A Numerical Study of Combining RBF Interpolation and Finite Differences to Approximate Differential Operators

TL;DR

This study compares the accuracy of a hybrid RBF interpolation and finite difference method with traditional RBF-FD for approximating differential operators in a 2D Poisson problem.

Contribution

It provides a comparative analysis of a hybrid RBF-FD approach against standard RBF-FD, highlighting their relative accuracy in solving PDEs.

Findings

Hybrid method's accuracy varies with parameters

Hybrid approach can outperform standard RBF-FD in some cases

Results inform choice of method for meshless PDE approximation

Abstract

This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference stencils. We compare the accuracy of this method and RBF-FD on a two-dimensional Poisson problem for standard five-point and nine-point stencils and different method parameters.