A novel method for deriving the diffraction transfer matrix and its application to multi-body interactions in water waves

A matrix method was developed by Kagemoto and Yue (1986) to compute interactions between multiple three-dimensional bodies subjected to linear water waves. The approach leads to a significant reduction in computational time versus the direct method, in which the boundary value problem is solved for all bodies simultaneously. An essential component of the theory is the so-called diffraction transfer matrix, a linear operator defined for each unique geometry. However, the diffraction transfer matrix is not a standard product of a linear wave computation, for one, because it is based around an unusual representation of incident waves, that is, as partial cylindrical waves. In this paper, a new method is presented to compute the diffraction transfer matrix from plane incident waves, which enables one to derive it from standard wave-body software or experiments. Additionally, a new linear operator - the force transfer matrix, is presented, which can also be determined by usual means. Herein, the interaction theory calculation is verified against direct method results from the linear wave-body software, WAMIT, and then applied to compute absorbed power and wave field effects on a medium-sized array in spectral seas and on a large farm of 101 wave energy converters in regular waves.