Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients

Sergey V. Dolgov, Vladimir A. Kazeev and Boris N. Khoromskij

Mathematics and Computers in Simulation (MATCOM), 2018, vol. 145, issue C, 136-155

Abstract: We consider a one-dimensional second-order elliptic equation with a high-dimensional parameter in a hypercube as a parametric domain. Such a problem arises, for example, from the Karhunen–Loève expansion of a stochastic PDE posed in a one-dimensional physical domain. For the discretization in the parametric domain we use the collocation on a tensor-product grid. The paper is focused on the tensor-structured solution of the resulting multiparametric problem, which allows to avoid the curse of dimensionality owing to the use of the separation of parametric variables in the tensor train and quantized tensor train formats.

Keywords: Elliptic equations; Parametric problems; Tensor formats; Sherman–Morrison correction; Preconditioning (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:145:y:2018:i:c:p:136-155

DOI: 10.1016/j.matcom.2017.10.009

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