Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients - a survey of analysis and implementation
Abstract
This article provides a survey of recent research efforts on the application of quasi-Monte Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion coefficients. It considers, and contrasts, the uniform case versus the lognormal case, single-level algorithms versus multi-level algorithms, first order QMC rules versus higher order QMC rules, and deterministic QMC methods versus randomized QMC methods. It gives a summary of the error analysis and proof techniques in a unified view, and provides a practical guide to the software for constructing and generating QMC points tailored to the PDE problems. The analysis for the uniform case can be generalized to cover a range of affine parametric operator equations.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2016
- DOI:
- 10.48550/arXiv.1606.06613
- arXiv:
- arXiv:1606.06613
- Bibcode:
- 2016arXiv160606613K
- Keywords:
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- Mathematics - Numerical Analysis