CAD model simplification error estimation for electrostatics problems

TL;DR

This paper presents a method to estimate the error introduced by CAD model simplification in electrostatics simulations, aiding in assessing the trade-off between model simplicity and solution accuracy.

Contribution

It introduces an energy norm-based bound for the error in quantities of interest due to defeaturing, applicable to electrostatics and potentially other elliptic PDEs.

Findings

The error bound effectively quantifies simplification impact.

Numerical results demonstrate bound efficiency for various defeaturing scenarios.

Method aids in decision-making for model simplification in engineering analysis.

Abstract

Simplifying the geometry of a CAD model using defeaturing techniques enables more efficient discretisation and subsequent simulation for engineering analysis problems. Understanding the effect this simplification has on the solution helps to decide whether the simplification is suitable for a specific simulation problem. It can also help to understand the functional effect of a geometry feature. The effect of the simplification is quantified by a user-defined quantity of interest which is assumed to be (approximately) linear in the solution. A bound on the difference between the quantity of interest of the original and simplified solutions based on the energy norm is derived. The approach is presented in the context of electrostatics problems, but can be applied in general to a range of elliptic partial differential equations. Numerical results on the efficiency of the bound are provided for electrostatics problems with simplifications involving changes inside the problem domain as well as changes to the boundaries.