On the field Lagrangians in micromagnetics
On the field Lagrangians in micromagnetics
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微磁学中的拉格朗日场
DOI：
10.1109/tmag.1986.1064664
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发表时间：
1986
影响因子：
2.1
通讯作者：
A. Thiele
中科院分区：
文献类型：
--
作者：
P. Asselin;A. Thiele
微磁计算通常从磁体能量的表达式开始，该表达式包含表示非局域偶极-偶极相互作用的六重积分。这一项用于数值应用程序中的长时间运行。存在两个不出现非局部项的替代场拉格朗日；这种局部性是以在方程中引入新变量为代价获得的。两个拉格朗日量中只有一个与能量的局域极小值一一对应。讨论了两场拉格朗日与能量的相互关系。推导了二维情况下的特殊公式，并讨论了可能的数值应用。
Micromagnetic calculations are commonly carried out starting from an expression for the energy of a magnetic body which contains a six-fold integral representing the nonlocal dipole-dipole interactions. This term is responsible for the long running times in numerical applications. There exist two alternative field Lagrangians in which nonlocal terms do not appear; this locality is obtained at the cost of introducing new variables in the equations. Only one of the two Lagrangians has local minima in one-to-one correspondence with those of the energy. The interrelation of the two field Lagrangians with the energy is discussed. Special formulas are derived for the two-dimensional case, and possible numerical applications are discussed.