Abstract of Sergey V. Dolgov

Tensor Structure of Solutions to Elliptic Problems with Jumping Coefficients
(joint work with B.N. Khoromskij and E.E. Tyrtyshnikov)
We study the separability properties of solutions of the elliptic equations with piecewise constant coefficients in Rd, d>1. We prove that the tensor rank of the canonical approximation of the discrete solution tensor is linearly proportional to the separation rank of the reciprocal coefficients tensor. We develop the quasi-direct tensor structured algorithm that computes the low rank solution getting rid of the ``curse of dimension'', based only on the rank structured decomposition of the reciprocal coefficients tensor and the solution of the related Poisson equation.


Lars Grasedyck (MPI Leipzig, Germany)
Wolfgang Hackbusch (MPI Leipzig, Germany)
Boris Khoromskij (MPI Leipzig, Germany)