scholarly journals Accurate Solution of Bayesian Inverse Uncertainty Quantification Problems Combining Reduced Basis Methods and Reduction Error Models

2016 ◽  
Vol 4 (1) ◽  
pp. 380-412 ◽  
Author(s):  
A. Manzoni ◽  
S. Pagani ◽  
T. Lassila
Keyword(s):  
Uncertainty Quantification ◽  
Accurate Solution ◽  
Reduced Basis ◽  
Error Models ◽  
Reduced Basis Methods ◽  
Reduction Error

Reduced Basis Methods for Uncertainty Quantification

2017 ◽  
Vol 5 (1) ◽  
pp. 813-869 ◽  
Author(s):  
Peng Chen ◽  
Alfio Quarteroni ◽  
Gianluigi Rozza
Keyword(s):  
Uncertainty Quantification ◽  
Reduced Basis ◽  
Reduced Basis Methods

Stochastic Reduced Basis Methods

AIAA Journal ◽  
2002 ◽  
Vol 40 (8) ◽  
pp. 1653-1664 ◽  
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane
Keyword(s):  
Reduced Basis ◽  
Reduced Basis Methods

Comparison of advanced reduced-basis methods for transient structural analysis

AIAA Journal ◽  
1993 ◽  
Vol 31 (9) ◽  
pp. 1712-1719 ◽  
Author(s):  
David M. McGowan ◽  
Susan W. Bostic
Keyword(s):  
Structural Analysis ◽  
Reduced Basis ◽  
Reduced Basis Methods

Reduced Basis Methods for Fractional Laplace Equations via Extension

2019 ◽  
Vol 41 (6) ◽  
pp. A3552-A3575 ◽  
Author(s):  
Harbir Antil ◽  
Yanlai Chen ◽  
Akil Narayan
Keyword(s):  
Reduced Basis ◽  
Laplace Equations ◽  
Reduced Basis Methods

Electromagnetic wave scattering by random surfaces: Shape holomorphy

2017 ◽  
Vol 27 (12) ◽  
pp. 2229-2259 ◽  
Author(s):  
Carlos Jerez-Hanckes ◽  
Christoph Schwab ◽  
Jakob Zech
Keyword(s):  
Uncertainty Quantification ◽  
Electromagnetic Waves ◽  
Convergence Rates ◽  
Order Reduction ◽  
Reduced Basis ◽  
Approximation Techniques ◽  
Field Patterns ◽  
Time Harmonic ◽  
First Order Second Moment ◽  
Domain Perturbations

For time-harmonic electromagnetic waves scattered by either perfectly conducting or dielectric bounded obstacles, we show that the fields depend holomorphically on the shape of the scatterer. In the presence of random geometrical perturbations, our results imply strong measurability of the fields, in weighted spaces in the exterior of the scatterer. These findings are key to prove dimension-independent convergence rates of sparse approximation techniques of polynomial chaos type for forward and inverse computational uncertainty quantification. Also, our shape-holomorphy results imply parsimonious approximate representations of the corresponding parametric solution families, which are produced, for example, by greedy strategies such as model order reduction or reduced basis approximations. Finally, the presently proved shape holomorphy results imply convergence of shape Taylor expansions of far-field patterns for fixed amplitude domain perturbations in a vicinity of the nominal domain, thereby extending the widely used asymptotic linearizations employed in first-order, second moment domain uncertainty quantification.

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