Sspectral Numerical Solution of Stochastic Partial Differential Equations

目前还不存在求解随机非均质多孔介质流动的通用解析方法。目前的方法是微扰法或蒙特卡罗模拟。前者只能处理较小的方差，而后者的计算非常耗时或昂贵。该奖项将探索谱方法在随机多孔介质流动计算效率方面的适用性。谱方法在非线性问题中并不新鲜，但尚未应用于该问题。机构支持是足够的，PI有资格进行研究，我建议支持。

There does not exist a general analytical method for solving flow through a randomly heterogeneous porous medium. Current methods are either perturbation methods or Monte Carlo simulations. The former can only deal with small variances while the latter is very time consuming or expensive to compute. This Expedited Award for Novel Research will explore the applicability of the spectral method for computational efficiency for flow through random porous media. Spectral methods are not new to nonlinear problems but had not been applied to this problem. The Institutional support is adequate and the PI is qualified to carry out the research, I recommend support.