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…
An Efficient Energy Stable Structure Preserving Method for The Landau-Lifshitz Equation
Changjian Xie, Yingxi Miao, Haocheng Yang
One of the main difficulties in micromagnetics simulation is the norm preserving constraints at the continuous or the discrete level. Another difficulty is the s…
A novel third-order accurate and stable scheme for micromagnetic simulations
Changjian Xie
High-fidelity numerical simulation serves as a cornerstone for exploring magnetization dynamics in micromagnetics. This work introduces a novel third-order temporally accurate and…
Enhancing Micromagnetics Simulations with a Third-Order Semi-Implicit Projection Method
Changjian Xie, Cheng Wang
Micromagnetics depends on high-fidelity numerical methods for magnetization dynamics. This work proposes a third-order temporal accuracy scheme for the Landau-Lifshitz-Gilbert equa…
Convergence analysis of a third order semi-implicit projection method for Landau-Lifshitz-Gilbert equation
Changjian Xie, Cheng Wang
The convergence analysis of a third-order scheme for the highly nonlinear Landau-Lifshitz-Gilbert equation with a non-convex constraint is considered. In this paper, we first prese…
Efficient And Stable Third-order Method for Micromagnetics Simulations
Changjian Xie, Cheng Wang
To address the magnetization dynamics in ferromagnetic materials described by the Landau-Lifshitz-Gilbert equation under large damping parameters, a third-order accurate numerical…
Error Analysis of Third-Order in Time and Fourth-Order Linear Finite Difference Scheme for Landau-Lifshitz-Gilbert Equation under Large Damping Parameters
Changjian Xie, Cheng Wang
This work proposes and analyzes a fully discrete numerical scheme for solving the Landau-Lifshitz-Gilbert (LLG) equation, which achieves fourth-order spatial accuracy and third-ord…
Instability of Numerical Method for Micromagnetics Simulations with Large Damping Parameters
Changjian Xie, Cheng Wang
We propose and implement a third-order accurate numerical scheme for the Landau-Lifshitz-Gilbert equation, which describes magnetization dynamics in ferromagnetic materials under l…