在COMSOL Multiphysics中实现H-$ϕ$公式以模拟大块超导体的磁化并与H-公式比较
Implementation of the H-$ϕ$ formulation in COMSOL Multiphysics for simulating the magnetization of bulk superconductors and comparison with the H-formulation
摘要：
H公式被广泛用于高温超导体的模拟，它是一种非常通用且易于实现的方法，可以模拟涉及超导材料的电磁现象。然而，在无电流域中模拟全矢量场不必要地增加了模型的自由度，从而增加了计算时间。在这方面的贡献，我们实现了众所周知的H-$ϕ$制定COMSOL Multiphysics为了比较的H和H-$ϕ$配方的计算的背景下，大块超导体的磁化的数值性能。我们表明，H-$ϕ$制定可以减少自由度的数量和计算时间的近一个因素的两个给定的相对误差。证明了用这两种制剂获得的磁场的准确度是相似的。计算的H-$ϕ$制定的好处被证明远远超过其实施所增加的复杂性，特别是在3-D。最后，我们确定H和H-$ϕ$配方的理想元素顺序是四次在2-D和立方在3-D，对应于最高的元素顺序在COMSOL中实现。
英文摘要：
The H-formulation, used abundantly for the simulation of high temperature superconductors, has shown to be a very versatile and easily implementable way of modeling electromagnetic phenomena involving superconducting materials. However, the simulation of a full vector field in current-free domains unnecessarily adds degrees of freedom to the model, thereby increasing computation times. In this contribution, we implement the well known H-$ϕ$ formulation in COMSOL Multiphysics in order to compare the numerical performance of the H and H-$ϕ$ formulations in the context of computing the magnetization of bulk superconductors. We show that the H-$ϕ$ formulation can reduce the number of degrees of freedom and computation times by nearly a factor of two for a given relative error. The accuracy of the magnetic fields obtained with both formulations are demonstrated to be similar. The computational benefits of the H-$ϕ$ formulation are shown to far outweigh the added complexity of its implementation, especially in 3-D. Finally, we identify the ideal element orders for both H and H-$ϕ$ formulations to be quartic in 2-D and cubic in 3-D, corresponding to the highest element orders implementable in COMSOL.
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