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Multiscale Methods and Uncertainty Quantification
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- Elfverson, Daniel, 1986- (author)
- Uppsala universitet,Avdelningen för beräkningsvetenskap,Numerisk analys
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- Målqvist, Axel, Docent (thesis advisor)
- Uppsala universitet,Avdelningen för beräkningsvetenskap
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- Legoll, Frédéric, Professor (opponent)
- École Nationale des Ponts et Chaussées, Paris
- (creator_code:org_t)
- ISBN 9789155493363
- Uppsala : Acta Universitatis Upsaliensis, 2015
- English 32 s.
- Series: Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, 1651-6214 ; 1287
- Doctoral thesis (other academic/artistic)
Abstract
Subject headings
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- In this thesis we consider two great challenges in computer simulations of partial differential equations: multiscale data, varying over multiple scales in space and time, and data uncertainty, due to lack of or inexact measurements.We develop a multiscale method based on a coarse scale correction, using localized fine scale computations. We prove that the error in the solution produced by the multiscale method decays independently of the fine scale variation in the data or the computational domain. We consider the following aspects of multiscale methods: continuous and discontinuous underlying numerical methods, adaptivity, convection-diffusion problems, Petrov-Galerkin formulation, and complex geometries.For uncertainty quantification problems we consider the estimation of p-quantiles and failure probability. We use spatial a posteriori error estimates to develop and improve variance reduction techniques for Monte Carlo methods. We improve standard Monte Carlo methods for computing p-quantiles and multilevel Monte Carlo methods for computing failure probability.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- multiscale methods
- finite element method
- discontinuous Galerkin
- Petrov-Galerkin
- a priori
- a posteriori
- complex geometry
- uncertainty quantification
- multilevel Monte Carlo
- failure probability
- Beräkningsvetenskap med inriktning mot numerisk analys
- Scientific Computing with specialization in Numerical Analysis
Publication and Content Type
- vet (subject category)
- dok (subject category)
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