Fast evaluation of demagnetizing field in three-dimensional micromagentics using multipole approximation

Xiaobo Tan; John S. Baras; P. S. Krishnaprasad

doi:10.1117/12.388764

19 June 2000 Fast evaluation of demagnetizing field in three-dimensional micromagentics using multipole approximation

Xiaobo Tan, John S. Baras, P. S. Krishnaprasad

Proceedings Volume 3984, Smart Structures and Materials 2000: Mathematics and Control in Smart Structures; (2000) https://doi.org/10.1117/12.388764
Event: SPIE's 7th Annual International Symposium on Smart Structures and Materials, 2000, Newport Beach, CA, United States

Abstract

Computational micromagnetics in three dimensions is of increasing interest with the development of magnetostrictive sensors and actuators. In solving the Landau-Lifshitz-Gilbert (LLG) equation, the governing equation of magnetic dynamics for ferromagnetic materials, we need to evaluate the effective field. The effective field consists of several terms, among which the demagnetizing field is of long-range nature. Evaluating the demagnetizing field directly requires work of O(N²) for a grid of N cells and thus it is the bottleneck in computational micromagnetics. A fast hierarchical algorithm using multipole approximation is developed to evaluate the demagnetizing field. We first construct a mesh hierarchy and divide the grid into boxes of different levels. The lowest level box is the whole grid while the highest level boxes are just cells. The approximate field contribution from the cells contained in a box is characterized by the box attributes, which are obtained via multipole approximation. The algorithm computes field contributions from remote cells using attributes of appropriate boxes containing those cells, and it computes contributions from adjacent cells directly. Numerical results have shown that the algorithm requires work of O(NlogN) and at the same time it achieves high accuracy. It makes micromagnetic simulation in three dimensions feasible.

Citation Download Citation

Xiaobo Tan, John S. Baras, and P. S. Krishnaprasad "Fast evaluation of demagnetizing field in three-dimensional micromagentics using multipole approximation", Proc. SPIE 3984, Smart Structures and Materials 2000: Mathematics and Control in Smart Structures, (19 June 2000); https://doi.org/10.1117/12.388764

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