报告题目：An adaptive multiresolution discontinuous Galerkin method for time-dependent transport equations in multi-dimensions

报告人：Yingda Cheng, Department of Mathematics Michigan State University

时  间：2016年7月22日    下午4:00-5:00

地  点：东区管理科研楼  数学科学学院1218室

内容提要：

We develop  an adaptive multiresolution discontinuous Galerkin (DG) scheme for  time-dependent transport equations in multi-dimensions.  The method is constructed using   multiwavlelets  on tensorized nested grids. Adaptivity is realized by   error thresholding based on the hierarchical surplus, and the Runge-Kutta DG (RKDG) scheme is employed as the reference time evolution algorithm.

We show that the scheme performs similarly to a sparse grid DG method when the solution is smooth, reducing computational cost in multi-dimensions. When  the solution is no longer smooth, the adaptive algorithm can automatically capture fine local structures.   The method is therefore very suitable for deterministic kinetic simulations. Numerical results including several benchmark tests, the Vlasov-Poisson  (VP) and oscillatory VP systems are provided.