Displaying similar documents to “A comparison of approaches for the construction of reduced basis for stochastic Galerkin matrix equations”

Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters

Béreš, Michal

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In this contribution, we present a solution to the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with uncertain material coefficients in the separable form. The SG system of equations is kept in the compressed tensor form and its solution is a very challenging task. Here, we present the reduced basis (RB) method as a solver which looks for a low-rank representation of the solution. The construction of the RB consists of iterative expanding of the basis...

Covariate-based stochastic parameterization of baroclinic ocean eddies

Nick Verheul, Jan Viebahn, Daan Crommelin (2017)

Mathematics of Climate and Weather Forecasting

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In this study we investigate a covariate-based stochastic approach to parameterize unresolved turbulent processes within a standard model of the idealised, wind-driven ocean circulation. We focus on vertical instead of horizontal coarse-graining, such that we avoid the subtle difficulties of horizontal coarsegraining. The corresponding eddy forcing is uniquely defined and has a clear physical interpretation related to baroclinic instability.We propose to emulate the baroclinic eddy forcing...

Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components

Lakshmi Kanta Patra, Suchandan Kayal, Phalguni Nanda (2018)

Applications of Mathematics

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We focus on stochastic comparisons of lifetimes of series and parallel systems consisting of independent and heterogeneous new Pareto type components. Sufficient conditions involving majorization type partial orders are provided to obtain stochastic comparisons in terms of various magnitude and dispersive orderings which include usual stochastic order, hazard rate order, dispersive order and right spread order. The usual stochastic order of lifetimes of series systems with possibly different...

Transforming stochastic matrices for stochastic comparison with the st-order

Tuğrul Dayar, Jean-Michel Fourneau, Nihal Pekergin (2010)

RAIRO - Operations Research

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We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.

Polynomial chaos in evaluating failure probability: A comparative study

Eliška Janouchová, Jan Sýkora, Anna Kučerová (2018)

Applications of Mathematics

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Recent developments in the field of stochastic mechanics and particularly regarding the stochastic finite element method allow to model uncertain behaviours for more complex engineering structures. In reliability analysis, polynomial chaos expansion is a useful tool because it helps to avoid thousands of time-consuming finite element model simulations for structures with uncertain parameters. The aim of this paper is to review and compare available techniques for both the construction...

Controlling the stochastic sensitivity in thermochemical systems under incomplete information

Irina Bashkirtseva (2018)

Kybernetika

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Complex dynamic regimes connected with the noise-induced mixed-mode oscillations in the thermochemical model of flow reactor are studied. It is revealed that the underlying reason of such excitability is in the high stochastic sensitivity of the equilibrium. The problem of stabilization of the excitable equilibrium regimes is investigated. We develop the control approach using feedback regulators which reduce the stochastic sensitivity and keep the randomly forced system near the stable...

Attainability analysis in the problem of stochastic equilibria synthesis for nonlinear discrete systems

Irina Bashkirtseva, Lev Ryashko (2013)

International Journal of Applied Mathematics and Computer Science

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A nonlinear discrete-time control system forced by stochastic disturbances is considered. We study the problem of synthesis of the regulator which stabilizes an equilibrium of the deterministic system and provides required scattering of random states near this equilibrium for the corresponding stochastic system. Our approach is based on the stochastic sensitivity functions technique. The necessary and important part of the examined control problem is an analysis of attainability. For...