A Convergent Implicit Finite Element Discretization of the Maxwell-Landau-Lifshitz-Gilbert Equation
A Convergent Implicit Finite Element Discretization of the Maxwell-Landau-Lifshitz-Gilbert Equation
复制标题
Maxwell-Landau-Lifshitz-Gilbert方程的收敛隐式有限元离散化
DOI：
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发表时间：
2008
影响因子：
2.9
通讯作者：
A. Prohl
中科院分区：
文献类型：
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作者：
L. Baňas;S. Bartels;A. Prohl
我们提出了一个隐式的，完全离散的计划的数值解的Maxwell-Landau-Lifshitz-Gilbert方程是基于线性有限元，并满足离散球约束以及离散能量法。当数值参数趋于零时，Maxwell-Landau-Lifshitz-Gilbert方程的解在弱解处弱积累.一个实用的线性化的非线性计划，提出了收敛的数值参数的某些缩放。计算研究表明有限时间爆破行为，并在铁磁体的基准问题的研究组合的电磁现象。
We propose an implicit, fully discrete scheme for the numerical solution of the Maxwell-Landau-Lifshitz-Gilbert equation which is based on linear finite elements and satisfies a discrete sphere constraint as well as a discrete energy law. As numerical parameters tend to zero, solutions weakly accumulate at weak solutions of the Maxwell-Landau-Lifshitz-Gilbert equation. A practical linearization of the nonlinear scheme is proposed and shown to converge for certain scalings of numerical parameters. Computational studies are presented to indicate finite-time blow-up behavior and to study combined electromagnetic phenomena in ferromagnets for benchmark problems.