Spectral Gap Computations for Linearized Boltzmann Operators
Spectral Gap Computations for Linearized Boltzmann Operators
复制标题
线性玻尔兹曼算子的谱间隙计算
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
I. Gamba
中科院分区：
文献类型：
--
作者：
Chenglong Zhang;I. Gamba
线性玻尔兹曼算子的光谱间隙的定量信息对于证明玻尔兹曼模型的合理性和弛豫到平衡的研究至关重要。这项工作首次提供了光谱间隙存在和相应近似值的数值证据。线性化玻尔兹曼算子被投影到不连续伽辽金网格上，产生“碰撞矩阵”。然后通过约束最小化问题来近似原始光谱间隙问题，目标函数是“碰撞矩阵”的瑞利商，约束是守恒定律。然后应用守恒校正。我们还展示了可积角截面情况下近似瑞利商与真实光谱间隙的收敛性。实现了一些分布式特征求解器以及混合OpenMP和MPI并行计算。提供了可积和不可积角截面的数值结果。
The quantitative information on the spectral gaps for the linearized Boltzmann operator is of primary importance on justifying the Boltzmann model and study of relaxation to equilibrium. This work, for the first time, provides numerical evidences on the existence of spectral gaps and corresponding approximate values. The linearized Boltzmann operator is projected onto a Discontinuous Galerkin mesh, resulting in a "collision matrix". The original spectral gap problem is then approximated by a constrained minimization problem, with objective function being the Rayleigh quotient of the "collision matrix" and with constraints being the conservation laws. A conservation correction then applies. We also showed the convergence of the approximate Rayleigh quotient to the real spectral gap for the case of integrable angular cross-sections. Some distributed eigen-solvers and hybrid OpenMP and MPI parallel computing are implemented. Numerical results on integrable as well as non-integrable angular cross-sections are provided.