Abstract
The discontinuous enrichment method (DEM) [4] for the Helmholtz equation approximates the solution as a sum of a piecewise polynomial continuous function and element-wise supported plane waves [5]. 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 [8] and the ultra weak variational formulation [1] also employ plane waves in the construction of discretizations. It was shown recently in [10] that DEM without the polynomial field is computationally more efficient than these methods.
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Farhat, C., Tezaur, R., Toivanen, J. (2013). A Domain Decomposition Solver for the Discontinuous Enrichment Method for the Helmholtz Equation. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_23
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DOI: https://doi.org/10.1007/978-3-642-35275-1_23
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