Calculation of Demagnetizing Field Distribution Based on Fast Fourier Transform of Convolution

Abstract

It is confirmed that the calculation of the demagnetizing field in micromagnetic simulations can be accelerated significantly by using the discrete convolution theorem and the fast Fourier transform (FFT). When the magnetization distribution is periodic, application of the theorem to the demagnetizing field calculation is straightforward. Unlike the previously reported FFT method which is based on the continuous Fourier transform of the demagnetizing field, the method can also be used in the case of non-periodic magnetization structures. It is also confirmed that the result obtained using the new FFT method coincides with that of the conventional direct method, as expected. The principle of calculation and the results of one- and two-dimensional calculations which show the validity and effectiveness of the developed method are presented.

Speedup of Micromagnetic Simulations with C++ AMP on Graphics Processing Units

“…The brute force calculation of demagnetization field is known to be proportional to the square of the number N of the computational cells [10]. However, this calculation can be accelerated by taking advantage of the discrete convolution theorem and the fast Fourier transform (FFT) [11].…”

Efficient methods for macroscopic magnetization simulation described by the assembly of simplified domain structure models

“…The convolution (3) is efficiently executed by using the fast Fourier transform (FFT) [6], which, however, often requires a large computational cost even with the use of FFT.…”

“…The demagnetizing field H st in the ADSM is obtained in the same way as in the micromagnetic simulation [6]; H st at cell i is given as ) ( ) ( ) ( where h st is the normalized demagnetizing field; h st is given as…”

Simulations of 3-D domain wall structures in thin films

“…The difficulty with this approach is the lack of an effective boundary condition for U . The second class of method is based on using (2.6) to compute the stray field [18][2] [19]. From (2.6), we have…”

“…It is well known that the most expensive part of the simulation is the calculation of demagnetization field (or stray field). The Fast Fourier Transform can be easily used to speed up the calculation [19] when the sample shape is of rectangular shape. Another difficulty in the simulation is the severe time step constraint introduced by the exchange field when standard explicit integrators (like Runge-Kutta scheme) are used.…”