论文标题
高阶混合有限元，用于铁电材料中极化过程的基于能量的模型
High-order mixed finite elements for an energy-based model of the polarization process in ferroelectric materials
论文作者
论文摘要
当前的贡献中介绍了铁电偏振过程的基于能量的模型。在基于能量的环境中，介电位移和应变（或位移）是主要的独立未知数。作为内部变量，选择了远期极化向量。然后，该模型由两个本构函数控制：自由能函数和耗散函数。给出了两个功能的选择。由于不可差的响应的耗散函数是不可差的，因此提议将问题定向。然后，可以提出一个变分方程，随后使用每个数量的有限元元素离散地离散。我们指出每个场需要哪种连续性（位移，介电位移和隔离极化）对于获得符合方法并提供相应的有限元素是必要的。选择元素使高斯的零费用定律完全满足。在单个牛顿迭代中，对所有未知数求解了离散的变分方程。我们介绍了在开源软件包NetGen/ngsolve中获得的数值示例。
An energy-based model of the ferroelectric polarization process is presented in the current contribution. In an energy-based setting, dielectric displacement and strain (or displacement) are the primary independent unknowns. As an internal variable, the remanent polarization vector is chosen. The model is then governed by two constitutive functions: the free energy function and the dissipation function. Choices for both functions are given. As the dissipation function for rate-independent response is non-differentiable, it is proposed to regularize the problem. Then, a variational equation can be posed, which is subsequently discretized using conforming finite elements for each quantity. We point out which kind of continuity is needed for each field (displacement, dielectric displacement and remanent polarization) is necessary to obtain a conforming method, and provide corresponding finite elements. The elements are chosen such that Gauss' law of zero charges is satisfied exactly. The discretized variational equations are solved for all unknowns at once in a single Newton iteration. We present numerical examples gained in the open source software package Netgen/NGSolve.
