J. Comp. Math., 30 (2012), pp. 14-23.


Low-rank Tensor Structure of Solutions to Elliptic Problems with Jumping Coefficients

Sergey Dolgov 1, Boris N. Khoromskij 2, Ivan Oseledets 3, Eugene E. Tyrtyshnikov 4

1 Moscow Institute of Physics and Technology, Russia
2 Max-Planck-Institute for Mathematics in Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany
3 Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina 8, 119991 Moscow, Russia
4 Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina 8, 119991 Moscow, Russia
4 Lomonosov Moscow State University, Russia; University of Siedlce, Poland (visiting professor)

Received 2011-2-26 Accepted 2011-8-20
Available online 2012-1-09
doi:10.4208/jcm.1110-m11si08

Abstract

We study the separability properties of solutions to elliptic equations with piecewise constant coefficients in \mathbb{R}^d, d \ge 2. The separation rank of the solution to diffusion equation with variable coefficients is presented.

Key words: Structured matrices, Elliptic operators, Poisson equation, Matrix approximations, Low-rank matrices, Tensors, Canonical decomposition.

AMS subject classifications: 65F30, 65F50, 65N35, 65F10.


Email: sergey.v.dolgov@gmail.com, bokh@mis.mpg.de, ivan.oseledets@gmail.com, tee@inm.ras.ru
 

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