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Since the advent of mesh-free methods as a tool for the numerical analysis ofsystems of Partial Differential Equations (PDEs), many variants of differentialoperator approximation have been proposed. In this work, we propose a localmesh-free strong-form method that combines the stability of Radial BasisFunction-Generated Finite Differences (RBF-FD) with the computationaleffectiveness of Diffuse Approximation Method (DAM), forming a so-called hybridmethod. To demonstrate the advantages of a hybrid method, we evaluate itscomputational complexity and accuracy of the obtained numerical solution bysolving a two-dimensional Poisson problem with an exponentially strong sourcein the computational domain. Finally, we employ the hybrid method to solve athree-dimensional Boussinesq's problem on an isotropic half-space and show thatthe implementation overhead can be justified.

A hybrid RBF-FD and WLS mesh-free strong-form approximation method