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MiS Preprint
12/2011
Low-rank Tensor Structure of Solutions to Elliptic Problems with Jumping Coefficients
Sergey Dolgov, Boris N. Khoromskij, Ivan V. Oseledets and Eugene E. Tyrtyshnikov
Abstract
We study the separability properties of solutions to elliptic equations with a piecewise constant diffusion coefficient in $\mathbb{R}^d$, $d \ge 2$. It is proved that the solution can be approximated with a sum of $O(M^{d-1})$ products of univariate functions, where $M$ is a number of cells with constant coefficient in each direction. For discrete solutions in the 2D case the better estimate was obtained in series of numerical experiments: the separation rank of the solution is only proportional to the separation rank of the coefficient instead of the number of cells.
