Multi-level Monte Carlo finite volume methods for shallow water equations with uncertain topography in multi-dimensions
Open access
Date
2011-11Type
- Report
ETH Bibliography
yes
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Abstract
The initial data and bottom topography, used as inputs in shallow water models, are prone to uncertainty due to measurement errors. We model this uncertainty statistically in terms of random shallow water equations. We extend the Multi-Level Monte Carlo (MLMC) algorithm to numerically approximate the random shallow water equations efficiently. The MLMC algorithm is suitably modified to deal with uncertain (and possibly uncorrelated) data on each node of the underlying topography grid by the use of a hierarchical topography representation. Numerical experiments in one and two space dimensions are presented to demonstrate the efficiency of the MLMC algorithm. Show more
Permanent link
https://doi.org/10.3929/ethz-a-010400202Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Shallow water equations; Energy stable schemes; Uncertainty quantification; Multi- Level Monte Carlo; ParallelizationOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
03851 - Mishra, Siddhartha / Mishra, Siddhartha
Funding
247277 - Automated Urban Parking and Driving (EC)
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ETH Bibliography
yes
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