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

机译：任意形状的磁性材料中退磁场的3D计算

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摘要

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 Cray 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; Brunotte 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 * 32 * 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.
机译：傅立叶变换技术用于计算任意形状的磁性材料中的消磁场。这项技术也称为“ 0填充”算法，已经用于立方或平行六面体材料（Yuan和Neal，1992; Yuan，1992; Berkov等，1993; Patterson，1993; Fabian等， 1996）。它提供精确度，效率并可以有效并行化。我们已将其适应于任意几何形状的材料。该材料被放置在一个平行六面体的盒子里，盒子里装有被称为虚拟域的空气。新算法具有最初算法的主要质量：它的效率（虚拟域中N个网格元素的计算数量为O（N log N）阶，而不是直接卷积的O（N〜2）阶） ，在选择材料几何形状时具有一定的灵活性。在本文中，我们证明了该算法可以达到预期的效果。我们介绍在Cray T3E并行计算机上获得的结果，该结果用于被空气包围的立方体和一块磁记录头。将它们与用Flux3D软件计算的场进行比较（Imhoff等，1990; Brunotte等，1992; Chen和Konrad，1997）。他们在任何地方都可以很好地比较多维数据集。对于头部，除了在包括材料与空气之间的界面在内的薄弱区域（磁场变化较大）之外，它们的比较也很好。还在均匀磁化的球体中计算了该场，并将其与分析值进行了比较。对于具有32 * 32 * 32元素的网格，结果与完全在球体内的网格元素的平均结果相差在0.055％以内。我们已经注意到球体内边界附近存在峰。

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