论文标题
具有低级别求解器的随机不连续的盖尔金方法，用于对流扩散方程
Stochastic Discontinuous Galerkin Methods with Low--Rank Solvers for Convection Diffusion Equations
论文作者
论文摘要
我们通过近似溶液的统计矩来研究对流扩散方程的数值行为。随机的盖尔金方法将原始随机问题转变为确定性对流扩散方程的系统，用于处理本研究中的随机域，而不连续的盖金方法由于其本地质量保守性而用于离散空间域。能量规范中得出了对不稳定模型问题的固定问题和稳定性估计的先验误差估计。为了解决随机盖尔金方法的维度的诅咒，我们利用了低级别的Krylov子空间方法，通过利用系统矩阵的Kronecker-生产结构来降低存储要求和计算复杂性。关于基准问题的数值实验说明了所提出方法的效率。
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of deterministic convection diffusion equations, is used to handle the stochastic domain in this study, whereas discontinuous Galerkin method is used to discretize spatial domain due to its local mass conservativity. A priori error estimates of the stationary problem and stability estimate of the unsteady model problem are derived in the energy norm. To address the curse of dimensionality of Stochastic Galerkin method, we take advantage of the low--rank Krylov subspace methods, which reduce both the storage requirements and the computational complexity by exploiting a Kronecker--product structure of system matrices. The efficiency of the proposed methodology is illustrated by numerical experiments on the benchmark problems.
