In this paper, two efficient and magnetization norm preserving numerical schemes based on the scalar auxiliary variable (SAV) method are developed for calculating the ground state in micromagnetic structures. The first SAV scheme is based on the original SAV method for the gradient flow model, while the second scheme features an updated scalar auxiliary variable to better align with the associated energy. To address the challenging constraint of pointwise constant magnetization length, an implicit projection method is designed, and verified by both SAV schemes. Both proposed SAV schemes partially preserve energy dissipation and exhibit exceptional efficiency, requiring two linear systems with constant coefficients to be solved. The computational efficiency is further enhanced by applying the Discrete Cosine Transform during the solving process. Numerical experiments demonstrate that our SAV schemes outperform commonly used numerical methods in terms of both efficiency and stability.

翻译：本文针对微磁结构基态计算，提出了两种基于标量辅助变量（SAV）方法的高效且保持磁化强度范数的数值格式。第一种SAV格式基于梯度流模型的原始SAV方法，而第二种格式则采用更新的标量辅助变量，以更好地匹配相关能量。为处理点态恒定磁化强度长度这一具有挑战性的约束，设计了一种隐式投影方法，并通过两种SAV格式进行了验证。所提出的两种SAV格式均能部分保持能量耗散特性，并展现出卓越的计算效率，仅需求解两个具有常系数的线性系统。在求解过程中应用离散余弦变换进一步提升了计算效率。数值实验表明，我们的SAV格式在计算效率和稳定性方面均优于常用的数值方法。