Please join us Friday at 3 PM in 103A Walker to hear Dr. Nadun Kulasekera Mudiyanselag speak on...
Title: Radial Basis Finite Difference Method (RBF-FD) approach for solving partial differential equations (PDEs) with interfaces
Abstract: In this talk, I present a novel method for solving the groundwater flow equations in the presence of a discontinuity in the conductivity properties of the soil across an interface. Geologically, an interface represents changes in flow, such as between layers or abrupt exposures. It could also model temperature fluctuation across an interface in different media. In order to tackle this problem, we introduce a new methodology that can modify finite difference differentiation weights to mimic the behavior of the continuity properties of the solutions of the PDEs. We validate our approach by implementing it on PDEs with linear, quadratic, and cubic interfaces.