Analysis-aware defeaturing: problem setting and a posteriori estimation

TL;DR

This paper formalizes the impact of geometrical feature removal on Poisson equation solutions, providing a reliable a posteriori estimator to quantify the error introduced by defeaturing in CAD models.

Contribution

It introduces a novel a posteriori error estimator for assessing the effects of defeaturing on PDE solutions, explicitly relating error to feature size.

Findings

The estimator is simple, reliable, and efficient up to oscillations.

It explicitly relates error to feature size.

Applicable in 2D and 3D geometries.

Abstract

Defeaturing consists in simplifying geometrical models by removing the geometrical features that are considered not relevant for a given simulation. Feature removal and simplification of computer-aided design models enables faster simulations for engineering analysis problems, and simplifies the meshing problem that is otherwise often unfeasible. The effects of defeaturing on the analysis are then neglected and, as of today, there are basically very few strategies to quantitatively evaluate such an impact. Understanding well the effects of this process is an important step for automatic integration of design and analysis. We formalize the process of defeaturing by understanding its effect on the solution of Poisson equation defined on the geometrical model of interest containing a single feature, with Neumann boundary conditions on the feature itself. We derive an a posteriori estimator of the energy error between the solutions of the exact and the defeatured geometries in $\mathbb{R}^n$, $n\in\{2,3\}$, that is simple, reliable and efficient up to oscillations. The dependence of the estimator upon the size of the features is explicit.