Solving PDEs on Surfaces Using Radial Basis Function Finite Differences

Grady Wright SCAIM Seminar
March 3, 2020 12:30 pm ESB 4133

We discuss some recent advances in developing meshfree methods based on radial basis function generated finite differences (RBF-FD) for numerically solving partial differential equations (PDEs) on surfaces. The primary advantages of these methods are 1) they only require a set of nodes on the surface of interest and the corresponding normal vectors; 2) they can give high orders of accuracy; and 3) they algorithmically accessible. Commonly perceived disadvantages are that these methods require too many tuning parameters and that they are not well suited for advection-dominated problems. A goal of this talk will be to demonstrate how to overcome these issues with the use of polyharmonic spline kernels augmented with polynomials and semi-Lagrangian advection methods.