Python + CUDA FFT Demagnetising Field Solver

Python + CUDA FFT solver for the demagnetising field arising from a magnetisation distribution on a regular Cartesian grid.

Implementation

The demagnetising field is computed as a convolution in Fourier space of the geometric (pre-computed) demagnetising tensor $N_{xy}$ and the magnetisation:

$\mathcal{F}(H_x) = \mathcal{F}(N_{xx}) * \mathcal{F}(M_x) + \mathcal{F}(N_{xy}) * \mathcal{F}(M_y) + \mathcal{F}(N_{xz}) * \mathcal{F}(M_z)$

$\mathcal{F}(H_y) = \mathcal{F}(N_{xy}) * \mathcal{F}(M_x) + \mathcal{F}(N_{yy}) * \mathcal{F}(M_y) + \mathcal{F}(N_{yz}) * \mathcal{F}(M_z)$

$\mathcal{F}(H_z) = \mathcal{F}(N_{xz}) * \mathcal{F}(M_x) + \mathcal{F}(N_{yz}) * \mathcal{F}(M_y) + \mathcal{F}(N_{zz}) * \mathcal{F}(M_z)$

All computation on the GPU is performed in single precision.

The demagnetising tensor is computed once via a C implementation using openMP parallelisation on the host, and transferred to the GPU.

Due to odd-even symmetries and diagonal symmetry of the demagnetising tensor, only 6 of 9 components are stored and approximately 1/8 of all interaction distances computed.

Accuracy

The calculated field is accurate down to the noise floor of single precision.

Example : Field due to a Permalloy disk in the vortex state

The flux-closure domain state minimises the in-plane demagnetising field at the expense of the out-of-plane component.

Required packacges:

CUDA >= 11.0

Python >= 3.10

cuPy

NumPy