Error-estimate-based Adaptive Integration For Immersed Isogeometric Analysis

TL;DR

This paper introduces an adaptive integration method based on error estimates for immersed isogeometric analysis, aiming to improve accuracy and efficiency in 3D simulations involving cut cells.

Contribution

It proposes a novel error-estimate-based adaptive integration scheme tailored for immersed isogeometric analysis, addressing integration challenges in complex simulations.

Findings

The adaptive scheme reduces integration error effectively.

It improves computational efficiency in 3D elasticity problems.

The method is validated through numerical experiments.

Abstract

The Finite Cell Method (FCM) together with Isogeometric analysis (IGA) has been applied successfully in various problems in solid mechanics, in image-based analysis, fluid-structure interaction and in many other applications. A challenging aspect of the isogeometric finite cell method is the integration of cut cells. In particular in three-dimensional simulations the computational effort associated with integration can be the critical component of a simulation. A myriad of integration strategies has been proposed over the past years to ameliorate the difficulties associated with integration, but a general optimal integration framework that suits a broad class of engineering problems is not yet available. In this contribution we provide a thorough investigation of the accuracy and computational effort of the octree integration scheme. We quantify the contribution of the integration error using the theoretical basis provided by Strang's first lemma. Based on this study we propose an error-estimate-based adaptive integration procedure for immersed isogeometric analysis. Additionally, we present a detailed numerical investigation of the proposed optimal integration algorithm and its application to immersed isogeometric analysis using two- and three-dimensional linear elasticity problems.