Integrating CAD and Numerical Analysis: 'Dirty Geometry' handling using the Finite Cell Method

TL;DR

This paper introduces a robust computational method that combines CAD and the Finite Cell Method to accurately analyze models with flawed or imprecise geometries, enabling direct calculations on 'dirty' models.

Contribution

It presents a novel approach combining intersection and flood fill algorithms to handle flawed geometries within the Finite Cell Method framework.

Findings

Effective handling of flawed geometries demonstrated through numerical examples

Robust Point Membership Classification algorithm developed for 'dirty' models

Enables direct analysis of imprecise CAD models without extensive preprocessing

Abstract

This paper proposes a computational methodology for the integration of Computer Aided Design (CAD) and the Finite Cell Method (FCM) for models with "dirty geometries". FCM, being a fictitious domain approach based on higher order finite elements, embeds the physical model into a fictitious domain, which can be discretized without having to take into account the boundary of the physical domain. The true geometry is captured by a precise numerical integration of elements cut by the boundary. Thus, an effective Point Membership Classification algorithm that determines the inside-outside state of an integration point with respect to the physical domain is a core operation in FCM. To treat also "dirty geometries", i.e. imprecise or flawed geometric models, a combination of a segment-triangle intersection algorithm and a flood fill algorithm being insensitive to most CAD model flaws is proposed to identify the affiliation of the integration points. The present method thus allows direct computations on geometrically and topologically flawed models. The potential and merit for practical applications of the proposed method is demonstrated by several numerical examples.