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Multilevel Uncertainty Quantification Methods for Robust Design of Industrial Applications

Boek - Dissertatie

The size and complexity of mathematical models used in many areas of science and engineering is ever increasing. Likewise, the number of parameters used in these models is expanding. Uncertainty affects almost all of these parameters. Quantification of the effect of these uncertain parameters on the model output is coming to play an ever more important role in applications. This is the topic of uncertainty quantification (UQ).Dealing with a large number of uncertain parameters poses enormous challenges, even for modern supercomputers, if conventional UQ algorithms are used. These algorithms can require many expensive model evaluations, because of the nearly inevitable tendency of the computational cost to increase exponentially with the number of parameters. Monte Carlo (MC)-type methods have shown to avoid this so-called curse of dimension. However, the classic MC method is often viewed as impractical due to its expense. Fortunately, so-called multilevel sampling methods can dramatically reduce the cost of an MC simulation. The Multilevel Monte Carlo (MLMC) method, for example, reduces the computational cost by performing many model evaluations with low accuracy, and corresponding low cost. Subsequently, one adds fewer and fewer evaluations of a correction term with ever increasing accuracy, but also increasing cost.The aim of this work is to develop and investigate several instances of these multilevel methods, that are useful for UQ problems involving a large number of uncertain parameters. As we pay special attention to models described by partial differential equations (PDEs), the fast and robust computation of every model evaluation is crucial. This can be achieved using Multigrid (MG) methods. MG methods use a hierarchy of coarse approximations much similar to the hierarchy used in multilevel sampling methods. This leaves room for many algorithmic improvements.In a final part, we apply some of the methods developed in this thesis to a real-life engineering problem from computational fluid dynamics (CFD).This research was funded by project IWT/SBO EUFORIA: 'Efficient Uncertainty Quantification For Optimization in Robust design of Industrial Applications' (IWT-140068) of the Agency for Innovation by Science and Technology, Flanders, Belgium.
Jaar van publicatie:2019