In this paper, we propose a robust concurrent multiscale method for continuum-continuum coupling based on the cut finite element method. The computational domain is defined in a fully non-conforming fashion by approximate signed distance functions over a fixed background grid and decomposed into microscale and macroscale regions by a novel zooming technique. The zoom interface is represented by a signed distance function which is allowed to intersect the computational mesh arbitrarily. We refine the mesh inside the zooming region hierarchically for high-resolution computations. In the examples considered here, the microstructure can possess void, and hard inclusions and the corresponding geometry is defined by a signed distance function interpolated over the refined mesh. In our zooming technique, the zooming interface is allowed to intersect the microstructure interface in a arbitrary way. Then, the coupling between the subdomains is applied using Nitsche's method across interfaces. This multiresolution framework proposes an efficient stabilized algorithm to ensure the stability of elements cut by the zooming and the microstructure interfaces. It is tested for several multiscale examples to demonstrate its robustness and efficiency for elasticity and plasticity problems.
翻译:在本文中, 我们提出一个强大的并行多尺度方法, 用于根据切分的限定元素法进行连续连续连续连接。 计算域以完全不兼容的方式, 由固定背景网格上的近似签名距离函数来定义, 并通过新的缩放技术将缩放界面分解成微观规模和宏观规模区域。 缩放界面以一个签名距离函数来表示, 允许任意地将计算网格相交。 我们根据高分辨率计算, 按等级改进缩放区域内的网格。 在此处所考虑的例子中, 微结构可以拥有空虚, 硬包容和相应的几何法由精细化网格上的一个签名远程函数来定义。 在我们的缩放技术中, 缩放界面可以任意地将微结构界面相互分割。 然后, 将子域之间的连接应用 Nitsche 方法。 这个多分辨率框架建议一种有效的稳定算法, 以确保缩放和微结构界面所切割的元素的稳定性。 它测试了多个多尺度的图像, 以显示其稳度和效率问题。