论文标题
参数域中流的分离响应表面：先验和后验PGD算法的比较
Separated response surfaces for flows in parametrised domains: comparison of a priori and a posteriori PGD algorithms
论文作者
论文摘要
降低的订单模型（ROM）通常用于解决参数问题并设计廉价的响应表面以评估实时的兴趣数量。文献中有许多ROM家族，其中选择并不总是一项琐碎的任务。这项工作介绍了先验性能和后验正确的概括分解（PGD）算法的比较，该算法是在几何参数化域中不可压缩的Stokes流量问题的比较。由于几何参数会影响解决方案歧管和计算空间域，因此这个问题尤其具有挑战性。由于考虑了多个几何参数，并且分析了参数的扩展范围，因此难度进一步增加，这会导致流量特征的显着变化。使用一组涉及几何参数式参数化的微晶状体的数值实验，通过其准确性和计算成本进行了广泛的比较，将两种PGD算法进行了广泛的比较，这是所需的全阶求解数量的函数。
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.
