RESTRICTION MATRICES FOR EXPLOITING SYMMETRY IN 3D WAVE PROPAGATION ANALYSIS BY ENERGETIC BEM

A lot of physical and engineering problems often deal with structures which have various geometrical symmetries. If the discretization of such problems is suitably adapted to respect symmetry properties, one can save computational costs and memory storage reducing the original problem to a family of smaller ones and obtaining the global solution from the superposition of the partial results. Here, we apply a technique for taking into account equivariance properties in the numerical treatment of space-time BIEs related to 3D wave propagation problems which are invariant under a finite group G of congruences of R3. This technique is based upon suitable restriction matrices strictly related to a system of unitary, irreducible, pairwise not-equivalent matrix representations of G. These restriction matrices will be applied in the framework of 3D energetic Galerkin boundary element method (BEM), where the discretization matrices have a block lower triangular Toeplitz structure, and the diagonal block, to be inverted at each time step, is typically dense. Numerical results will be shown to demonstrate the effectiveness of the proposed technique.