Towards High-Performance Linear Potential Flow BEM Solver with Low-Rank Compressions

The interaction of water waves with floating bodies can be modeled with linear potential flow theory and numerically solved with the boundary element method (BEM). This method requires the construction of dense matrices and the resolution of the corresponding linear systems. The cost of this method in terms of time and memory grows at least quadratically with the size of the mesh, and the resolution of large problems (such as large farms of wave energy converters) can, thus, be very costly. Approximating some blocks of the matrix with data-sparse matrices can limit this cost. While matrix compression with low-rank blocks has become a standard tool in the larger BEM community, the present paper provides its first application (to our knowledge) to linear potential flows. In this paper, we assess how efficiently low-rank blocks can approximate interaction matrices between distant meshes when using the Green function of linear potential flow. Due to the complexity of this Green function, a theoretical study is difficult, and numerical experiments are used to test the approximation method. Typical results on large arrays of floating bodies show that 99% of the accuracy can be reached with 10% of the coefficients of the matrix.