In this talk, a multilevel space-time multiplicative Schwarz method is introduced for solving parabolic equations on both spatial and temporal directions. In the implementation, the proposed method is treated as preconditioner for GMRES, that is, a coupled system arising from the discretization of the parabolic equation is solved by using a multiplicative Schwarz preconditioned GMRES algorithm. We develop an optimal convergence theory to show that the convergence rate is bounded and independent of the spatial mesh sizes, the time step size, the num- ber of subdomains, the number of levels, and the window size. Some numerical results obtained on a parallel computer with thousands of processors are pre- sented to confirm the theory in terms of optimality and scalability.
李世顺,信阳师范大学特聘教授。2011年6月博士毕业于浙江大学数学系。2013年11月-2014年11月美国科罗拉多大学计算机系博士后,2018年1月-2018年12月中国科学院深圳先进技术研究院访问学者。2020年7月-2020年12月澳门大学访问学者。研究方向为区域分解方法和并行算法。目前主要研究基于高阶时间格式的时空并行区域分解算法。相关成果发表在SISC.,SINUM,NLA,AUM和BIT等期刊上。