A Domain Decomposition Solver for the Discontinuous Enrichment Method for the Helmholtz Equation
The discontinuous enrichment method (DEM)  for the Helmholtz equation approximates the solution as a sum of a piecewise polynomial continuous function and element-wise supported plane waves . A weak continuity of the plane wave part is enforced using Lagrangemultipliers. The plane wave enrichment improves the accuracy of solutions considerably. In the mid-frequency range, severalfold savings in terms of degrees of freedom over comparable higher order polynomial discretizations have been observed, which translates into even larger savings in compute time [6, 9]. The partition of unity method  and the ultra weak variational formulation  also employ plane waves in the construction of discretizations. It was shown recently in  that DEM without the polynomial field is computationally more efficient than these methods.
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