We study the iterative methods for large moment systems derived from the linearized Boltzmann equation. By Fourier analysis, it is shown that the direct application of the block symmetric Gauss-Seidel (BSGS) method has slower convergence for smaller Knudsen numbers. Better convergence rates for dense flows are then achieved by coupling the BSGS method with the micro-macro decomposition, which treats the moment equations as a coupled system with a microscopic part and a macroscopic part. Since the macroscopic part contains only a small number of equations, it can be solved accurately during the iteration with a relatively small computational cost, which accelerates the overall iteration. The method is further generalized to the multiscale decomposition which splits the moment system into many subsystems with different orders of magnitude. Both one- and two-dimensional numerical tests are carried out to examine the performances of these methods. Possible issues regarding the efficiency and convergence are discussed in the conclusion.

翻译：我们研究了基于线性化玻尔兹曼方程建立的大规模矩系统的迭代方法。通过傅里叶分析表明，直接应用块对称高斯-赛德尔（BSGS）方法在较小克努森数下收敛速度较慢。通过将BSGS方法与微-宏分解耦合，实现了稠密流场中更优的收敛速率。该方法将矩方程视为由微观部分和宏观部分组成的耦合系统。由于宏观部分仅包含少量方程，可在迭代过程中以较低计算成本精确求解，从而加速整体迭代过程。该方法进一步推广至多尺度分解，将矩系统拆分为若干数量级不同的子系统。我们开展了一维和二维数值实验以检验这些方法的性能，并在结论中讨论了关于效率和收敛性的潜在问题。