The work presents and experimentally analyzes a meshfree method of the oversampled Radial Basis Function-generated Finite Difference (oversampled RBF-FD) method. This method uses radial basis functions to approximate operators in order to numerically solve partial differential equations (PDE), which describe scalar and vector fields. In contrast to the classic RBF-FD approach, the method constructs an overdetermined system of linear equations that accounts for the behaviour of the operator on an extended set of points. One of the key challenges arising due to the overdetermined system is ensuring accuracy in the enforcement of boundary conditions. For this purpose, a scaling is used to weight the influence of the boundary conditions. Two variants of the method are derived, both of which are based on a connection with a continuous problem. Both versions are tested on the examples of the Poisson problem and the deformation of the cantilever beam. A comparison with the classic RBF-FD method is carried out, as well as an analysis of the influence of scaling on the accuracy of the approximation. Finally, we address some details of the implementation of the method, such as the data structures used and the approach used to solve the linear systems of equations.
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