Three-dimensional element configurations for the discontinuous enrichment method for acoustics

Hexahedral and tetrahedral elements are proposed for the discontinuous enrichment method (DEM) for boundary-value problems governed by the Helmholtz equation. A procedure for obtaining sets of approximately uniform spherical enrichment directions, with high flexibility in the choice of their number, is constructed. Conditioning considerations indicate preferred representations of the oscillatory basis functions. Dispersion properties are used to rate the performance of different element configurations. Numerical tests assess accuracy, indicating that high-order DEM elements exhibit little dispersion. The dispersion and the numerical results are in a good agreement. The proposed configurations of DEM elements become more competitive as the number of enrichments and Lagrange multipliers is increased.