AI 中文总结
本文提出电磁去耦（EMD）预处理子，将离散系统分解为矢量和标量势分量，在四类涡流模型上测试，迭代次数和求解时间较传统不完全乔列斯基预处理子最多减20倍，支持并行化，兼容多种求解方法，适用于大规模电磁仿真。
AI 中文摘要
本文针对涉及外电路耦合的涡流问题，提出了一种高效且可扩展的预处理策略，该方法名为电磁去耦（Electro-Magnetic Decoupling, EMD）预处理子，它将离散系统分解为矢量和标量势分量，并为各分量应用定制化预处理子。特别地，对标量分量应用强预处理以解决离散拉普拉斯算子导致的谱退化问题。该方法在四个具有不同频率、导体拓扑结构和激励类型的涡流模型上进行了评估，与传统的不完全乔列斯基预处理子相比，EMD方法的迭代次数最多减少20倍，迭代求解器时间最多缩短20倍。此外，该方法支持物理层面的并行化，可高效处理独立激励的导体域。EMD框架与代数多重网格、区域分解法以及直接求解器兼容，为大规模电磁仿真提供了灵活性和鲁棒性。
英文摘要
This paper proposes an efficient and scalable preconditioning strategy for eddy current problems involving coupled external circuits. The approach, named Electro-Magnetic Decoupling (EMD) preconditioner, decomposes the discrete system into vector and scalar potential components and applies tailored preconditioners to each. In particular, strong preconditioning is applied to the scalar component to address the spectral degradation induced by the discrete Laplacian. The method was evaluated on four eddy current models with varying frequencies, conductor topologies, and excitation types. Compared to the conventional incomplete Cholesky preconditioner, the EMD approach achieved up to 20 times fewer iteration counts and up to 20 times faster iterative solver time. Moreover, the method supports physics-level parallelization, allowing efficient treatment of independently excited conductor domains. The EMD framework is compatible with algebraic multigrid, domain decomposition, and direct solvers, offering flexibility and robustness for large-scale electromagnetic simulations.
Journal refvol. 62, no. 7, pp. 7203906-7203906, July 2026
