题目：Toward Discontinuous Galerkin Methods for Parallel in Time: An Iterative Approach for Time Integration报告人: 李小舟   电子科技大学数学科学学院  时间： 2018年7月3日 下午 3:00-4:00 地点： 管理科研楼 1518摘要：
We present a new class of iterative methods for solving initial value problems (IVP) based on discontinuous Galerkin (DG) methods.  We start from the weak DG formulation arising from non-linear equations and derive the new iterative methods by using different iterative schemes.  Based on our new approach, we can systematically construct explicit, implicit and semi-implicit schemes with arbitrary order of accuracy.  We also show that the same schemes can be constructed by solving a series of correction equations based on the DG weak formulation.  The accuracy of the schemes is proven to be min{2p+1, K} with p the degree of the DG polynomial basis and K the number of iterations.  The stability has been explored numerically, showing that the implicit schemes are A-stable and the explicit schemes are competitive with existing methods.  
  Furthermore, we combine this technique with a multi-level strategy to accelerate its convergence speed.  Also, the new multi-level scheme is intended to provide a flexible framework for high order space-time discretizations and to be coupled with space-time multi-grid techniques for solving partial differential equations (PDEs).  
Besides its standard applications as time integrator, the newly proposed method, due to its structure, is a competitive and promising candidate for the parallel in time algorithms such as Parareal, PFASST, multigrid in time, etc.