Sspectral Numerical Solution of Stochastic Partial Differential Equations

目前还没有一种通用的分析方法来求解随机非均质多孔介质中的渗流问题。目前的方法要么是摄动法，要么是蒙特卡罗模拟法。前者只能处理很小的方差，而后者计算起来非常耗时或昂贵。这一新奇研究快速奖将探索频谱方法在随机多孔介质中流动计算效率方面的适用性。谱方法对于非线性问题并不新鲜，但还没有被应用于这个问题。制度支持是充分的，PI有资格开展研究，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.