The primary aim of this paper is the derivation and the proof of a simple and tractable formula for the stray field energy in micromagnetic problems. The formula is based on an expansion in terms of Arar-Boulmezaoud functions. It remains valid even if the magnetization is not of constant magnitude or if the sample is not geometrically bounded. The paper continuous with a direct and important application which consists in a fast summation technique of the stray field energy. The convergence of this technique is established and its efficiency is proved by various numerical experiences.

翻译：本文的首要目标是推导并证明微磁学问题中杂散场能量的一个简单且易处理的公式。该公式基于Arar-Boulmezaoud函数的展开，即使磁化强度非恒定或样品几何无界时仍保持有效。文章继而给出一个直接且重要的应用——杂散场能量的快速求和技术。本文建立了该技术收敛性，并通过多种数值实验验证了其效率。