Space-time domain decomposition algorithms for parabolic equations

发布时间：2025-11-05 作者：浏览次数：

Speaker:	李世顺	DateTime:	2025年11月10日（周一）上午10:00-11:00
Brief Introduction to Speaker: 李世顺，信阳师范大学教授。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。主持天元基金、青年基金和面上项目等国家自然科学基金。目前主要研究时空并行区域分解算法的理论与应用。相关成果发表在SIAM J. Sci. Comput.，SIAM J. Numer. Anal.，Numer. Linear Algebra Appl.和BIT等期刊上。		Place:	国交2号楼201会议室
Abstract:In this talk, we first introduce several space-time domain decomposition algorithms for solving parabolic equations discretized by lower order schemes in time and finite element in space. Specifically, we utilize Schwarz algorithms to solve the resulting coupled system and derive solutions across multiple time steps. Next, we present a family of Block Implicit Methods (BIM), which can be formally described by a tableau containing two matrices and two vectors. We prove that the traditional finite element theory for parabolic problems discretized by the backward Euler or Crank-Nicolson schemes can also be extended for BIM. Finally, some numerical results obtained on a parallel computer with thousands of processors are reported to demonstrate the effectiveness of BIM.

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