论文标题
基于切割有限元素
A reduced order model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements
论文作者
论文摘要
在目前的工作中，我们研究了一种剪切的有限元方法，用于源自第四阶非线性几何PDE的二阶方程的参数化系统，即cahn-hilliard系统。每当出现强大的非线性时，我们都设法解决了此类方法的不稳定性问题，并利用它们的灵活性对固定背景几何形状和网状特征 - 可以避免，例如在参数化的几何形状中，在整个阶水平上进行重新捕捉，以及在降低水平上引用几何形状的转换。作为一个最终目标，我们设法找到了一个有效的全局，涉及几何流形，并且独立于几何变化，减少订单基础。即使在数值实验验证的伪随机的初始数据中，pod-galerkin方法也表现出其强度。
In the present work, we investigate a cut finite element method for the parameterized system of second-order equations stemming from the splitting approach of a fourth order nonlinear geometrical PDE, namely the Cahn-Hilliard system. We manage to tackle the instability issues of such methods whenever strong nonlinearities appear and to utilize their flexibility of the fixed background geometry -- and mesh -- characteristic, through which, one can avoid e.g. in parametrized geometries the remeshing on the full order level, as well as, transformations to reference geometries on the reduced level. As a final goal, we manage to find an efficient global, concerning the geometrical manifold, and independent of geometrical changes, reduced order basis. The POD-Galerkin approach exhibits its strength even with pseudo-random discontinuous initial data verified by numerical experiments.
