论文标题
在comsol多物理学中实施H- $ ϕ $配方，以模拟散装超导体的磁化并与H形成进行比较
Implementation of the H-$ϕ$ formulation in COMSOL Multiphysics for simulating the magnetization of bulk superconductors and comparison with the H-formulation
论文作者
论文摘要
大量用于模拟高温超导体的H配置已证明是一种非常通用且易于实现的方法，用于对涉及超导材料的电磁现象进行建模。但是，不必要的无电流域中完整矢量场的模拟为模型增加了自由度，从而增加了计算时间。在此贡献中，我们在COMSOL多物理学中实现了众所周知的H- $ ϕ $配方，以比较在计算散装超导体磁化的背景下H和H $ ϕ $配方的数值性能。我们表明，对于给定的相对误差，H-$ ϕ $公式可以将自由度和计算时间的程度减少近两个。证明用两种制剂获得的磁场的准确性相似。 h- $ ϕ $配方的计算益处远远超过其实施的额外复杂性，尤其是在3-D中。最后，我们确定了H和H $ ϕ $公式的理想元素订单，在2-D中是四分之一的，在3-D中是四分之一，对应于Comsol中可实现的最高元素订单。
The H-formulation, used abundantly for the simulation of high temperature superconductors, has shown to be a very versatile and easily implementable way of modeling electromagnetic phenomena involving superconducting materials. However, the simulation of a full vector field in current-free domains unnecessarily adds degrees of freedom to the model, thereby increasing computation times. In this contribution, we implement the well known H-$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.
