A duality principle for a semi-linear model in micro-magnetism

TL;DR

This paper introduces a duality principle for a semi-linear micro-magnetism model, utilizing convex analysis and Legendre transforms to create a concave dual formulation that facilitates numerical solutions.

Contribution

It develops a new dual variational formulation for semi-linear micro-magnetism models, emphasizing concavity and computational suitability, along with establishing optimality conditions.

Findings

Dual variational formulation is concave and suitable for numerical methods.

Sufficient conditions of optimality are established.

The approach leverages convex analysis and Legendre transforms.

Abstract

This article develops a duality principle for a semi-linear model in micro-magnetism. The results are obtained through standard tools of convex analysis and the Legendre transform concept. We emphasize the dual variational formulation presented is concave and suitable for numerical computations. Moreover, sufficient conditions of optimality are also established.