报告人: 吴树林 （香港理工大学博士后）

报告题目: Let Parareal-CN Work Well

报告摘要：For time-dependent PDEs, suitable space discretization together with the Trapezoidal rule gives the Crank-Nicolson (CN) scheme, which is widely used in many fields. If we directly embed the CN scheme into the parareal algorithm as a component, it is found that the resulting Parareal-CN algorithm has very bad convergence property, namely ρ->1 as △x->0, where ρdenotes the convergence factor of the Parareal-CN algorithm and △x denotes the space discretization size. In this talk, I propose a simple strategy to let the Parareal-CN algorithm possesses a constant convergence factor around 0.3, which is independent of △x. Furthermore, by using the "scaling" technique, I will show that the convergence factor can be reduced to 0.2. The optimal scaling factor is 1.28. Another interesting finding is that, when the scaling factor, namley a, satisfies a∈[1, √2], it holds that 0.2≤ρ≤0.3. This result has a practical meaning, because it implies that we can use the diagonalization technique to yield parallel correction grid correction for the parareal iterations !

报告时间: 2016年12月20日（星期二）上午10:00-11:00

报告地点: 科技楼南楼702室