3D computation of the demagnetizing field in a magnetic material of arbitrary shape

A Fourier Transform technique is used to compute the demagnetizing field in a magnetic material of arbitrary shape. This technique, also known as the "0-padding" algorithm, has already been utilized for cubic or parallelepipedic material (Yuan and Neal, 1992; Yuan. 1992; Berkov et al., 1993: Patterson, 1993; Fabian et al., 1996). It offers preciseness. efficiency and can be parallelized effectively. We have adapted it to materials of arbitrary geometry. The material is placed in a parallelepipedic box containing air called the fictitious domain. The new algorithm has the main quality of the initial one: its efficiency (the number of computations is of order O(N log N) for N mesh elements in the fictitious domain instead of O(N-2) for the direct convolution product), with some flexibility in the choice of the material geometry. In this paper, we prove that the algorithm gives the expected result. We present results obtained on the Gray T3E parallel computer for a cube surrounded by air, for reference, and a piece of a magnetic recording head. They are compared to the field computed with the Flux3D software (Imhoff et al., 1990; Brunette et al., 1992; Chen and Konrad, 1997). They compare qualitatively well everywhere for the cube. For the head, they also compare well except in a thin region including the interface between material and air where the field undergoes a big variation. The field was also calculated in a sphere magnetized uniformly and compared to its analytical value. For a mesh with 32 x 32 x 32 elements, the results agree within 0.055% in average over the mesh elements completely inside the sphere. We have noted the presence of peaks near the border inside the sphere. (C) 2000 Elsevier Science B.V. All rights reserved.