论文标题
关于平衡保留光谱方法的稳定性
On the stability of equilibrium preserving spectral methods for the homogeneous Boltzmann equation
论文作者
论文摘要
由于高精度和使用快速算法的可能性，光谱方法代表了近似Boltzmann碰撞操作员的有效方法。另一方面，某些当地不变的损失导致了错误的长期行为。最近，通过构建平衡保留光谱方法，已经提出了一种克服这种缺点的方法，而没有牺牲光谱精度。尽管能够以任意精度捕获稳态，但该方法的理论特性从未在细节上进行研究。在本文中，使用Filbet和Mouhot为均匀的Boltzmann方程开发的扰动参数，我们证明了平衡保留方法的稳定性，收敛性和光谱准确的长时间行为。
Spectral methods, thanks to the high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the Boltzmann collision operator. On the other hand, the loss of some local invariants leads to the wrong long time behavior. A way to overcome this drawback, without sacrificing spectral accuracy, has been proposed recently with the construction of equilibrium preserving spectral methods. Despite the ability to capture the steady state with arbitrary accuracy, the theoretical properties of the method have never been studied in details. In this paper, using the perturbation argument developed by Filbet and Mouhot for the homogeneous Boltzmann equation, we prove stability, convergence and spectrally accurate long time behavior of the equilibrium preserving approach.
