标题： 具有磁滞的磁场问题的半光滑牛顿法 显示英文标题

标题： A semi-smooth Newton method for magnetic field problems with hysteresis

摘要： 铁磁材料表现出各向异性、饱和性和磁滞性。 我们在这里从理论和数值的角度研究了将一种增量矢量磁滞模型引入非线性磁场问题的方法，该模型用于表示这种复杂行为。 我们证明了与每个材料点上的磁场和通量相关的磁滞算子是强单调且Lipschitz连续的。 这使得我们可以确保相应磁场问题及其适当的有限元离散化的适定性。 我们进一步证明了磁滞算子是半光滑的，推导出它们广义雅可比矩阵的一个候选解，并建立了应用半光滑牛顿法（带线搜索）求解离散非线性场问题迭代解时全局线性和局部超线性收敛性。 这些结果对于涉及单一钉扎力和静磁标量势公式化的磁滞模型进行了详细证明。 扩展到多个钉扎力和矢量势公式化是可能的，并且简要概述了相关方法。 通过数值测试进一步说明了这些理论结果。 显示英文摘要

摘要： Ferromagnetic materials exhibit anisotropy, saturation, and hysteresis. We here study the incorporation of an incremental vector hysteresis model representing such complex behavior into nonlinear magnetic field problems both, from a theoretical and a numerical point of view. We show that the hysteresis operators, relating magnetic fields and fluxes at every material point, are strongly monotone and Lipschitz continuous. This allows to ensure well-posedness of the corresponding magnetic field problems and appropriate finite element discretizations thereof. We further show that the hysteresis operators are semi-smooth, derive a candidate for their generalized Jacobians, and establish global linear and local superlinear convergence of a the semi-smooth Newton method with line search applied to the iterative solution of the discretized nonlinear field problems. The results are proven in detail for a hysteresis model involving a single pinning force and the scalar potential formulation of magnetostatics. The extension to multiple pinning forces and the vector potential formulation is possible and briefly outlined. The theoretical results are further illustrated by numerical tests.