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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. [ABSTRACT FROM AUTHOR]

Abstract: We develop a new PML formulation for the linearized shallow-water equations including the Coriolis force. The construction process is based on the uncoupling of the velocity components with the depth of water. Then the damping effect is only applied to the propagative modes just as was formerly done by Nataf to the linearized Euler equations to enforce the long-time stability. We assess numerically the performance of the new absorbing condition and we illustrate in particular that it is stable for long-time simulations. [Copyright &y& Elsevier]