Victor Bayona
Department of Mathematics, Universidad Carlos III in Madrid
Radial Basis Function (RBF) methods are becoming increasingly popular as a meshfree methodology, from fitting data to numerically solving differential equations. These methods offer many inherent properties such as geometric flexibility, opportunities for non-uniform resolution and advantageous trade-offs between accuracy and computational costs.
In this talk, we introduce the use of RBFs through the local formulation (also known as RBF-FD), which can be interpreted as a natural generalization of Finite Differences (FD). By supplementing multivariate polynomials with RBFs (or using RBFs only) to generate the stencil weights, structured grids become unnecessary. Instead, using scattered nodes greatly improves the geometric flexibility, allowing for local refinement and effective handling of curved boundaries. We discuss some of its features and provide examples of application.