13 papers
Efficient Hermitian and skew-Hermitian splitting methods for linear systems in micromagnetic simulations
Yingxi Miao, Changjian Xie
For the Landau-Lifshitz equation, the discrete linear systems obtained by our semi-implicit method possess the following properties: they are large-sparse systems with non-Hermitia…
Efficient Multigrid Methods for Semi-implicit Landau-Lifshitz Schemes in Micromagnetic Simulations
Changjian Xie
An efficient aggregation-based multigrid approach is developed in this work to solve linear algebraic systems generated by discretizing the Landau-Lifshitz equation in micromagneti…
Improved Energy Stable Symmetric Gauss-Seidel Projection Method for Micromagnetics Simulations
Yingxi Miao, Changjian Xie
The Gauss-Seidel projection method (GSPM) constitutes an efficient and numerically stable numerical framework for micromagnetic simulations of ferromagnetic media. This scheme atta…
A Comparative Study of Projected and Unprojected Schemes for Micromagnetic Simulations
Changjian Xie
In micromagnetic simulations, the constant magnitude of the magnetization can be derived from the continuity equation. Since the time evolution of the magnetization in the continui…
A New Fractional Step Structure Preserving Method for The Landau-Lifshitz-Gilbert Equation
Changjian Xie
In this paper, we propose a structure preserving method using a Crank-Nicolson's type method with an implicit Gauss-Seidel fractional iteration. Such a method is of first-order acc…
Semi-implicit Structure Preserving Method for The Landau-Lifshitz Equation
Changjian Xie
A critical challenge inherent to the projection method applied to the Landau-Lifshitz equation is the deficiency of rigorous theoretical justifications for the stability of its pro…