Gegenbauer reconstruction method with edge detection for multi-dimensional uncertainty propagation

Kawai, Shigetaka; Yamazaki, Wataru; Oyama, Akira

doi:10.1016/j.jcp.2022.111505

Cited by 4 publications

(2 citation statements)

References 42 publications

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“…In summary, we may conclude that the proposed

hp

‐adaptive collocation method based on Leja nodes is a reliable approach for surrogate modeling and UQ for functions with reduced regularity, as well as for functions featuring large gradients or sharp transitions. We expect, that the computational demand of the proposed method can be further reduced when combined with methods that detect the critical areas in the parameter domain beforehand 14,17,86 . Then, a reduced number of

h

‐refinement steps is expected, which in turn should reduce the overall complexity.…”

Section: Discussionmentioning

confidence: 98%

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An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use

Galetzka

Loukrezis

Georg

et al. 2023

Numerical Meth Engineering

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This article introduces an hp-adaptive multi-element stochastic collocation method, which additionally allows to re-use existing model evaluations during either h-or p-refinement. The collocation method is based on weighted Leja nodes. After h-refinement, local interpolations are stabilized by adding and sorting Leja nodes on each newly created sub-element in a hierarchical manner.For p-refinement, the local polynomial approximations are based on total-degree or dimension-adaptive bases. The method is applied in the context of forward and inverse uncertainty quantification to handle non-smooth or strongly localized response surfaces. The performance of the proposed method is assessed in several test cases, also in comparison to competing methods.

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“…In summary, we may conclude that the proposed

hp

h

‐refinement steps is expected, which in turn should reduce the overall complexity.…”

Section: Discussionmentioning

confidence: 98%

“…We expect, that the computational demand of the proposed method can be further reduced when combined with methods that detect the critical areas in the parameter domain beforehand. 14,17,86 Then, a reduced number of h-refinement steps is expected, which in turn should reduce the overall complexity.…”

Section: Discussionmentioning

confidence: 99%