Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids
TLDR
In this article, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation.About:
This article is published in Journal of Computational Physics.The article was published on 2022-01-01 and is currently open access. It has received 0 citations till now. The article focuses on the topics: Free boundary problem & Surrogate model.read more
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The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: In this article, a general recovery technique is developed for determining the derivatives (stresses) of the finite element solutions at nodes, which has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems.
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.
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The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
O. C. Zienkiewicz,J. Z. Zhu +1 more
TL;DR: In this paper, the authors derived a theorem showing the dependence of the effectivity index for the Zienkiewicz-Zhu error estimator on the convergence rate of the recovered solution.
Journal ArticleDOI
High dimensional polynomial interpolation on sparse grids
TL;DR: The error bounds show that the polynomial interpolation on a d-dimensional cube, where d is large, is universal, i.e., almost optimal for many different function spaces.
Journal ArticleDOI
Note on a Method for Calculating Corrected Sums of Squares and Products
TL;DR: In this paper, a method for calculating corrected sum of squares and products is presented. But this method is not suitable for counting the number of items in a set. And it is computationally difficult.