Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems

Recently, a discontinuous Galerkin finite element method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of Helmholtz problems in the mid-frequency regime. In this paper, this method is extended to three dimensions and several new elements are proposed. Computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher-order Galerkin method