几何约束下磁畴壁模型的相变数值解  

Phase Transition Numerical Solutions in Geometrically Constrained Magnetic Domain Wall Models

作　　者：张燕美[1] 王波[1,2] 

机构地区：[1]河南大学数学与统计学院,河南开封475004 [2]河南大学应用数学所,河南开封475004

出　　处：《河南大学学报（自然科学版）》2016年第4期495-499,共5页Journal of Henan University:Natural Science

基　　金：国家自然科学基金项目(40805020);河南省高等学校青年骨干教师资助计划项目(2014GGJS-021);河南大学新兴交叉及特色学科培育计划(0000A40450)

摘　　要：通过研究带几何约束的磁畴壁模型的数值解,观察了磁畴壁的总能量达到极小值时的物理状态.用梯度流法把求能量极小值问题转化为求解偏微分方程的初边值问题,利用有限差分法对该微分方程进行离散得到相应的差分格式,然后对得到的差分格式分别进行局部截断误差分析和稳定性分析.最后给出数值算例,数值结果表明:本文给出的差分格式对于求解能量极小值问题的方程是切实可行的.In this paper, the physical state when the total energy of the magnetic domain wall reaches its least value is observed by researching numerical solution of the geometrically constrained magnetic domain wall model. We used the gradient flow method to transform the energy minimum problem into the initial-boundary-value problem of partial differential equation. According to finite difference method, a difference scheme was established for the partial differential equation. Then the local truncation error analysis and stability analysis were used for the attained difference scheme. At last a numerical example was given, and the numerical results show that the dif{erence scheme is feasible for solving the energy minimization problem of equation.

关 键 词：有限差分法 梯度流法 磁畴壁 数值解 

分 类 号：O241.82[理学—计算数学]