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Cécile Piret : Overcoming the Gibbs Phenomenon Using a Modified Radial Basis Functions Method

The Radial Basis Functions (RBF) method is not immune from the disastrous effects of the Gibbs phenomenon. When interpolating or solving PDEs whose solutions are piecewise smooth functions, the RBF method loses its notorious spectral accuracy. In this talk, a new method will be presented, based on the RBF method, which incorporates singularities using Heaviside functions and which keeps track of their location using the level set method. The resulting sharp interface method will be shown to recover the lost spectral accuracy and thus overcome the Gibbs phenomenon altogether.

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