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 8-node quadrilateral element. The method utilizes an iterative solver, multipole expansion of Green's function, and hierarchical algorithm using quadrant-tree. For solving hydroelastic problem efficiently using iterative solver, a new algorithm, where the equations of motions representing plate vibration are solved at each iterative step, has been introduced. The numerical benchmark calculations have shown the efficiency of the method both in storage requirement of O(N) and computation time of O(N log N), where N is the number of unknowns for the velocity potential.


The Boundary Element Method (BEM) using the free surface Green function has been used as a basic tool for solving diffraction/radiation problems of a floating body. However, when the method is applied to a Very Large Floating Structure (VLFS) such as a Mega-Float, the large requirement of computer resources with O(N2Therefore, the computation for a VLFS has been tackled by the finite element method (FEM) where band storage characteristics of the system matrix are utilized, by the semi-analytical approaches, or by the BEM utilizing higher-order panels such as B-spline functions (see e.g. Ohtsubo and Sumi, 2000). This paper employs an alternative approach using Fast Multipole Method (FMM) (Rokhlin, 1985; Barnes and Hut, 1986; Greengard and Rokhlin, 1987; Greengard, 1988; Fukui and Katsumoto, 1997, 1998).) for storage and with either O(N2) or O(N3) for CPU time, which depends on the selection of the solver either as iterative type or LU-factorization type (N: the number of unknowns), has made the computation of velocity potentials by BEM impractical.

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