7 research outputs found
An hpâadaptive multiâelement stochastic collocation method for surrogate modeling with information reâuse
This article introduces an hpâadaptive multiâelement stochastic collocation method, which additionally allows to reâuse existing model evaluations during either hâ or pârefinement. The collocation method is based on weighted Leja nodes. After hârefinement, local interpolations are stabilized by adding and sorting Leja nodes on each newly created subâelement in a hierarchical manner. For pârefinement, the local polynomial approximations are based on totalâdegree or dimensionâadaptive bases. The method is applied in the context of forward and inverse uncertainty quantification to handle nonâsmooth or strongly localized response surfaces. The performance of the proposed method is assessed in several test cases, also in comparison to competing methods
Kontextsensitive Modellhierarchien fĂŒr Quantifizierung der höherdimensionalen Unsicherheit
We formulate four novel context-aware algorithms based on model hierarchies aimed to enable an efficient quantification of uncertainty in complex, computationally expensive problems, such as fluid-structure interaction and plasma microinstability simulations. Our results show that our algorithms are more efficient than standard approaches and that they are able to cope with the challenges of quantifying uncertainty in higher-dimensional, complex problems.Wir formulieren vier kontextsensitive Algorithmen auf der Grundlage von Modellhierarchien um eine effiziente Quantifizierung der Unsicherheit bei komplexen, rechenintensiven Problemen zu ermöglichen, wie Fluid-Struktur-Wechselwirkungs- und Plasma-MikroinstabilitÀtssimulationen. Unsere Ergebnisse zeigen, dass unsere Algorithmen effizienter als StandardansÀtze sind und die Herausforderungen der Quantifizierung der Unsicherheit in höherdimensionalen, komplexen Problemen bewÀltigen können