scholarly journals Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations

2020 ◽  
Vol 145 (3) ◽  
pp. 655-692
Author(s):  
Martin Eigel ◽  
Manuel Marschall ◽  
Max Pfeffer ◽  
Reinhold Schneider
Keyword(s):  
Tensor Representations ◽  
Stochastic Galerkin

scholarly journals Adaptive stochastic Galerkin FEM with hierarchical tensor representations

2016 ◽  
Vol 136 (3) ◽  
pp. 765-803 ◽  
Author(s):  
Martin Eigel ◽  
Max Pfeffer ◽  
Reinhold Schneider
Keyword(s):  
Tensor Representations ◽  
Stochastic Galerkin

scholarly journals H(4) tensor representations for the lattice Landau gauge gluon propagator and the estimation of lattice artefacts

2021 ◽  
Vol 103 (7) ◽  
Author(s):  
Guilherme T. R. Catumba ◽  
Orlando Oliveira ◽  
Paulo J. Silva
Keyword(s):  
Gluon Propagator ◽  
Landau Gauge ◽  
Tensor Representations

Macromodeling of I/O Buffers via Compressed Tensor Representations and Rational Approximations

2016 ◽  
Vol 6 (10) ◽  
pp. 1522-1534 ◽  
Author(s):  
Gianni Signorini ◽  
Claudio Siviero ◽  
Stefano Grivet-Talocia ◽  
Igor S. Stievano
Keyword(s):  
Rational Approximations ◽  
Tensor Representations

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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