Alternative approaches of evaluating diffraction transfer matrix and radiation characteristics using the hybrid source-dipole formulation

The interaction theory presented by Kagemoto and Yue (1986) significantly reduces the computational burden in the wave interaction problem of multiple surface-piercing bodies, particularly arrays of wave energy converters in recent years. Two essential operators of the theory are the so-called Diffraction Transfer Matrix and Radiation Characteristics. Many subsequent researchers (Goo and Yoshida, 1990; Flavià et al., 2018) have implemented the theory using the source distribution method in evaluating the two linear operators of a single unique geometry. However, nowadays, a great majority of boundary element method codes have been written by virtue of the hybrid source-dipole distribution method on account of its high accuracy. In this regard, the present work aims to introduce a full set of mathematical formulations, as well as a complete derivation process of evaluating the two operators based on the hybrid source-dipole distribution method. The proposed formulations are then applied to two benchmark geometries, as given by McNatt et al. (2015) and Flavià et al. (2018). Good agreement is found between the present results and those from the literature. Moreover, two alternative approaches to solve the diffraction problem have been compared to assess both their accuracy and efficiency. It is found that the two methods present similar levels of accuracy but very different computational burden.