[HTML][HTML] Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification

R Crisovan, D Torlo, R Abgrall, S Tokareva - Journal of computational and …, 2019 - Elsevier
In this work, we present a model order reduction (MOR) technique for hyperbolic
conservation laws with applications in uncertainty quantification (UQ). The problem consists …

Entropy-conservative discontinuous Galerkin methods for the shallow water equations with uncertainty

J Bender, P Öffner - Communications on Applied Mathematics and …, 2024 - Springer
In this paper, we develop an entropy-conservative discontinuous Galerkin (DG) method for
the shallow water (SW) equation with random inputs. One of the most popular methods for …

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

S Tokareva, A Zlotnik, V Gyrya - Applied Mathematical Modelling, 2024 - Elsevier
We develop a weakly intrusive framework to simulate the propagation of uncertainty in
solutions of generic hyperbolic partial differential equation systems on graph-connected …

Weighted essentially non-oscillatory stochastic galerkin approximation for hyperbolic conservation laws

L Schlachter, F Schneider, O Kolb - Journal of Computational Physics, 2020 - Elsevier
In this paper we extensively study the stochastic Galerkin scheme for uncertain systems of
conservation laws, which appears to produce oscillations already for a simple example of …

[BOOK][B] Entropies and symmetrization of hyperbolic stochastic Galerkin formulations

S Gerster, M Herty - 2018 - doc.global-sci.org
Stochastic quantities of interest are expanded in generalized polynomial chaos expansions
using stochastic Galerkin methods. An application to hyperbolic differential equations does …

Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

JJ Harmon, S Tokareva, A Zlotnik, PJ Swart - arxiv preprint arxiv …, 2024 - arxiv.org
We propose a predictor-corrector adaptive method for the study of hyperbolic partial
differential equations (PDEs) under uncertainty. Constructed around the framework of …

The Tensor-Train Stochastic Finite Volume Method for Uncertainty Quantification

S Walton, S Tokareva, G Manzini - arxiv preprint arxiv:2404.06574, 2024 - arxiv.org
The stochastic finite volume method offers an efficient one-pass approach for assessing
uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality …

Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries

M Petrella, S Tokareva, EF Toro - Journal of Computational Physics, 2019 - Elsevier
Abstract We present a Stochastic Finite Volume-ADER (SFV-ADER) methodology for
Uncertainty Quantification (UQ) in the general framework of systems of hyperbolic balance …

Stochastic Active Discretizations for Accelerating Temporal Uncertainty Management of Gas Pipeline Loads

JJ Harmon, S Tokareva, A Zlotnik - arxiv preprint arxiv:2403.16929, 2024 - arxiv.org
We propose a predictor-corrector adaptive method for the simulation of hyperbolic partial
differential equations (PDEs) on networks under general uncertainty in parameters, initial …

Stabilization and uncertainty quantification for systems of hyperbolic balance laws

S Gerster, M Herty, S Göttlich, M Frank - 2020 - publications.rwth-aachen.de
Wir betrachten die Wohlgestelltheit und die Stabilisierung von eindimensionalen Systemen
von hyperbolischen partiellen Differentialgleichungen auf Netzwerken. Das p-System ist von …