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Separated response surfaces for flows in parametrised domains: comparison of a priori and a posteriori PGD algorithms
arXiv - CS - Computational Engineering, Finance, and Science Pub Date : 2020-09-04 , DOI: arxiv-2009.02176 Matteo Giacomini, Luca Borchini, Ruben Sevilla, Antonio Huerta
arXiv - CS - Computational Engineering, Finance, and Science Pub Date : 2020-09-04 , DOI: arxiv-2009.02176 Matteo Giacomini, Luca Borchini, Ruben Sevilla, Antonio Huerta
Reduced order models (ROM) are commonly employed to solve parametric problems
and to devise inexpensive response surfaces to evaluate quantities of interest
in real-time. There are many families of ROMs in the literature and choosing
among them is not always a trivial task. This work presents a comparison of the
performance of a priori and a posteriori proper generalised decomposition (PGD)
algorithms for an incompressible Stokes flow problem in a geometrically
parametrised domain. This problem is particularly challenging as the geometric
parameters affect both the solution manifold and the computational spatial
domain. The difficulty is further increased because multiple geometric
parameters are considered and extended ranges of values are analysed for the
parameters and this leads to significant variations in the flow features. Using
a set of numerical experiments involving geometrically parametrised
microswimmers, the two PGD algorithms are extensively compared in terms of
their accuracy and their computational cost, expressed as a function of the
number of full-order solves required.
中文翻译:
参数化域中流动的分离响应面:先验和后验 PGD 算法的比较
降阶模型 (ROM) 通常用于解决参数问题并设计廉价的响应面以实时评估感兴趣的数量。文献中有许多 ROM 家族,在其中进行选择并不总是一项微不足道的任务。这项工作对几何参数化域中不可压缩斯托克斯流问题的先验和后验适当广义分解 (PGD) 算法的性能进行了比较。这个问题特别具有挑战性,因为几何参数会影响解流形和计算空间域。由于考虑了多个几何参数并分析了参数值的扩展范围,因此难度进一步增加,这导致流动特征的显着变化。
更新日期:2020-09-07
中文翻译:
参数化域中流动的分离响应面:先验和后验 PGD 算法的比较
降阶模型 (ROM) 通常用于解决参数问题并设计廉价的响应面以实时评估感兴趣的数量。文献中有许多 ROM 家族,在其中进行选择并不总是一项微不足道的任务。这项工作对几何参数化域中不可压缩斯托克斯流问题的先验和后验适当广义分解 (PGD) 算法的性能进行了比较。这个问题特别具有挑战性,因为几何参数会影响解流形和计算空间域。由于考虑了多个几何参数并分析了参数值的扩展范围,因此难度进一步增加,这导致流动特征的显着变化。