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

A simple formula of the magnetic potential and of the stray field energy induced by a given magnetization