二维位势问题快速多极虚边界元解

Fast Multipole Virtual Boundary Element Method for Solving Two-dimensional Potential Problems

快速多极虚边界元法是近期发展起来的一种数值算法;其对大规模复杂问题的计算,能在保证求解精度的前提下,使计算量和存储量均比常规虚边界元法具有在数量级上的减少.本文给出了二维位势问题快速多极虚边界元法的求解思想,并进行了数值论证;由文中的数值结果可知,本文方法具有可行性,且有较好的计算精度.

Fast muhipole VBEM （virtual boundary element method） is a new algorithm developed for VBEM recently. The computational cost and memory requirement of fast multipole VBEM is lower an order of magnitude than that of traditional VBEM without changing accuracy, which makes it possible to solve large scale problems on a desktop. In this paper, the problcms of 2D potential are studied. Numerical examples are presented to demonstrate the feasibility, accuracy and efficiency of the method.