  We construct solvers for an isogeometric multi-patch discretization, where
the patches are coupled via a discontinuous Galerkin approach, which allows the
consideration of discretizations that do not match on the interfaces. We solve
the resulting linear system using a Dual-Primal IsogEometric Tearing and
Interconnecting (IETI-DP) method. We are interested in solving the arising
patch-local problems using iterative solvers since this allows the reduction of
the memory footprint. We solve the patch-local problems approximately using the
Fast Diagonalization method, which is known to be robust in the grid size and
the spline degree. To obtain the tensor structure needed for the application of
the Fast Diagonalization method, we introduce an orthogonal splitting of the
local function spaces. We present a convergence theory that confirms that the
condition number of the preconditioned system only grows poly-logarithmically
with the grid size. The numerical experiments confirm this finding. Moreover,
they show that the convergence of the overall solver only mildly depends on the
spline degree. We observe a mild reduction of the computational times and a
significant reduction of the memory requirements in comparison to standard
IETI-DP solvers using sparse direct solvers for the local subproblems.
Furthermore, the experiments indicate good scaling behavior on distributed
memory machines.
