Wiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise
Wiener Chaos Versus Stochastic Collocation Methods for Linear Advection-Diffusion-Reaction Equations with Multiplicative White Noise
复制标题
乘性白噪声线性平流扩散反应方程的维纳混沌与随机配置方法
DOI：
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发表时间：
2015
影响因子：
2.9
通讯作者：
G. Karniadakis
中科院分区：
文献类型：
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作者：
Zhongqiang Zhang;M. Tretyakov;B. Rozovskii;G. Karniadakis
比较了带乘性白色噪声的线性对流反应扩散方程的Wiener混沌方法和随机配置方法。这两种方法都是基于一个递归的多级算法的长时间集成。我们推导出这两种方法的误差估计，并比较它们的数值性能。数值结果表明，对于带交换噪声的对流扩散反应方程，递推多级随机配置法的二阶矩为$Delta$（时间步长）阶，而递推多级Wiener混沌法的二阶矩为$Delta^{mathsf {N}}+Delta^2$（$mathsf{N}$为Wiener混沌的阶数）阶，与理论误差估计一致.然而，对于非交换噪声，这两种方法都是一阶二阶矩。
We compare Wiener chaos and stochastic collocation methods for linear advection-reaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multistage algorithm for long-time integration. We derive error estimates for both methods and compare their numerical performance. Numerical results confirm that the recursive multistage stochastic collocation method is of order $Delta$ (time step size) in the second-order moments while the recursive multistage Wiener chaos method is of order $Delta^{mathsf{N}}+Delta^2$ ($mathsf{N}$ is the order of Wiener chaos) for advection-diffusion-reaction equations with commutative noises, in agreement with the theoretical error estimates. However, for noncommutative noises, both methods are of order one in the second-order moments.