We discuss our recent advances in developing meshfree methods based on radial basis function generated finite differences (RBF-FD) for numerically solving biologically relevant 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.
BIO: Grady Wright received his PhD in Applied Mathematics from the University of Colorado at Boulder in 2003. He spent the next four years as a National Science Foundation (NSF) Postdoctoral Fellow at the University of Utah before joining the Department of Mathematics at Boise State. Wright, now a full professor, has also held visiting research positions at the National Center for Atmospheric Research and the Mathematical Institute at the University of Oxford. His research interests are in computational mathematics, including approximation theory and numerical methods for differential equations arising in the biological and geophysical sciences. Wright is currently the Treasurer of the SIAM PNW section; he also was the Co-Chair of SIAM PNW conference at Seattle University in October 2019.