In this paper we consider 2D interior and exterior wave propagation Neumann problems reformulated in terms of a space–time hypersingular boundary integral equation (BIE) with retarded potential. This latter is set in the so-called energetic weak form, recently proposed in literature and then approximated by Galerkin Boundary Element Method (GBEM). We illustrate a technique for exploiting symmetry in the time-marching procedure used to solve the final discretization linear system, if the problem is invariant under a finite group G of congruences of R^2. Both Abelian and non-Abelian groups are considered. Applications of restriction matrices to energetic GBEM under the weaker assumption of partial geometrical symmetry, where the boundary has disconnected components, one of which at least is invariant, are proposed. We conclude presenting and discussing various numerical simulations.
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