报告人：Dr.  Jiang Yan

Michigan State University

地点：1218

报告1：时间：12月23日上午：9:30―10:30

Titile: A WENO-based Method of Lines Transpose Approach for Vlasov Simulations

Abstract: In this talk, I will use the high order implicit Method of Lines Transpose (MOLT) method based on a weighted essentially non-oscillatory (WENO) methodology is developed for one-dimensional linear transport equations and further applied to the Vlasov�Poisson (VP) simulations via dimensional splitting. In the MOLT framework, the time variable is first discretized by a diagonally implicit strong-stability-preserving Runge�Kutta method, resulting in a boundary value problem (BVP) at the discrete time levels. Then an integral formulation coupled with a high order WENO methodology is employed to solve the BVP. As a result, the proposed scheme is high order accurate in both space and time and free of oscillations even though the solution is discontinuous or has sharp gradients. Moreover, the scheme is able to take larger time step evolution compared with an explicit MOL WENO scheme with the same order of accuracy.

报告2：时间：12月23日下午：3:00―4:00

Title: A kernel-based high order numerical scheme for time depend problems

Abstract: In this talk, I will introduce a novel numerical scheme, in which the spatial derivatives are represented as a special kernel based formulation of the solutions. We use this method to solve the nonlinear advection-diffusion equations and Hamilton-Jacobi equations. Moreover, theoretical investigations indicated that the proposed scheme is A-stable up to third order accuracy when combining with the SSP-RK scheme.