A note on the relative efficiency of methods for computing the transient free-surface Green function

• The standard method is found to be more efficient than ODE-based methods.
• Of the ODE methods, Chuang et al. (2007) and RK44 are faster than Li et al. (2015).
• The standard method also includes the effects of finite water depth.

A number of papers have appeared recently on computing the time-domain, free-surface Green function. Two papers in particular, Chuang et al. (2007) and Li et al. (2015) considered the method developed by Clement (1998) who showed that this Green function is the solution to a fourth-order Ordinary Differential Equation (ODE). This ODE has been suggested as a means for speeding up the calculation of the Green function coefficients compared to the standard algorithms developed for example by Newman (1992). Clement solved the ODE using the classical fourth-order, four-step Runge–Kutta scheme (RK44) with a fixed time step size. The two papers mentioned above proposed alternative numerical methods which are claimed to be more efficient. In this note we consider the relative efficiency of these four methods on a representative test case, and conclude that the standard method is the most efficient. Of the ODE-based methods, the method of Chuang et al. (2007) is found to be slightly more efficient than the RK44 method, while the method of Li et al. (2015) is at least an order of magnitude less efficient. It is also pointed out that ODE methods have yet to be extended to include finite water depth.