Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

Jan Nordström; Markus Wahlsten

doi:10.1016/j.jcp.2014.10.061

Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

Jan Nordström, Markus Wahlsten

Linköping University

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for the Euler equations.

Original language	English
Pages (from-to)	1-22
Number of pages	22
Journal	Journal of Computational Physics
Volume	282
DOIs	https://doi.org/10.1016/j.jcp.2014.10.061
Publication status	Published - 1 Feb 2015
Externally published	Yes

Keywords

Boundary conditions
Hyperbolic system
Initial boundary value problems
Robust design
Stability
Stochastic data
Summation by parts
Uncertainty quantification
Variance reduction
Well posed

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2014.10.061

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abstract = "We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for the Euler equations.",

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AU - Wahlsten, Markus

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N2 - We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for the Euler equations.

AB - We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for the Euler equations.

KW - Boundary conditions

KW - Hyperbolic system

KW - Initial boundary value problems

KW - Robust design

KW - Stability

KW - Stochastic data

KW - Summation by parts

KW - Uncertainty quantification

KW - Variance reduction

KW - Well posed

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

Abstract

Keywords

ASJC Scopus subject areas

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