  The simulation of electromagnetic devices with complex geometries and
large-scale discrete systems benefits from advanced computational methods like
IsoGeometric Analysis and Domain Decomposition. In this paper, we employ both
concepts in an Isogeometric Tearing and Interconnecting method to enable the
use of parallel computations for magnetostatic problems. We address the
underlying non-uniqueness by using a graph-theoretic approach, the tree-cotree
decomposition. The classical tree-cotree gauging is adapted to be feasible for
parallelization, which requires that all local subsystems are uniquely
solvable. Our contribution consists of an explicit algorithm for constructing
compatible trees and combining it with a dual-primal approach to enable
parallelization. The correctness of the proposed approach is proved and
verified by numerical experiments, showing its accuracy, scalability and
optimal convergence.
