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arXiv · 2206.14435

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

Armin Galetzka·Dimitrios Loukrezis·Niklas Georg·Herbert De Gersem·Ulrich Römer
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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.

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Armin Galetzka, Dimitrios Loukrezis, Niklas Georg, Herbert De Gersem, Ulrich Römer. 2022-06-29. An $hp$-adaptive multi-element stochastic collocation method for surrogate modeling with information re-use. https://doi.org/10.1002/nme.7234

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