论文标题
使用Fenics和UQTK求解随机PDE
Solving Stochastic PDEs Using FEniCS and UQtk
论文作者
论文摘要
侵入性（无样品）光谱随机有限元法（SSFEM）是解决随机偏微分方程（PDE）的强大数值工具。但是，它在学术和工业应用中并不广泛地采用，因为它需要对PDE求解器进行侵入性调整，而PDE求解器需要与非侵入性（采样）SSFEM相比，需要进行大量的编码工作。在本文中，使用随机PDE的示例，我们证明，可以使用Fenics（一种通用有限元包和UQTK）来缓解侵入性方法的实施挑战 - 库的集合和工具，用于量化不确定性。此外，还提供了算法细节和代码片段，以帮助计算科学家为其应用实施这些方法。本文摘自作者的论文[1]。
The intrusive (sample-free) spectral stochastic finite element method (SSFEM) is a powerful numerical tool for solving stochastic partial differential equations (PDEs). However, it is not widely adopted in academic and industrial applications because it demands intrusive adjustments in the PDE solver, which require substantial coding efforts compared to the non-intrusive (sampling) SSFEM. Using an example of stochastic PDE, in this article, we demonstrate that the implementational challenges of the intrusive approach can be alleviated using FEniCS -- a general purpose finite element package and UQTk -- a collection of libraries and tools for the quantification of uncertainty. Furthermore, the algorithmic details and code snippets are provided to assist computational scientists in implementing these methods for their applications. This article is extracted from the author's thesis [1].
