Fast multipole method for wave diffraction/radiation problems and its applications to VLFS

This paper presents an accelerated higher-order boundary element method for wave diffraction/radiation problems and its applications, especially for wave response analysis of VLFS (Very Large Floating Structures). The Fast Multipole Method (FMM) has been implemented on the higher-order boundary element code using an 8-node quadrilateral element. The method utilizes an iterative solver, multipole expansion of Green's function, and a hierarchical algorithm using a quadrant-tree. For solving a hydroelastic problem efficiently using an iterative solver, a new algorithm has been introduced, where the equations of motions representing plate vibration are solved at each iterative step. The numerical benchmark calculations have shown the efficiency of the method both in the storage requirement of O(N) and computation time of O(N log N), where N is the number of unknowns for the velocity potential.