Journal ArticleDOI
Investigations on the restrictions of stochastic collocation methods for high dimensional and nonlinear engineering applications
TLDR
In this article , Tamellini et al. compare the efficiency and accuracy of different unbounded sparse grids (Gauss-Hermite, Gauss-Leja and Kronrod-Patterson) with Monte Carlo simulations.About:
This article is published in Probabilistic Engineering Mechanics.The article was published on 2022-06-01. It has received 5 citations till now. The article focuses on the topics: Sparse grid & Solver.read more
Citations
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Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures
TL;DR: In this paper , a probabilistic approach to phase-field brittle and ductile fracture with random material and geometric properties is proposed within this work, which is devoted to providing a mathematical framework for modeling uncertainty through stochastic analysis of a microstructure undergoing brittle/ductile failure.
Journal ArticleDOI
Anisotropic multi-element polynomial chaos expansion for high-dimensional non-linear structural problems
TL;DR: In this article , an hp-adaptive variant of ME-gPCE, referred to as anisotropic multi-element polynomial chaos expansion (AME-GPCE), was proposed, where the basis functions of the local gPCE are selected adaptively within each local element.
Journal ArticleDOI
A nonlinear stochastic finite element method for solving elastoplastic problems with uncertainties
Zhibao Zheng,Udo Nackenhorst +1 more
TL;DR: In this article, a nonlinear stochastic finite element method was proposed to solve the history-dependent stochastically elastoplastic problems. But the complexity of the proposed method does not increase dramatically with the dimensionality of the problem.
Journal ArticleDOI
Time-separated stochastic mechanics for the simulation of viscoelastic structures with local random material fluctuations
Hendrik Geisler,Philipp Junker +1 more
TL;DR: In this paper , the TSM is extended for viscoelastic structures with local random material fluctuations, and the method requires a low number of deterministic FEM simulations to approximate stress and reaction force, thus remarkably reducing the computational effort compared to classical Monte Carlo simulations.
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Globally supported surrogate model based on support vector regression for nonlinear structural engineering applications
TL;DR: In this article , support vector regression (SVR) is used to deal with discontinuous and high non-smooth outputs in a global surrogate modeling of mechanical systems with elasto-plastic material behavior.
References
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Journal ArticleDOI
Aleatory or epistemic? Does it matter?
TL;DR: In this article, the sources and characters of uncertainties in engineering modeling for risk and reliability analyses are discussed, and they are generally categorized as either aleatory or epistemic, if the modeler sees a possibility to reduce them by gathering more data or by refining models.
Journal ArticleDOI
High-Order Collocation Methods for Differential Equations with Random Inputs
Dongbin Xiu,Jan S. Hesthaven +1 more
TL;DR: A high-order stochastic collocation approach is proposed, which takes advantage of an assumption of smoothness of the solution in random space to achieve fast convergence and requires only repetitive runs of an existing deterministic solver, similar to Monte Carlo methods.
Journal ArticleDOI
A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
TL;DR: This work demonstrates algebraic convergence with respect to the total number of collocation points and quantifies the effect of the dimension of the problem (number of input random variables) in the final estimates, indicating for which problems the sparse grid stochastic collocation method is more efficient than Monte Carlo.
Journal ArticleDOI
An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis
Géraud Blatman,Bruno Sudret +1 more
TL;DR: A non-intrusive method that builds a sparse PC expansion and an adaptive regression-based algorithm is proposed for automatically detecting the significant coefficients of the PC expansion in a suitable polynomial chaos basis.
Journal ArticleDOI
Multilevel Monte Carlo methods
TL;DR: A review of the progress in multilevel Monte Carlo path simulation can be found in this article, where the authors highlight the simplicity, flexibility and generality of the multi-level Monte Carlo approach.
Related Papers (5)
A Multilevel Stochastic Collocation Method for Schrödinger Equations with a Random Potential
Tobias Jahnke,Benny Stein +1 more