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

Abstract

This paper 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 localised response surfaces. The performance of the proposed method is assessed in several test cases, also in comparison to competing methods.

31 pages, 13 figures

References in corpus (1)

• Robust Adaptive Least Squares Polynomial Chaos Expansions in High-Frequency Applications

Cited by in corpus (2)

• Multivariate sensitivity-adaptive polynomial chaos expansion for high-dimensional surrogate modeling and uncertainty quantification
• Active Learning-based Domain Adaptive Localized Polynomial Chaos Expansion