论文标题
SOLIDFMM：在固体谐波上的高度优化的操作库，用于快速多极方法
Solidfmm: A highly optimised library of operations on the solid harmonics for use in fast multipole methods
论文作者
论文摘要
我们提出SolidFMM，这是一个高度优化的C ++库，用于固体谐波，因为它们在快速多极方法中需要它们。该库提供了翻译操作M2M，M2L和L2L的有效，矢量化的实现，并作为免费软件可用。虽然复杂性$ O（p^3）$的渐近性，但对于所有实际相关的扩展订单，翻译运算符的经验复杂性的经验复杂性为$ O（p^2）$，表现优于大小命令的幼稚实现。
We present solidfmm, a highly optimised C++ library for the solid harmonics as they are needed in fast multipole methods. The library provides efficient, vectorised implementations of the translation operations M2M, M2L, and L2L, and is available as free software. While asymptotically of complexity $O(P^3)$, for all practically relevant expansion orders, the translation operators display an empirical complexity of $O(P^2)$, outperforming the naïve implementation by orders of magnitude.
