A New Fractional Step Structure Preserving Method for The Landau-Lifshitz-Gilbert Equation

TL;DR

This paper introduces a novel structure-preserving numerical method for the Landau-Lifshitz-Gilbert equation that ensures stability, accuracy, and length preservation, verified through 1D and 3D tests.

Contribution

It presents a new fractional step method combining Crank-Nicolson and Gauss-Seidel iteration for improved stability and structure preservation.

Findings

First-order accuracy in time and second-order in space.

Method is stable and preserves length.

Numerical tests confirm accuracy and stability.

Abstract

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 accuracy in time and second-order accuracy in space, stable and length preserving. Such a proposed method brings great benefits for the theoretical analysis. The numerical accuracy, norm preserving and stability are verified for 1D and 3D tests.