical symmetry in the numerical treatment of boundary integral equations with the Symmetric Galerkin Boundary Element Method (SGBEM). This technique will be based upon suitable restriction matrices strictly related to the group and to the mesh defined on the boundary. Hence, we can decompose the related SGBEM problem into independent subproblems of reduced dimension with respect to the original one. Shape functions for each subproblem can be obtained from classical BEM basis, ordered as a vector, applying restriction matrices suitably constructed starting from group representation theory.