Heterogeneous multiscale methods for the Landau-Lifshitz equation

TL;DR

This paper introduces a finite difference heterogeneous multiscale method for efficiently solving the Landau-Lifshitz equation with oscillatory diffusion coefficients, combining higher order discretization and damping.

Contribution

It presents a novel multiscale approach that effectively handles highly oscillatory coefficients in the Landau-Lifshitz equation with improved accuracy and efficiency.

Findings

The method achieves accurate approximations for periodic coefficients.

Numerical examples demonstrate robustness for general coefficients.

Parameter influence on error is systematically analyzed.

Abstract

In this paper, we present a finite difference heterogeneous multiscale method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient. The approach combines a higher order discretization and artificial damping in the so-called micro problem to obtain an efficient implementation. The influence of different parameters on the resulting approximation error is discussed. Numerical examples for both periodic as well as more general coefficients are given to demonstrate the functionality of the approach.