Fast computation for large magnetostatic systems adapted for micromagnetism
In this paper, an efficient method is developed for computing the magnetostatic field for ferromagnetic materials on large structured meshes. The problem is discretized using a finite volume approximation. The discrete operator is proved to preserve the main properties of the continuous model, and a lower estimate of its lower eigenvalue is given. Using the fact that the discrete operator has a block-Toeplitz structure for cubic meshes in parallelepipedic domains, a fast solving method is built. Based upon the use of fast Fourier transform, this method allows to reduce the computational cost to from $n^2$ to $O(n\log(n))$ but also to reduce the storage to $O(n)$ instead of $n^2$ where $n$ is the number of cells in the mesh.