An extension of the well-known Neville–Aitken's algorithm for interpolation on the Grassmann manifold $G_m({ℝ}^n)$ in the framework of parametric model order reduction is presented. Interpolation points on $G_m({ℝ}^n)$ are the subspaces spanned by bases obtained by Proper Orthogonal Decomposition of available solutions associated with the chosen parameter sampling. The Neville–Aitken's algorithm is performed recursively via the geodesic barycenter of two points. Three CFD applications are presented: (i) the Von Karman vortex shedding street, (ii) the lid-driven cavity with inflow and (iii) the flow induced by a rotating solid. Numerical results are relevant with respect to accuracy while the asymptotic complexity is comparable to the state of the art.

中文翻译：

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Neville-Aitken 插值算法在 Grassmann 流形上的推广：降阶模型的应用

著名的 Neville-Aitken 算法的扩展，用于在 Grassmann 流形上进行插值 $G_{米}({ℝ}^n)$在参数化模型降阶框架中提出。插值点$G_{米}({ℝ}^n)$是由与所选参数采样相关的可用解的适当正交分解获得的基所跨越的子空间。Neville-Aitken 算法通过两点的测地线重心递归执行。提出了三个 CFD 应用程序：(i) Von Karman 涡旋脱落街道，(ii) 具有流入的盖子驱动腔和 (iii) 由旋转固体引起的流动。数值结果与准确性相关，而渐近复杂性与现有技术相当。