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arXiv · 1305.3162

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

Lukas Exl·Thomas Schrefl
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Abstract

We present a quasi-linearly scaling, first order polynomial finite element method for the solution of the magnetostatic open boundary problem by splitting the magnetic scalar potential. The potential is determined by solving a Dirichlet problem and evaluation of the single layer potential by a fast approximation technique based on Fourier approximation of the kernel function. The latter approximation leads to a generalization of the well-known convolution theorem used in finite difference methods. We address it by a non-uniform FFT approach. Overall, our method scales O(M + N + N log N) for N nodes and M surface triangles. We confirm our approach by several numerical tests.

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Lukas Exl, Thomas Schrefl. 2013-05-14. Non-uniform FFT for the finite element computation of the micromagnetic scalar potential. https://doi.org/10.1016/j.jcp.2014.04.013

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