Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification

2015 ◽  
Vol 68 (2) ◽  
pp. 596-623 ◽  
Author(s):  
J. Winokur ◽  
D. Kim ◽  
F. Bisetti ◽  
O. P. Le Maître ◽  
O. M. Knio
Keyword(s):  
Uncertainty Quantification ◽  
Spectral Projection ◽  
Projection Methods ◽  
Pseudo Spectral

scholarly journals UNCERTAINTY QUANTIFICATION IN STEADY STATE SIMULATIONS OF A MOLTEN SALT SYSTEM USING POLYNOMIAL CHAOS EXPANSION ANALYSIS

2021 ◽  
Vol 247 ◽  
pp. 15008
Author(s):  
Mario Santanoceto ◽  
Marco Tiberga ◽  
Zoltán Perkó ◽  
Sandra Dulla ◽  
Danny Lathouwers
Keyword(s):  
Molten Salt ◽  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Reference Model ◽  
Spectral Projection ◽  
Projection Methods ◽  
Polynomial Chaos Expansion ◽  
Maximum Temperature ◽  
Chaos Expansion ◽  
Coupled Models

Uncertainty Quantification (UQ) of numerical simulations is highly relevant in the study and design of complex systems. Among the various approaches available, Polynomial Chaos Expansion (PCE) analysis has recently attracted great interest. It belongs to nonintrusive spectral projection methods and consists of constructing system responses as polynomial functions of the stochastic inputs. The limited number of required model evaluations and the possibility to apply it to codes without any modification make this technique extremely attractive. In this work, we propose the use of PCE to perform UQ of complex, multi-physics models for liquid fueled reactors, addressing key design aspects of neutronics and thermal fluid dynamics. Our PCE approach uses Smolyak sparse grids designed to estimate the PCE coefficients. To test its potential, the PCE method was applied to a 2D problem representative of the Molten Salt Fast Reactor physics. An in-house multi-physics tool constitutes the reference model. The studied responses are the maximum temperature and the effective multiplication factor. Results, validated by comparison with the reference model on 103 Monte-Carlo sampled points, prove the effectiveness of our PCE approach in assessing uncertainties of complex coupled models.

Investigation of Biotransport in a Tumor With Uncertain Material Properties Using a Nonintrusive Spectral Uncertainty Quantification Method

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Alen Alexanderian ◽  
Liang Zhu ◽  
Maher Salloum ◽  
Ronghui Ma ◽  
Meilin Yu
Keyword(s):  
Uncertainty Quantification ◽  
Material Properties ◽  
Statistical Models ◽  
Gaussian Random Field ◽  
Concentration Field ◽  
Random Variable ◽  
Spectral Projection ◽  
Velocity Fields ◽  
Efficient Computation ◽  
Uncertain Material Properties

In this study, statistical models are developed for modeling uncertain heterogeneous permeability and porosity in tumors, and the resulting uncertainties in pressure and velocity fields during an intratumoral injection are quantified using a nonintrusive spectral uncertainty quantification (UQ) method. Specifically, the uncertain permeability is modeled as a log-Gaussian random field, represented using a truncated Karhunen–Lòeve (KL) expansion, and the uncertain porosity is modeled as a log-normal random variable. The efficacy of the developed statistical models is validated by simulating the concentration fields with permeability and porosity of different uncertainty levels. The irregularity in the concentration field bears reasonable visual agreement with that in MicroCT images from experiments. The pressure and velocity fields are represented using polynomial chaos (PC) expansions to enable efficient computation of their statistical properties. The coefficients in the PC expansion are computed using a nonintrusive spectral projection method with the Smolyak sparse quadrature. The developed UQ approach is then used to quantify the uncertainties in the random pressure and velocity fields. A global sensitivity analysis is also performed to assess the contribution of individual KL modes of the log-permeability field to the total variance of the pressure field. It is demonstrated that the developed UQ approach can effectively quantify the flow uncertainties induced by uncertain material properties of the tumor.

Role of the LBB Condition in Weak Spectral Projection Methods

2001 ◽  
Vol 174 (1) ◽  
pp. 405-420 ◽  
Author(s):  
F. Auteri ◽  
J.-L. Guermond ◽  
N. Parolini
Keyword(s):  
Spectral Projection ◽  
Projection Methods ◽  
Lbb Condition

scholarly journals Legendre spectral projection methods for Urysohn integral equations

2014 ◽  
Vol 263 ◽  
pp. 88-102 ◽  
Author(s):  
Payel Das ◽  
Mitali Madhumita Sahani ◽  
Gnaneshwar Nelakanti
Keyword(s):  
Integral Equations ◽  
Spectral Projection ◽  
Projection Methods ◽  
Urysohn Integral Equations
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