论文标题
扩展组有限元法
Extended Group Finite Element Method
论文作者
论文摘要
非线性有限元离散化的插值方法通常用于消除与非线性系统重复组装相关的计算成本。尽管组有限元公式将非线性项插入有限元近似空间，但我们提出了针对非线性量身定制的单独近似空间的使用。在许多情况下，这允许将离散的非线性问题重新重新重新制定为具有代数约束的二次问题。此外，非线性术语的替代通常会将一般的非线性形式转移到三线性形式中，可以通过三阶张量很容易地描述。与原始组有限元方法相比，使用各种学术基准问题研究了数值好处以及优势。
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation interpolates nonlinear terms onto the finite element approximation space, we propose the use of a separate approximation space that is tailored to the nonlinearity. In many cases, this allows for the exact reformulation of the discrete nonlinear problem into a quadratic problem with algebraic constraints. Furthermore, the substitution of the nonlinear terms often shifts general nonlinear forms into trilinear forms, which can easily be described by third-order tensors. The numerical benefits as well as the advantages in comparison to the original group finite element method are studied using a wide variety of academic benchmark problems.
