Solving the Stochastic Steady-State Diffusion Problem using
Solving the Stochastic Steady-State Diffusion Problem using
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使用以下方法求解随机稳态扩散问题
DOI：
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发表时间：
2006
期刊：
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通讯作者：
Darran G. Furnival
中科院分区：
文献类型：
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作者：
H. Elman;Darran G. Furnival
研究了求解随机稳态扩散问题的多重网格法。我们在扩散系数为有限卡尔胡宁-洛展式的温和假设下进行操作。用有限元方法离散问题，用多项式混沌方法离散问题的随机部分。我们将多重网格算法应用于随机问题，其中空间离散化在不同网格之间变化，而随机离散化保持不变。然后，我们从理论和实验上证明了收敛速度与空间离散化和随机离散化无关。
We study multigrid for solving the stochastic steady-state diffusion problem. We operate under the mild assumption that the diffusion coefficient takes the form of a finite Karhunen-Loexpansion. The prob- lem is discretized using a finite-element methodology using the polynomial chaos method to discretize the stochastic part of the problem. We apply a multigrid algorithm to the stochastic problem in which the spatial discretization is varied from grid to grid while the stochastic discretization is held constant. We then show, theoretically and experimentally, that the convergence rate is independent of the spatial discretization, as in the deterministic case, and the stochastic discretization.