The Exponential Scalar Auxiliary Variable Approach for the Landau-Lifshitz Equation

Abstract

In this paper, we present two structure-preserving numerical schemes for the Landau-Lifshitz equation by combining the exponential scalar auxiliary variable method with the projection method. These schemes preserve both the length constraint and the modified energy dissipation law, ensuring numerical stability and accuracy. Moreover, they are particularly well-suited for studying the Landau-Lifshitz equation with higher-order energy terms, which have often been overlooked in earlier studies but have a significant impact on the stability, dynamics, and thermal behavior of magnetic skyrmions. We establish the unique solvability and energy stability of the schemes, and provide a rigorous error analysis. Numerical experiments are conducted to demonstrate the accuracy and effectiveness of the proposed schemes.