An efficient radial basis functions mesh deformation with greedy algorithm based on recurrence Choleskey decomposition and parallel computing

The mesh deformation method based on radial basis functions (RBF) has many advantages and is widely used. RBF based mesh deformation method mainly has two steps: data reduction and displacement interpolation. The data reduction step includes solving interpolation weight coefficients and searching for the node with the maximum interpolation error. The data reduction schemes based on greedy algorithm is used to select an optimum reduced set of surface mesh nodes. In this paper, a parallel mesh deformation method based on parallel data reduction and displacement interpolation is proposed. The proposed recurrence Choleskey decomposition method (RCDM) can decrease the computational cost of solving interpolation weight coefficients from O(Nc4) to O(Nc3), where Nc denotes the number of support nodes. The technology of parallel computing is used to accelerate the searching for the node with the maximum interpolation error and displacement interpolation. The combination of parallel data reduction and parallel interpolation can greatly improve the efficiency of mesh deformation. Two typical deformation problems of the ONERA M6 and DLR-F6 wing-body-Nacelle-Pylon configuration are taken as the test cases to validate the proposed approach and can get up to 19.57 times performance improvement with the proposed approach. Finally, the aeroelastic response of HIRENASD wing-body configuration is used to verify the efficiency and robustness of the proposed method.