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Wahlsten, Markus
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Wahlsten, Markus
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Computational MathematicsFaculty of Science & Engineering
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Computational Mathematics
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Uncertainty quantification for wave propagation and flow problems with random dataPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2018 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Linköping: Linköping University Electronic Press, 2018. , p. 26
##### Series

Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1921
##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-146966DOI: 10.3384/diss.diva-146966ISBN: 9789176853399 (print)OAI: oai:DiVA.org:liu-146966DiVA, id: diva2:1196053
##### Public defence

2018-05-04, Ada Lovelace, B-huset, Campus Valla, Linköping, 13:15 (English)
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt547",{id:"formSmash:j_idt547",widgetVar:"widget_formSmash_j_idt547",multiple:true}); Available from: 2018-04-09 Created: 2018-04-09 Last updated: 2018-04-09Bibliographically approved
##### List of papers

In this thesis we study partial differential equations with random inputs. The effects that different boundary conditions with random data and uncertain geometries have on the solution are analyzed. Further, comparisons and couplings between different uncertainty quantification methods are performed. The numerical simulations are based on provably strongly stable finite difference formulations based on summation-by-parts operators and a weak implementation of boundary and interface conditions.

The first part of this thesis treats the construction of variance reducing boundary conditions. It is shown how the variance of the solution can be manipulated by the choice of boundary conditions, and a close relation between the variance of the solution and the energy estimate is established. The technique is studied on both a purely hyperbolic system as well as an incompletely parabolic system of equations. The applications considered are the Euler, Maxwell's, and Navier--Stokes equations.

The second part focuses on the effect of uncertain geometry on the solution. We consider a two-dimensional advection-diffusion equation with a stochastically varying boundary. We transform the problem to a fixed domain where comparisons can be made. Numerical results are performed on a problem in heat transfer, where the frequency and amplitude of the prescribed uncertainty are varied.

The final part of the thesis is devoted to the comparison and coupling of different uncertainty quantification methods. An efficiency analysis is performed using the intrusive polynomial chaos expansion with stochastic Galerkin projection, and nonintrusive numerical integration. The techniques are compared using the non-linear viscous Burgers' equation. A provably stable coupling procedure for the two methods is also constructed. The general coupling procedure is exemplified using a hyperbolic system of equations.

1. Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations$(function(){PrimeFaces.cw("OverlayPanel","overlay761621",{id:"formSmash:j_idt608:0:j_idt616",widgetVar:"overlay761621",target:"formSmash:j_idt608:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Robust Boundary Conditions for Stochastic Incompletely Parabolic Systems of Equations$(function(){PrimeFaces.cw("OverlayPanel","overlay1059403",{id:"formSmash:j_idt608:1:j_idt616",widgetVar:"overlay1059403",target:"formSmash:j_idt608:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. The effect of uncertain geometries on advection–diffusion of scalar quantities$(function(){PrimeFaces.cw("OverlayPanel","overlay1137413",{id:"formSmash:j_idt608:2:j_idt616",widgetVar:"overlay1137413",target:"formSmash:j_idt608:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Stochastic Galerkin Projection and Numerical Integration for Stochastic Investigations of the Viscous Burgers’ Equation$(function(){PrimeFaces.cw("OverlayPanel","overlay1192511",{id:"formSmash:j_idt608:3:j_idt616",widgetVar:"overlay1192511",target:"formSmash:j_idt608:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. An efficient hybrid method for uncertainty quantification$(function(){PrimeFaces.cw("OverlayPanel","overlay1192501",{id:"formSmash:j_idt608:4:j_idt616",widgetVar:"overlay1192501",target:"formSmash:j_idt608:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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