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

## 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.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22382178

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 282; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; BOUNDARY-VALUE PROBLEMS; COMPARATIVE EVALUATIONS; CONVERGENCE; MATHEMATICAL SOLUTIONS; MAXWELL EQUATIONS; STABILITY; STOCHASTIC PROCESSES

### Citation Formats

```
Nordström, Jan, E-mail: jan.nordstrom@liu.se, and Wahlsten, Markus, E-mail: markus.wahlsten@liu.se.
```*Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations*. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2014.10.061.

```
Nordström, Jan, E-mail: jan.nordstrom@liu.se, & Wahlsten, Markus, E-mail: markus.wahlsten@liu.se.
```*Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations*. United States. doi:10.1016/J.JCP.2014.10.061.

```
Nordström, Jan, E-mail: jan.nordstrom@liu.se, and Wahlsten, Markus, E-mail: markus.wahlsten@liu.se. Sun .
"Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations". United States.
doi:10.1016/J.JCP.2014.10.061.
```

```
@article{osti_22382178,
```

title = {Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations},

author = {Nordström, Jan, E-mail: jan.nordstrom@liu.se and Wahlsten, Markus, E-mail: markus.wahlsten@liu.se},

abstractNote = {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.},

doi = {10.1016/J.JCP.2014.10.061},

journal = {Journal of Computational Physics},

number = ,

volume = 282,

place = {United States},

year = {Sun Feb 01 00:00:00 EST 2015},

month = {Sun Feb 01 00:00:00 EST 2015}

}

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