A new multilevel grid deformation method

Recently, we introduced and mathematically analysed a new method for grid deformation [12]. This method is a generalisation of the method proposed by Liao [4, 6, 14]. In this article, we investigate the practical aspects of our method. As it requires searching the grid several times per grid point, efficient search methods are crucial for deforming grids in reasonable time, so that we propose and investigate distance and raytracing search for this purpose. By splitting up the deformation process in a sequence of easier subproblems, we significantly enhance the robustness of our deformation method. The computational speed and the accuracy of the method are improved substantially exploiting the grid hierarchy in the corresponding multilevel deformation algorithm. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 10 in our numerical tests compared to the basic deformation algorithm. This gives our new method the potential for tackling complex domains and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user’s needs.