一种用于高效计算逆迟滞算子的半光滑牛顿法
A semi-smooth Newton method for efficient evaluation of the inverse hysteresis operator
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中文总结 AI 辅助
该研究针对能量基矢量迟滞模型的非光滑性问题，提出半光滑牛顿法计算其逆迟滞算子，可无缝集成到磁场模拟并获全局线性收敛结果，经实验验证有效。
中文摘要 AI 辅助
我们研究基于能量的矢量迟滞模型的数值计算及其在基于矢量势公式的有限元模拟中的应用。迟滞模型固有的非光滑性给数值分析和实现带来挑战。利用凸分析工具，我们从能量密度角度刻画了正向和逆迟滞算子，该刻画保证了所得模型的适定性，并基于广义半光滑牛顿法为其计算提供了鲁棒算法，还能无缝集成到磁场模拟中，在每个载荷步产生非线性非光滑优化问题。我们讨论了有限元离散化，提出了用于迭代求解的半光滑牛顿法，并建立了与网格无关收敛率的全局线性收敛性，数值实验验证了理论结果。
英文摘要
We study the numerical evaluation of an energy-based vector hysteresis model and its incorporation into finite element simulations based on a vector potential formulation. The inherent non-smoothness of the hysteresis model poses challenges for both numerical analysis and implementation. Using tools from convex analysis, we characterize the forward and inverse hysteresis operators in terms of energy densities. This characterization yields well-posedness of the resulting models and leads to robust algorithms for their evaluation based on generalized semi-smooth Newton methods. It furthermore enables a seamless integration into magnetic field simulations, leading to nonlinear and non-smooth optimization problems at every load step. We discuss the finite element discretization, present a semi-smooth Newton method for the iterative solution, and establish global linear convergence with mesh-independent convergence rates. The theoretical results are illustrated by numerical experiments.
