  Isogeometric Analysis (IgA) is a versatile method for the discretization of
partial differential equations on complex domains, which arise in various
applications of science and engineering. Some complex geometries can be better
described as a computational domain by a multi-patch approach, where each patch
is determined by a tensor product Non-Uniform Rational Basis Splines (NURBS)
parameterization. This allows on the one hand to consider the problem of the
complex assembly of mass or stiffness matrices (or tensors) over the whole
geometry locally on the individual smaller patches, and on the other hand it is
possible to perform local mesh refinements independently on each patch,
allowing efficient local refinement in regions of high activity where higher
accuracy is required, while coarser meshes can be used elsewhere. Furthermore,
the information about differing material models or properties that are to apply
in a subdomain of the geometry can be included in the patch in which this
subdomain is located. For this it must be ensured that the approximate solution
is continuous over the entire computational domain and therefore at the
interfaces of two (or more) patches. The most promising approach for this
problem, which transfers the idea of Finite Element Tearing and Interconnecting
(FETI) methods into the isogeometric setup, was the IsogEometric Tearing and
Interconnecting (IETI) method, where by introducing a constraints matrix and
associated Lagrange multipliers and formulating it into a dual problem,
depending only on the Lagrange multipliers, continuity at the interfaces was
ensured in solving the resulting system. In this paper we illustrate that
low-rank methods based on the tensor-train format can be generalised for a
multi-patch IgA setup, which follows the IETI idea.
