Â鶹Éçmadou

Abstract

The Landau-Lifshitz-Gilbert (LLG) equation is a well-established model for describing the dynamics of magnetisation in ferromagnetic materials. However, it is strictly valid only at zero kelvin and becomes increasingly inaccurate as the temperature approaches the Curie point. To account for thermal effects, the Landau-Lifshitz-Bloch (LLB) equation has been proposed in the physics literature as a more appropriate model at elevated temperatures.

In this talk, I will describe the model and present fully discrete finite element schemes for the numerical approximation of the LLB equation. Assuming sufficient regularity of the exact solution, I will discuss stability and optimal-order convergence results for the proposed schemes. In the temperature regime below the Curie point, additional regularisation procedures are employed due to the presence of a singular term in the equation. Numerical experiments will be shown to support the theoretical findings.

If time permits, I will also discuss the stochastic LLB equation for the regime above the Curie temperature. In this setting, regularisation procedures are again performed, partly due to the limited regularity theory for strong solutions.

This talk is based in part on joint work with Ben Goldys, Kim-Ngan Le, and Thanh Tran.