S. Dolgov, B.N. Khoromskij, I. Oseledets, and E.E. Tyrtyshnikov. Low-rank tensor structure of solutions to elliptic problems with jumping coefficients. Journal of Computational Mathematics, 30(1):14–23, 2012.
We study the separability properties of solutions to elliptic equations with piecewise constant coeffcients in R^d, d >2. The separation rank of the solution to diffusion equation with variable coefficients is presented
Structured matrices, Elliptic operators, Poisson equation, Matrix approxima- tions, Low-rank matrices, Tensors, Canonical decomposition.