Efficient mesh deformation based on randomized RBF solvers

Abstract

Mesh deformation methods [7] have been widely used for the past decades in various fields such as fluid-structure interaction, aerodynamic shape optimization, unsteady and aeroelastic computational fluid dynamics. Such methods are particularly interesting in order to update meshes during a simulation without the need to perform an (often expensive) full regeneration of the mesh, e.g. when facing moving boundaries or geometry update during a structural optimization loop.Among the numerous existing methods, radial basis functions interpolation (RBF) [1] is particularly suitable for unstructured mesh applications due to its simplicity and the high quality of the resulting mesh. One key aspect of RBF-based mesh deformation is the resolution of a dense linear system, which tends to be computationally expensive and high memory demanding when dealing with large-scale meshes [2, 3], thus being a major drawback of the method. This could be mitigated using an iterative solver instead of a direct one during the resolution step, thus saving the memory needed to store the factorization. However, some radial basis functions lead to ill-conditioned systems, requiring the use of an efficient preconditioner which tends to complexify the problem.