论文标题
与非切割碰撞内核的均匀玻尔兹曼方程的快速傅立叶光谱法
A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels
论文作者
论文摘要
我们引入了一种快速的傅立叶光谱方法，用于具有非切割碰撞核的空间均匀玻尔兹曼方程。此类内核在偏差角中包含不可积分的奇异性，这些偏差在广泛的相互作用势（例如，反功率定律电位）中产生。尽管身体更大，但非切割核在分析和数字中都带来了许多困难，因此在大多数研究（众所周知的毕业生的角度截止假设）中经常被切断。我们证明，快速傅立叶光谱方法的一般框架可以扩展以处理非切割内核，从而达到与截止情况相当的精度/效率。我们还通过几个数值示例表明，非切割玻尔兹曼方程的解决方案具有平滑效果，这是截止情况下缺少的惊人属性。
We introduce a fast Fourier spectral method for the spatially homogeneous Boltzmann equation with non-cutoff collision kernels. Such kernels contain non-integrable singularity in the deviation angle which arise in a wide range of interaction potentials (e.g., the inverse power law potentials). Albeit more physical, the non-cutoff kernels bring a lot of difficulties in both analysis and numerics, hence are often cut off in most studies (the well-known Grad's angular cutoff assumption). We demonstrate that the general framework of the fast Fourier spectral method can be extended to handle the non-cutoff kernels, achieving the accuracy/efficiency comparable to the cutoff case. We also show through several numerical examples that the solution to the non-cutoff Boltzmann equation enjoys the smoothing effect, a striking property absent in the cutoff case.
