2022/09/16 by Ajit Desai, Desai, Ajit
Decision Sciences · #Analysis of PDEs (math.AP) #Computational Engineering #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Finance #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2209.07882
openalex publication_date 2022/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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].