Table of Contents
Algorithms, Volume 13, Issue 5 (May 2020) – 25 articles
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Cover Story (view full-size image) Civil engineering applications are often characterized by large uncertainties regarding the [...] Read more. Civil engineering applications are often characterized by large uncertainties regarding the material parameters. Discretization of the underlying equations is typically done by means of the Galerkin finite element method. The uncertain material parameter can then be expressed as a random field represented by means of a Karhunen–Loève expansion. Computation of the stochastic responses remains very costly, even when state-of-the-art multilevel Monte Carlo is used. A significant cost reduction can be achieved by using p-refined multilevel quasi-Monte Carlo (p-MLQMC). This novel method is based on a variance reduction scheme by employing a hierarchical p-refinement discretization of the problem, which is then combined with a rank-1 lattice rule. In this work, we developed algorithms for the p-MLQMC method and benchmarked them on two model problems. View this paper