Speaker
Description
In this talk, I will present recent advancements in the development of SLTK, a custom research library designed for the numerical solution of PDEs on complex domains. By employing semi-Lagrangian schemes on unstructured grids, SLTK adapts various techniques from computational geometry and computer graphics to the context of partial differential equations.
Specifically, I will introduce a generalized point location method for the efficient tracking of characteristics in advection and advection-diffusion problems, including R-tree spatial indexing for the treatment of boundary conditions.
Furthermore, I will present a mass-conservative method for the tracking and remapping of mesh elements deformed by a transport field in continuity and Fokker-Planck equations, also introducing an exact geometric folding algorithm for managing flux-type boundary conditions.
Finally, I will present some numerical results obtained by applying SLTK to optimal control problems, Mean Field Games, and fluid dynamics on possibly non-convex domains with arbitrary holes.
This is a joint work with R. Ferretti (Roma Tre University) and G. Tatafiore (Sapienza University of Rome).