Non-uniform FFT for the finite element computation of the micromagnetic scalar potential

摘要

We present a quasi-linearly scaling, first order polynomial finite elementmethod for the solution of the magnetostatic open boundary problem by splittingthe magnetic scalar potential. The potential is determined by solving aDirichlet problem and evaluation of the single layer potential by a fastapproximation technique based on Fourier approximation of the kernel function.The latter approximation leads to a generalization of the well-knownconvolution theorem used in finite difference methods. We address it by anon-uniform FFT approach. Overall, our method scales O(M + N + N log N) for Nnodes and M surface triangles. We confirm our approach by several numericaltests.