Renewable forms of energy are becoming increasingly important to consider, as the global energy demand continues to grow. Wave energy is one of these widely available forms, but it is largely unexploited. A common design for a wave energy converter is called a point absorber or buoy. The buoy typically floats on the surface or just below the surface of the water, and captures energy from the movement of the waves. It can use the motion of the waves to drive a pump to generate electricity and to create potable water. Since a single buoy can only capture a limited amount of energy, large-scale wave energy production necessitates the deployment of buoys in large numbers called arrays. However, the efficiency of arrays of buoys is affected by highly complex intra-buoy interactions. The contributions of this article are two-fold. First, we present an approximation of the buoy interactions model that results in a 350-fold computational speed-up to enable the use inside of iterative optimisation algorithms, Second, we study arrays of fully submerged three-tether buoys, with and without shared mooring points.