An efficient multidomain RBF mesh deformation method based on MPI/OpenMP hybrid parallel interpolation

Radial basis function (RBF) interpolation has been prevalent in mesh deformation schemes due to its great quality-preserving ability and generality. However, the cost time scales as $O\left({N_s}^3\right)$, where $N_s$ is the number of surface nodes, which makes full RBF interpolation prohibitively expensive to implement for large mesh. The key improvement is the application of efficient reduced-data methods. But the greedy-type reduced-data method remains expensive when applied to large-scale meshes, requiring iterative linear system solutions and interpolation error calculations to generate the reduced dataset. Furthermore, a supplementary surface correction procedure must be implemented to ensure exact surface shape. In this paper, a novel multidomain method is proposed that stochastically splits the surface nodes into $n$ small subsets and a small sub-RBF interpolant is constructed on each subset. The mesh deformation is computed by the weight of sub-RBF interpolations. Since the above processes are independent, this method is perfectly parallel. The computational complexity analysis reveals that this method reduces the solution cost to $O({N_s}^3/n^2)$ for a serial algorithm, and this method can be faster than the multiscale method Kedward et al.(2017) in all stages. By appropriately selecting the weighting coefficients, the exact surface shape is naturally preserved and the surface correction issue is eliminated. Further enhancements are achieved by dividing the volume into near-surface, intermediate, far-surface and stationary domains based on their distances from the surface. These domains can adopt distinct weighting schemes and utilize varying numbers of radial centers. The efficiency and accuracy of this method are analyzed in detail using two-dimensional (2D) airfoils, a three-dimensional (3D) scramjet combustor and a 3D hypersonic vehicle examples. In comparison with the conventional greedy method and the contemporary multiscale method, this method gains higher efficiency and comparable mesh quality.