A mixed concurrent multiscale method via CutFEM technology.

In this paper, we develop a novel unfitted multiscale framework that combines two separate scales represented by only one single computational mesh. Our framework relies on a mixed zooming technique where we zoom at regions of interest to capture micro-scale properties and then mix the micro and macro-scale properties in a transition region. Furthermore, we use homogenization techniques to derive macro model material properties. Our multiscale framework is based on the CutFEM discretization technique where the elements are arbitrarily intersected with two microstructure and zooming surface interfaces. To address the issues with ill-conditioning of the multiscale system matrix due to the arbitrary intersections, we add stabilization terms acting on the jumps of the normal gradient over cut elements faces. We show that our multiscale framework is stable and is capable to reproduce mechanical responses for heterogeneous structures with good accuracy in a mesh-independent manner. The efficiency of our methodology is exemplified by 2D and 3D numerical simulations of linear elasticity problems.