Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial
It serves as an educational entry point for researchers in QMC and PDE analysis, but is incremental in nature.
This tutorial overviews quasi-Monte Carlo methods for PDEs with random coefficients, providing a step-by-step analysis for the uniform case with first-order QMC rules, aiming to bridge QMC experts and PDE practitioners.
This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an accompanying software package which is also briefly discussed here. Embedded in this article is a step-by-step tutorial of the required analysis for the setting known as the uniform case with first order QMC rules. The aim of this article is to provide an easy entry point for QMC experts wanting to start research in this direction and for PDE analysts and practitioners wanting to tap into contemporary QMC theory and methods.