Evaluating high order discontinuous Galerkin discretization of the Boltzmann collision integral in egin{document}$ mathcal{O}(N^2) $end{document} operations using the discrete fourier transform
Evaluating high order discontinuous Galerkin discretization of the Boltzmann collision integral in egin{document}$ mathcal{O}(N^2) $end{document} operations using the discrete fourier transform
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使用离散傅里叶变换评估 egin{document}$ mathcal{O}(N^2) $end{document} 运算中玻尔兹曼碰撞积分的高阶不连续伽辽金离散化
DOI：
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发表时间：
2019
影响因子：
1
通讯作者：
J. Limbacher
中科院分区：
文献类型：
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作者：
A. Alekseenko;J. Limbacher
我们提出了一个计算玻尔兹曼碰撞算符的数值算法， egin{document}$O（N^2）$end{document}操作基于速度变量的高阶间断Galerkin离散。为了制定的方法，伽辽金投影的碰撞算子写在一个双线性圆卷积的形式。离散傅立叶变换的应用允许将六重卷积和重写为频率空间中的三重加权卷积和。新算法的实现和测试的空间均匀的情况下，并导致在相当大的改善速度相比，直接评估。分裂和非分裂形式的碰撞算子被认为是，这是形式的碰撞算子，有单独的和同时的评估的增益和损失方面，分别。在使用非分裂形式的模拟中，在守恒量中观察到较小的数值误差。
We present a numerical algorithm for evaluating the Boltzmann collision operator with egin{document}$O(N^2)$end{document} operations based on high order discontinuous Galerkin discretizations in the velocity variable. To formulate the approach, Galerkin projection of the collision operator is written in the form of a bilinear circular convolution. An application of the discrete Fourier transform allows to rewrite the six fold convolution sum as a three fold weighted convolution sum in the frequency space. The new algorithm is implemented and tested in the spatially homogeneous case, and results in a considerable improvement in speed as compared to the direct evaluation. Split and non-split forms of the collision operator are considered, which are forms of the collision operator that have separate and simultaneous evaluations of the gain and loss terms, respectively. Smaller numerical errors are observed in the conserved quantities in simulations using the non-split form.