Radial Basis Functions in Mesh Deformation

Deformation methods based on RBF-interpolation are independent of the volume mesh and flow solver type, because the algorithm is working on completely arbit­rary clouds of points without using any connectivity information. Additionally, for the mesh updates of consecutive optimization steps or an unsteady aeroelastic sim­ulation, only a matrix-vector multiplication is necessary for each mesh node. The computationally most expensive part is to compute the interpolation matrix for this multiplication. It can be calculated once in the beginning of the entire simulation and remains unchanged, since it only depends on the base points, but not on the deform­ation vectors. Consequently, the method can be perfectly parallelized (using MPI and partitioned grids), because each process has to apply the interpolation matrix only to its own grid nodes. But it is also clear that the dimension of the interpolation matrix highly influences the overall speed of the algorithm.