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Volume 30, Issue 1
Low-Rank Tensor Structure of Solutions to Elliptic Problems with Jumping Coefficients

Sergey Dolgov, Boris N. Khoromskij, Ivan Oseledets & Eugene E. Tyrtyshnikov

DOI: 10.4208/jcm.1110-m11si08

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

Published online: 2012-02

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65F30, 65F50, 65N35, 65F10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-14, author = {Sergey Dolgov, Boris N. Khoromskij, Ivan Oseledets and Eugene E. Tyrtyshnikov}, title = {Low-Rank Tensor Structure of Solutions to Elliptic Problems with Jumping Coefficients}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {1}, pages = {14--23}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1110-m11si08}, url = {http://global-sci.org/intro/article_detail/jcm/8413.html} }
TY - JOUR T1 - Low-Rank Tensor Structure of Solutions to Elliptic Problems with Jumping Coefficients AU - Sergey Dolgov, Boris N. Khoromskij, Ivan Oseledets & Eugene E. Tyrtyshnikov JO - Journal of Computational Mathematics VL - 1 SP - 14 EP - 23 PY - 2012 DA - 2012/02 SN - 30 DO - http://doi.org/10.4208/jcm.1110-m11si08 UR - https://global-sci.org/intro/article_detail/jcm/8413.html KW - Structured matrices, Elliptic operators, Poisson equation, Matrix approximations, Low-rank matrices, Tensors, Canonical decomposition. AB -

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.

Sergey Dolgov, Boris N. Khoromskij, Ivan Oseledets and Eugene E. Tyrtyshnikov. (2012). Low-Rank Tensor Structure of Solutions to Elliptic Problems with Jumping Coefficients. Journal of Computational Mathematics. 30 (1). 14-23. doi:10.4208/jcm.1110-m11si08
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