A multigrid solver for two-dimensional stochastic diffusion equations

O.P. Le Maitre; O.M. Knio; B.J. Debusschere; H.N. Najm; R.G. Ghanem

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A multigrid solver for two-dimensional stochastic diffusion equations

机译：二维随机扩散方程的多重网格求解器

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摘要

Steady and unsteady diffusion equations, with stochastic diffusivity coefficient and forcing term, are modeled in two dimensions by means of stochastic spectral representations. Problem data and solution variables are expanded using the Polynomial Chaos system. The approach leads to a set of coupled problems for the stochastic modes. Spatial finite-difference discretization of these coupled problems results in a large system of equations, whose dimension necessitates the use of iterative approaches in order to obtain the solution within a reasonable computational time. To accelerate the convergence of the iterative technique, a multigrid method, based on spatial coarsening, is implemented. Numerical experiments show good scaling properties of the method, both with respect to the number of spatial grid points and the stochastic resolution level.

机译：具有随机扩散系数和强迫项的稳态和非稳态扩散方程是通过随机频谱表示法在二维中建模的。问题数据和解决方案变量使用多项式混沌系统扩展。该方法导致随机模式的一系列耦合问题。这些耦合问题的空间有限差分离散化导致了一个大型方程组，其维数必须使用迭代方法才能在合理的计算时间内获得解。为了加速迭代技术的收敛，实现了一种基于空间粗化的多网格方法。数值实验表明，该方法在空间网格点数和随机分辨率水平方面都具有良好的缩放特性。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2003年第42期|p.4723-4744|共22页
作者
O.P. Le Maitre; O.M. Knio; B.J. Debusschere; H.N. Najm; R.G. Ghanem;
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作者单位

Universite d'Evry Val d'Essonne, Centre d'Etudes de Mecanique d'Ile de France, 40 Rue du Pelvoux CE 1455, 91 020 Evry cedex, France;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类自动化基础理论;工程基础科学;
关键词
stochastic problem; diffusion equation; multigrid; polynomial chaos; karhunen-loeve expansion; random media;

机译：随机问题扩散方程多重网格多项式混沌Karhunen-Loeve展开随机介质;

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机译：求解二维耦合方程组的多重网格迭代求解方法。（高温气冷堆）

A multigrid solver for two-dimensional stochastic diffusion equations

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