题目：Parallel-in-Time with Multigrid for Time-Dependent Diffusion Equations
摘要：Future computing speed must rely on the increased concurrency provided by more, instead of faster, processors. An immediate consequence of this is that solution algorithms, limited to spatial parallelism, for problems with evolutionary behavior entail long overall computation time, often exceeding computing resources available to resolve multidimensional PDEs. Thus, algorithms achieving parallelism in time are of especially high demand. Currently, parareal in time and multigrid-reduction-in-time (MGRIT) are two active choices. Observe that parareal can be interpreted as a two-level multigrid (reduction) method, its concurrency is still limited because of the sequential coarse-grid solve. MGRIT enables us to approximate simultaneously the evolution over all time points. It has been proven to be rather effective and analyzed sharply in the two-level setting for integer order parabolic and hyperbolic problems with the limitation that fine time-grid propagators are all the same. The main aim of the talk is to propose and analyze a non-intrusive optimal-scaling MGRIT solver for time-dependent diffusion equations, where we shall extend the scope of the MGRIT algorithm to time-dependent fine time-grid propagators. Some numerical results are given to show that theoretical results of the two-level variant deliver good predictions and significant speedups can be achieved when compared to parareal and the sequential time-stepping approach.
报告人简介：岳孝强，现任湘潭大学副教授。2009年本科毕业于湘潭大学数学与计算科学学院，2015年在湘潭大学获博士学位，师从舒适教授。主要从事高性能并行计算、多重网格与区域分解法等方面的研究。在Communications in Computational Physics，Computers & Fluids等学术期刊上已发表学术论文十余篇。主持国家自然科学基金青年项目、湖南省自然科学基金青年项目、湖南省教育厅一般项目多项。