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].

翻译：侵扰(无抽样)光谱微量元素法(SSFEM)是解决随机偏差部分方程式(PDEs)的有力数字工具,但在学术和工业应用中并未得到广泛采用,因为它要求对PDE求解器进行侵扰性调整,这需要与非侵扰(抽样)SSFEM相比作出大量编码努力。 本条中,我们以随机PDE为例,表明可以使用FENICS(通用限量元素包)和UQTk(不确定性量化的图书馆和工具集)来减轻侵扰性方法的实施挑战。此外,提供了算法细节和代码元件,以协助计算学家为应用这些方法而采用这些方法。 本条是从作者的论文[1]摘录的。