快速多极虚边界元法实施过程分析

Study on the Fast Multipole Virtual Boundary Element Method

快速多极算法的主要思想在于变革计算结构,采用该算法和广义极小残值法对传统虚边界元形成的方程组求解,可使得计算复杂度和存储量与自由度数成线性比例.为便于工程推广应用,本文对快速多极虚边界元法中的树结构、上行遍历和下行遍历等关键问题进行了细致讨论,同时完整的介绍了该方法的实施步骤.采用该算法可求解大规模复杂问题.

The main idea of fast multipole method（FMM） is to change the computational structure.The complexities of operation and memory about solution of the equations could be made to be of linear proportion to the freedoms of the problem with the FMM and generalized minimal residual algorithm（GMRES）.For the convenience of engineering application,some key issues on tree structure,upward pass and downward pass were particularly discussed.The procedure of the method was introduced.The large scale problems can be solved with this method.