Spring analogies and the point‐by‐point interpolating approaches have been widely used for the grid deformation, and both require solution of a linear system of equations. Depending on the problem, the resulting system of equations may be defined by a large‐dimensional matrix. Thus, sampling for a subset of the grids is essential in order to achieve an efficient grid deformation. This article presents an efficient grid deformation algorithm developed via deterministic data sampling. From the position data of the deformed grids, proper orthogonal decomposition and discrete empirical interpolation method are employed to define the subset of the grids. Herein, symmetric rank‐one update is considered to choose the additional grids (oversampling). And it facilitates the deterministic data sampling approach and realizes the improved stability within the data reduction procedure. Such deterministic data sampling approach is applied to the moving submesh approach and radial basis function (RBF) interpolations. Specifically, for an RBF interpolation, boundaries of a deformable body are directly introduced within the data reduction procedure to improve the computational efficiency. Two‐ and three‐dimensional examples are used to evaluate the relevant computational efficiency of the proposed methods. It is found that computational time consumed by the present method is two orders of magnitude smaller than that of the existing method while maintaining the quality of the deformed grids.

中文翻译：

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使用基于确定性采样的数据约简来有效地进行网格变形

弹簧类比和点对点内插方法已广泛用于网格变形，并且都需要求解线性方程组。根据问题的不同，方程组的结果可能由大尺寸矩阵定义。因此，为实现有效的网格变形，必须对一部分网格进行采样。本文提出了一种通过确定性数据采样开发的有效网格变形算法。从变形网格的位置数据中，采用适当的正交分解和离散经验插值方法来定义网格的子集。在此，对称等级更新被认为是选择附加网格（过采样）。并且它促进了确定性数据采样方法，并在数据缩减过程中实现了改进的稳定性。这种确定性的数据采样方法被应用于运动网格方法和径向基函数（RBF）插值。具体而言，对于RBF插值，将可变形体的边界直接引入数据缩减过程中以提高计算效率。使用二维和三维示例来评估所提出方法的相关计算效率。发现在保持变形网格的质量的同时，本方法消耗的计算时间比现有方法小两个数量级。这种确定性的数据采样方法被应用于运动网格方法和径向基函数（RBF）插值。具体而言，对于RBF插值，将可变形体的边界直接引入数据缩减过程中以提高计算效率。使用二维和三维示例来评估所提出方法的相关计算效率。发现在保持变形网格的质量的同时，本方法消耗的计算时间比现有方法小两个数量级。这种确定性的数据采样方法被应用于运动网格方法和径向基函数（RBF）插值。具体而言，对于RBF插值，将可变形体的边界直接引入数据缩减过程中以提高计算效率。使用二维和三维示例来评估所提出方法的相关计算效率。发现在保持变形网格的质量的同时，本方法消耗的计算时间比现有方法小两个数量级。使用二维和三维示例来评估所提出方法的相关计算效率。发现在保持变形网格的质量的同时，本方法消耗的计算时间比现有方法小两个数量级。使用二维和三维示例来评估所提出方法的相关计算效率。发现在保持变形网格的质量的同时，本方法消耗的计算时间比现有方法小两个数量级。