Comparison of Five Methods of Computing the Dirichlet–Neumann Operator for the Water Wave Problem
Comparison of Five Methods of Computing the Dirichlet–Neumann Operator for the Water Wave Problem
We compare the effectiveness of solving Dirichlet-Neumann problems via the Craig-Sulem (CS) expansion, the Ablowitz-Fokas-Musslimani (AFM) implicit formulation, the dual AFM formulation (AFM*), a boundary integral collocation method (BIM), and the transformed field expansion (TFE) method. The first three methods involve highly ill-conditioned intermediate calculations that we show can be …