Research Initiation Award: Techniques for Modeling of Electromagnetic Systems with Hysteresis on a Digital Computer

有许多物质具有一定程度的智能，使它们能够根据自己的历史调整自己的行为。这种性质有时被称为迟滞。在这种情况下，由于没有足够的分析工具或计算机工具来预测各种物理参数和特性，因此迟滞的存在往往使设备和系统的设计变得复杂。该项目的目标是开发具有磁滞的电磁系统建模的计算方法。研究将集中在以下两个问题上。一是建立和选择能准确反映本构规律的迟滞数学模型。二是发展了基于麦克斯韦方程组和本构定律确定电磁场的计算方法。​具有磁滞的电磁场问题的计算方法以前只在静态磁场的情况下讨论过。本文的目标是改进现有的滞回介质场计算方法，并将其推广到涉及电场和涡流的问题。为此，将采用一种新的、更通用的迟滞模型。有限元技术也被建议用于这些计算，因为在有限元方法的背景下，可以很容易地使用强大的工具来建模不同的几何形状。

There are many materials which posses a certain degree of intelligence allowing them to adjust their behavior on the basis of their history. This property is sometimes referred to as hysteresis. Design of devices and systems is often complicated by the presence of hysteresis because no adequate analytical or computer tools are available to predict various physical parameters and properties in this case. It is the objective of this project to develop computational methods for modeling of electromagnetic systems with hysteresis. The research will focus on the following two problems. One is the development and selection of mathematical models of hysteresis which can accurately represent constitutive laws. The other is the development of computational methods which can be used to determine electromagnetic fields on the basis of Maxwell's equations and constitutive laws. Computational methods for electromagnetic field problems with hysteresis have been addressed previously in the context of static magnetic fields only. It is the goal here to improve the existing methods of field computation in media with hysteresis and extend them to problems involving electric fields and eddy currents. To this end, a new, more general hysteresis model will be used. Finite element techniques are also suggested for these computations because powerful tools for modeling of different geometries in the context of the finite element method are readily available.