Abstract: Removing geometrical details is a classical operation in computer aided design when performing a simulation on a complex domain. Indeed, this procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, removing some important geometrical features may greatly impact the PDE solution’s accuracy, and unfortunately, this impact is rarely accurately measured. Indeed, analysing this effect is a time-consuming task that is often performed manually, based on the expertise of engineers. We therefore need a better understanding of the effect of geometrical model simplification, also called defeaturing, to improve our control on the simulations' accuracy along the design and analysis phases.
In this talk, we will mathematically formalise the process of defeaturing by looking at different types of complex geometries: domains with a boundary which is complex almost everywhere (for instance a fractal-like boundary), and domains with separable Boolean features (for instance a hole or a local protrusion) for which the process of defeaturing either adds or removes the features from the geometry. We will then concentrate in particular on the case of Boolean features, for which a reliable and efficient a posteriori estimator of the defeaturing error has been derived, in the energy norm. The proposed estimator is explicit with respect to the size of the considered features and with respect to their number, meaning that its effectivity index is independent from these quantities.
We will subsequently consider a finite element approximation of the defeatured problem, and the induced numerical error will be integrated to the proposed defeaturing error estimator. With an a posteriori estimator of the combined error coming from both the numerical approximation and the geometric simplification, we are able to design an adaptive strategy which returns a (partially) defeatured computational domain and a locally refined mesh, on which an accurate solution of the exact PDE at hand can be computed. During the talk, we will also show the results of some numerical experiments that illustrate the exposed results and the capabilities of the proposed adaptive strategy.