The fast multipole method to solve two kinds of Green’s Functions
Journal Title: Science Paper Online - Year 2007, Vol 2, Issue 1
Abstract
The higher order boundary element method (HOBEM) has been widely used in engineering calculations, but it is difficult to solve the large-scale problems because of large computation cost and computer storage needed to compute the Green’s function and its’ corresponding derivatives many times. In this paper, the fast multipole method is applied in HOBEM to overcome the embarrassing situation. The simple Green’s function (1/r) and the Green’s function satisfying the free surface boundary conditions are expanded in sphere coordinate and the cylinder coordinate system respectively, which can result in the computation cost and computer storage being decreased from O(N2) order to nearly O(N) order. The free-term coefficient and the CPV integrals are obtained by using a direct method in higher-order boundary integral equation. In order to verify this present numerical model, the flow diffraction from a stationary sphere in an unbounded domain and wave actions on a floating box are simulated respectively. The results show that this present method is accurate enough and more efficient to solve the large-scale problems.
Authors and Affiliations
Dezhi Ning , Bin Teng, Ying Gou
Keywords
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