Efficient grid deformation using deterministic sampling-based data reduction

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.