快速多极子展开技术在高阶边界元方法中的实现

高阶边界元法以较常数元方法计算精度高存储低而在工程计算中得到了广泛的应用，但由于其平方存储和计算量的本质，无法应用于大型工程问题中。本文将快速多极子方法（FMM）应用于高阶边界元中从而使其计算量和存储量分别降为O（Nlog N）和O（N）。通过无限区域中水流绕射算例的数值计算，对FMM高阶边界元法与传统高阶边界元法的运算速度和内存消耗进行了分析对比，结果表明对于大型计算问题FMM高阶边界元算法更加有效。

Implementation of the fast multipole expansion technique in the higher order BEM

Using the simple Green function as basic solution,this paper applies the fast multipole method(FMM) to the higher order boundary element method(HOBEM) so that the computation cost and storage of the computer are reduced to order of O(Nlog N) and O(N) respectively,where N is the number of unknowns.In the present algorithm,FMM is mainly applied to calculate the matrix/vector product and the resulting algebraic equation is solved by an iterative method.Numerical examinations,on the flow diffraction from a stationary sphere in an unbounded domain,are carried out to demonstrate the capability and accuracy of the present method.And the calculation results show that FMM HOBEM is much faster and more efficient than the traditional HOBEM with proportional square order computation cost and storage of the computer,and is suggested for use in large-scale engineering problems.