基于树-余树撕裂与互联的三维静磁学：一种双- primal 方法
Tree-Cotree-Based Tearing and Interconnecting for 3D Magnetostatics: A Dual-Primal Approach
AI总结：
本文提出一种基于树-余树分解和双- primal 方法的等几何撕裂与互联技术，用于静磁问题的并行计算，并通过数值实验验证了其准确性、可扩展性和最优收敛性。
摘要：
具有复杂几何形状和大规模离散系统的电磁设备仿真受益于先进的计算方法，如等几何分析和区域分解。本文中，我们将这两个概念应用于等几何撕裂与互联方法中，以实现静磁问题的并行计算。我们通过图论方法——树-余树分解来解决潜在的非唯一性问题。经典的树-余树规范被调整为适用于并行化，这要求所有局部子系统具有唯一解。我们的贡献在于提出一种显式算法来构造兼容的树，并将其与双- primal 方法相结合以实现并行化。所提方法的正确性通过数值实验得到证明和验证，显示了其准确性、可扩展性和最优收敛性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
