Exploitation of the geometrical symmetry in the boundary element method with the group representation theory

We describe an implementation of the Boundary Element Method for the 2-D Laplace´s problem where the domains under study present some geometrical symmetry. The boundary conditions do not share the symmetry so that intuitive reasoning cannot be used to take part of symmetry. So, we use the Group Representation Theory that presents a rationale in this context. It consists in reducing the original problem to a family of smaller ones, the global solution is obtained from superposition of the partial solutions. It leads to a substantial gain in memory volume and achieves large computational cost savings. We consider the non-abelian symmetry groups that represent the most general case. We present the case of the dihedral group D₃ as an example