A physics-informed parametrization and its impact on 2D IGABEM analysis

IF 8.7 2区 工程技术 Q1 Mathematics Engineering with Computers Pub Date : 2024-08-03 DOI:10.1007/s00366-024-02037-4
Konstantinos V. Kostas, Constantinos G. Politis, Issa Zhanabay, Panagiotis D. Kaklis
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Abstract

In this work, we study the effect of the geometry representation in the context of the IsoGeometric-Analysis-based Boundary Element Method (IGABEM) and we propose an algorithm for the construction of a physics-informed geometric representation which leads to approximation results of high accuracy that are comparable to known adaptive refinement schemes. As a model problem, we use a previously studied 2D potential flow problem around a cylinder; see Politis et al. (Proceedings of SIAM/ACM joint conference on geometric and physical modeling, California, pp 349–354, 2009. https://doi.org/10.1145/1629255.1629302L). This study involves a systematic examination of a series of transformations and reparametrizations and their effect on the achieved accuracy and convergence rate of the numerical solution to the problem at hand. Subsequently, a new parametrization is proposed based on a coarse-level approximation of the field-quantity solution, coupling in this way the geometry representation to the physics of the problem. Finally, the performance of our approach is compared against an exact-solution-driven adaptive refinement scheme and a posteriori error estimates for adaptive IGABEM methods. The proposed methodology delivers results of similar quality to the adaptive approaches, but without the computational cost of error estimates evaluation at each refinement step.

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物理信息参数化及其对二维 IGABEM 分析的影响
在这项工作中,我们研究了基于等几何分析的边界元素法(IGABEM)中几何表示法的影响,并提出了一种构建物理信息几何表示法的算法,该算法可获得与已知自适应细化方案相当的高精度近似结果。作为模型问题,我们使用了之前研究过的围绕圆柱体的二维势流问题;见 Politis 等人的论文集(《SIAM/ACM 几何与物理建模联合会议论文集》,加利福尼亚州,第 349-354 页,2009 年。https://doi.org/10.1145/1629255.1629302L)。本研究对一系列变换和重新参数化及其对问题数值解的精度和收敛速度的影响进行了系统检查。随后,基于场量解的粗略近似,提出了一种新的参数化方法,以这种方式将几何表示与问题的物理耦合在一起。最后,将我们方法的性能与精确求解驱动的自适应细化方案和自适应 IGABEM 方法的后验误差估计进行了比较。所提出的方法可提供与自适应方法质量相似的结果,但无需在每个细化步骤进行误差估计评估的计算成本。
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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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