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.

翻译：具有复杂几何形状和大规模离散系统的电磁设备仿真得益于等几何分析和区域分解等先进计算方法。本文在等几何撕裂与互连方法中综合运用这两种概念，以实现静磁学问题的并行计算。我们通过图论方法——树-余树分解——解决了底层解的非唯一性问题。经典的树-余树规范被改进以适应并行化需求，这要求所有局部子系统具有唯一可解性。我们的贡献在于提出了一种构建相容树的显式算法，并将其与对偶-原始方法相结合以实现并行化。通过数值实验证明并验证了所提方法的正确性，展示了其精确性、可扩展性和最优收敛性。