Boltzmann方程离散速度近似的卷积分解与快速求和方法
Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation
AI总结：
针对Boltzmann方程离散速度近似中直接数值评估的高计算成本问题，本文基于[27,28]的思想推导出快速求和技巧，将计算复杂度从O(N^{2d+1})降至O(\bar{N}^d N^d \log_2 N)，且几乎不损失精度。
摘要：
离散速度近似是计算Boltzmann碰撞算子的常用方法。这类方法的直接数值评估涉及高昂的计算成本，通常为$O(N^{2d+1})$，其中$d$是速度空间的维度。本文遵循[27,28]中引入的思想，推导出用于评估离散速度格式的快速求和技巧，使得计算成本从$O(N^{2d+1})$降至$O(\bar{N}^d N^d\log_2 N)$，其中$\bar{N} << N$，且几乎不损失精度。
英文摘要：
Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically $O(N^{2d+1})$ where $d$ is the dimension of the velocity space. In this paper, following the ideas introduced in [27,28], we derive fast summation techniques for the evaluation of discrete-velocity schemes which permits to reduce the computational cost from $O(N^{2d+1})$ to $O(\bar{N}^d N^d\log_2 N)$, $\bar{N} << N$, with almost no loss of accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
