Abstract: According to the calculation theory of FMM algorithm，and considering its parallel optimization and compiler optimization，this paper divides this algorithm into different sub-modules.The computing characteristics of every sub-modules，including calculation load，parallelism，communication and storage，are analyzed in detail.Based on the deep analysis of relationship between the N-Body question scale and octree level，a strategy of hierarchical space decomposition associating with question scale is presented.The experiments validate the correctness and feasibility of the presented strategy.

Key words: compiler optimization, N-Body, Fast Multipole Method, hierarchical space decomposition with an octree

摘要： 从编译优化和并行优化的角度出发，根据N-Body问题求解的FMM算法的原理，将算法分解为不同的子模块。详细分析了各子模块的计算特性，包括计算量分析、并行性分析、通信量分析和存储量分析。深入剖析问题规模与空间划分层数之间的关系，提出基于问题规模的空间划分策略。以实验验证了空间划分策略的可行性。

关键词: 编译优化, N体（N-Body）问题求解, 快速多极子方法（FMM）, 空间划分树