中文摘要：

该文将快速多极边界元法用于三维稳态传热问题的大规模数值计算。多极展开的引入使得该算法能够在单台个人电脑上完成30万自由度以上的传热边界元分析。统一展开的基本解能够处理混合边界。广义极小残差法作为快速多极边界元法的迭代求解器,数值算例分析了快速多极边界元法的计算效率。结果表明：快速多极边界元法的求解效率与常规算法相比有数量级的提高;在模拟复杂结构大规模传热问题上将具有良好的应用前景。

英文摘要：

The FMBEM （Fast Multipole Boundary Element Method） is applied to large scale numerical analysis of three-dimensional static thermal transfer problems. An introduction of the multipole expansion makes this algorithm applicable to perform boundary element analysis of thermal transfer problems with more than 300,000 unknowns on only one desktop computer. Mixed boundary conditions are achieved by using unified formulation of fundamental solutions. The Generalized Minimum Residue method is used as an iterative solver for the FMBEM. The computational efficiency of the FMBEM is tested in numerical examples. The results show that the FMBEM provides an order-of-magnitude increase in computational efficiency when compared with traditional solvers. This algorithm would be potential for the simulation of large scale thermal transfer analysis of complicated structures.