scholarly journals Parameter-Robust Stochastic Galerkin Mixed Approximation for Linear Poroelasticity with Uncertain Inputs

2021 ◽  
Vol 43 (4) ◽  
pp. B855-B883
Author(s):  
Arbaz Khan ◽  
Catherine E. Powell
Keyword(s):  
Stochastic Galerkin ◽  
Mixed Approximation

scholarly journals Preconditioning Stochastic Galerkin Saddle Point Systems

2010 ◽  
Vol 31 (5) ◽  
pp. 2813-2840 ◽  
Author(s):  
Catherine E. Powell ◽  
Elisabeth Ullmann
Keyword(s):  
Saddle Point ◽  
Stochastic Galerkin

scholarly journals Stability-preserving model order reduction for linear stochastic Galerkin systems

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Roland Pulch
Keyword(s):  
Dynamical System ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Electric Circuit ◽  
Physical Parameters ◽  
Science And Engineering ◽  
Model Order ◽  
Linear Dynamical Systems ◽  
Stochastic Galerkin ◽  
The Stability

Abstract Mathematical modeling often yields linear dynamical systems in science and engineering. We change physical parameters of the system into random variables to perform an uncertainty quantification. The stochastic Galerkin method yields a larger linear dynamical system, whose solution represents an approximation of random processes. A model order reduction (MOR) of the Galerkin system is advantageous due to the high dimensionality. However, asymptotic stability may be lost in some MOR techniques. In Galerkin-type MOR methods, the stability can be guaranteed by a transformation to a dissipative form. Either the original dynamical system or the stochastic Galerkin system can be transformed. We investigate the two variants of this stability-preserving approach. Both techniques are feasible, while featuring different properties in numerical methods. Results of numerical computations are demonstrated for two test examples modeling a mechanical application and an electric circuit, respectively.

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