A question that came up in the forward looking session was the comparison of different numerical methods for computing in the context of water waves. One example along these lines is the recent study of Wilkening & Vasan (2014) which compares 5 methods of computing the Dirichlet-Neumann operator for the water wave problem. The five methods were Craig-Sulem, Ablowitz-Fokas-Musslimani (AFM), dual AFM, boundary integral collocation and transformed field expansion. Two key test cases were large-amplitude standing waves in deep water, and a pair of interacting travelling waves. Details of the comparison can be found in the arXiv paper linked above.

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