Applied Math Colloquim: Yifan Hu (UMBC)

Title: Numerical Solutions to Partial Differential Equations and Applications in Plasma Physics

Abstract: Partial differential equations (PDE) are tools to model complex systems via partial derivatives. With one PDE or a system of PDEs, we may describe both temporal and spatial evolution of a system. In addition to exciting developments in the theoretical analysis of PDEs, numerical solutions to PDEs are extremely effective tools in physics, chemistry, biology, finance, and engineering. Equipped with powerful high performance computing software and hardware, we can  build, verify, and apply sophisticated algorithms for mission critical applications in these fields. In this talk, we present a brief overview of PDEs and their numerical solutions in the context of plasma physics research. We demonstrate the key pieces of accurate, robust, and efficient algorithms for plasma physics applications, in particular for the 1D1V Vlasov-Poisson equation and the 1D2V relativistic Vlasov-Maxwell system.