Fourier-Spectral Methods for the Vlasov-Poisson System
B9 R2325
In this talk we present an adaptive method for the numerical solution of the Vlasov-Poisson system in one space dimension with periodic boundary conditions in both space and velocity, which is based on Fourier discretisation in x and v and on high order fractional step method in time, allowing high accuracy and efficiency.
Overview
Vlasov-Poisson system provides a kinetic description of a plasma. Here we consider the simplest case of a one dimensional setting, describing the evolution of an electron distribution in a uniform ion background, with periodic boundary conditions. An accurate and efficient numerical method is proposed for the solution of the equations, based on discrete Fourier transform both in space and velocity, while a sixth order fractional step method is adopted for time discretisation. The Fourier method guarantees very high accuracy both in space and velocity. The accuracy of the numerical solution in v is monitored by the log plot of the Fourier transform in velocity. An adaptive technique is proposed to improve computational efficiency by adjusting the number of Fourier modes as time evolves. Several numerical tests will be shown, which confirm the accuracy of the proposed method.
Presenters
Giovanni Russo, Full Professor of Numerical Analysis, Department of Mathematics and Computer Science, University of Catania (UNICT)
Brief Biography
Giovanni Russo is Professor of Numerical Analysis at the University of Catania and Coordinator of its Ph.D. Program in Pure and Applied Mathematics. He earned a degree in Nuclear Engineering, magna cum laude, from the Politecnico di Milano and a Ph.D. in Physics from the University of Catania.
His research spans computational fluid dynamics, numerical methods for conservation laws and kinetic equations, and mathematical modeling and simulation of crystal growth. As an internationally recognized expert in applied and computational mathematics, Professor Russo has authored more than one hundred scientific publications in leading international journals. His work has made significant contributions to the development of advanced numerical methods for complex physical and engineering systems, particularly in fluid dynamics and kinetic modeling.
