Multilevel Solution Procedure for Oversampled RBF-FD
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In recent years the oversampled RBF-FD method \cite{Tominec} caused a small revolution in the field of strong-form meshless methods due to its good stability properties, high accuracy and solid theoretical foundations of the method. All the properties listed come with the price of high computational cost involved in the factorisation of the PDE discretization matrix, which is makes it difficult apply the method to large-scale problems that are regularly encountered in engineering. In this paper we propose a geometric multilevel procedure for use with oversampled RBF-FD. It shows good speed-ups compared to the direct solution method and is not limited by the demanding factorisation needed by the direct approach. We also explore some alternatives to the least-squares projection that help reduce the computational cost further by minimizing the amount of oversampling. We demonstrate the new solution procedure on problems in solidification and solid mechanics.
