Solving Stochastic PDEs Using FEniCS and UQtk

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].