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- W4281621944 abstract "We develop in this paper two classes of length preserving schemes for the Landau-Lifshitz equation based on two different Lagrange multiplier approaches. In the first approach, the Lagrange multiplier $lambda(bx,t)$ equals to $|nabla m(bx,t)|^2$ at the continuous level, while in the second approach, the Lagrange multiplier $lambda(bx,t)$ is introduced to enforce the length constraint at the discrete level and is identically zero at the continuous level. By using a predictor-corrector approach, we construct efficient and robust length preserving higher-order schemes for the Landau-Lifshitz equation, with the computational cost dominated by the predictor step which is simply a semi-implicit scheme. Furthermore, by introducing another space-independent Lagrange multiplier, we construct energy dissipative, in addition to length preserving, schemes for the Landau-Lifshitz equation, at the expense of solving one nonlinear algebraic equation. We present ample numerical experiments to validate the stability and accuracy for the proposed schemes, and also provide a performance comparison with some existing schemes." @default.
- W4281621944 created "2022-06-13" @default.
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- W4281621944 date "2022-06-06" @default.
- W4281621944 modified "2023-09-23" @default.
- W4281621944 title "Length preserving numerical schemes for Landau-Lifshitz equation based on Lagrange multiplier approaches" @default.
- W4281621944 doi "https://doi.org/10.48550/arxiv.2206.02882" @default.
- W4281621944 hasPublicationYear "2022" @default.
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