标题： 基于误差估计的浸入等几何分析自适应积分 显示英文标题

标题： Error-estimate-based Adaptive Integration For Immersed Isogeometric Analysis

摘要： 有限单元法（FCM）结合等几何分析（IGA）已被成功应用于固体力学、基于图像的分析、流体-结构相互作用以及许多其他应用中的各种问题。 等几何有限单元法的一个挑战性方面是切割单元的积分。 特别是在三维模拟中，与积分相关的计算工作量可能是模拟的关键组成部分。 过去几年提出了多种积分策略以改善与积分相关的困难，但目前尚无适用于广泛工程问题的通用最优积分框架。 在本研究中，我们对八叉树积分方案的精度和计算工作量进行了深入研究。 我们利用Strang第一引理提供的理论基础来量化积分误差的贡献。 基于这项研究，我们提出了一种基于误差估计的浸入式等几何分析自适应积分过程。 此外，我们还对所提出的最优积分算法进行了详细的数值研究，并将其应用于二维和三维线性弹性问题的浸入式等几何分析。 显示英文摘要

摘要： 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.