  In this paper, we investigate Dual-Primal Isogeometric Tearing and
Interconnecting (IETI-DP) methods for conforming Galerkin discretizations on
multi-patch computational domains with inexact subdomain solvers. Recently, the
authors have proven a condition number estimate for a IETI-DP method using
sparse LU factorizations for the subdomain problems that is explicit, among
other parameters, in the grid size and the spline degree. In the present paper,
we replace the sparse LU factorizations by fast diagonalization based
preconditioners to get a faster IETI-DP method while maintaining the same
explicit condition number bound.
