Greedy maximin distance sampling based model order reduction of prestressed and parametrized abdominal aortic aneurysms

Schein, Alexander, Gee, Michael W.
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Abstract

This work proposes a framework for projection-based model order reduction (MOR) of computational models aiming at a mechanical analysis of abdominal aortic aneurysms (AAAs). The underlying full-order model (FOM) is patient-specific, stationary and nonlinear. The quantities of interest are the von Mises stress and the von Mises strain field in the AAA wall, which result from loading the structure to the level of diastolic blood pressure at a fixed, imaged geometry (prestressing stage) and subsequent loading to the level of systolic blood pressure with associated deformation of the structure (deformation stage). Prestressing is performed with the modified updated Lagrangian formulation (MULF) approach. The proposed framework aims at a reduction of the computational cost in a many-query context resulting from model uncertainties in two material and one geometric parameter. We apply projection-based MOR to the MULF prestressing stage, which has not been presented to date. Additionally, we propose a reduced-order basis construction technique combining the concept of subspace angles and greedy maximin distance sampling. To further achieve computational speedup, the reduced-order model (ROM) is equipped with the energy-conserving mesh sampling and weighting hyper reduction method. Accuracy of the ROM is numerically tested in terms of the quantities of interest within given bounds of the parameter domain and performance of the proposed ROM in the many-query context is demonstrated by comparing ROM and FOM statistics built from Monte Carlo sampling for three different patient-specific AAAs.
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基于贪心最大距离采样的预应力及参数化腹主动脉瘤模型阶数降阶方法
本文提出了一种基于投影的模型降阶(MOR)的计算模型框架,旨在对腹主动脉瘤(AAAs)进行力学分析。其基础全阶模型(FOM)是特定于患者的、平稳的和非线性的。感兴趣的量是AAA壁的von Mises应力和von Mises应变场,这是由于在固定的成像几何形状下将结构加载到舒张压水平(预应力阶段),随后将结构加载到收缩压水平并伴有结构变形(变形阶段)。采用改进的拉格朗日公式(MULF)方法进行预应力。提出的框架旨在减少由于两种材料和一个几何参数的模型不确定性而导致的多查询上下文中的计算成本。我们将基于投影的MOR应用于MULF预应力阶段,这是迄今为止尚未提出的。此外,我们提出了一种结合子空间角度和贪心最大距离采样概念的降阶基构造技术。为了进一步提高计算速度,在降阶模型(ROM)中加入了节能的网格采样和加权超约简方法。根据给定参数域范围内感兴趣的数量,对ROM的准确性进行了数值测试,并通过比较从蒙特卡罗采样为三种不同的患者特定AAAs构建的ROM和FOM统计数据,证明了所提出的ROM在多查询上下文中的性能。
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来源期刊
Advanced Modeling and Simulation in Engineering Sciences
Advanced Modeling and Simulation in Engineering Sciences Engineering-Engineering (miscellaneous)
CiteScore
6.80
自引率
0.00%
发文量
22
审稿时长
30 weeks
期刊介绍: The research topics addressed by Advanced Modeling and Simulation in Engineering Sciences (AMSES) cover the vast domain of the advanced modeling and simulation of materials, processes and structures governed by the laws of mechanics. The emphasis is on advanced and innovative modeling approaches and numerical strategies. The main objective is to describe the actual physics of large mechanical systems with complicated geometries as accurately as possible using complex, highly nonlinear and coupled multiphysics and multiscale models, and then to carry out simulations with these complex models as rapidly as possible. In other words, this research revolves around efficient numerical modeling along with model verification and validation. Therefore, the corresponding papers deal with advanced modeling and simulation, efficient optimization, inverse analysis, data-driven computation and simulation-based control. These challenging issues require multidisciplinary efforts – particularly in modeling, numerical analysis and computer science – which are treated in this journal.
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