Efficient Implementation Algorithm for a Homogenized Energy Model with Thermal Relaxation

In this paper, we present a new algorithm to implement the homogenized energy hysteresis model with thermal relaxation for both ferroelectric and ferromagnetic materials. The approach conserves most of the accuracy of the original algorithm, but enables all erfc and exp functions to be calculated in advance, thereby requiring that only basic mathematical operations be performed in real time. This is done without a significant increase in memory usage. Using this approach, execution time of the model has been seen to improve by a factor of 70 for some applications, whereas the error only increases by five ten thousandths (0.05%) of the saturation polarization/magnetization. The model with negligible relaxation is also given, as it is used to illustrate some optimizations. Emphasis is placed on the efficient computation of these models, and theoretical development is left to the references.