A Symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation

Abstract : A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the pollution effect in the literature on numerical simulations of long-range wave propagation.
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Journal of Computational Physics, Elsevier, 2017, 330, pp.1069-1092. 〈10.1016/j.jcp.2016.09.062〉
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Hélène Barucq, Abderrahmane Bendali, M'B. Fares, Vanessa Mattesi, Sébastien Tordeux. A Symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation. Journal of Computational Physics, Elsevier, 2017, 330, pp.1069-1092. 〈10.1016/j.jcp.2016.09.062〉. 〈hal-01395861〉

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