Efficient and Parallel Solution of High-order Continuous Time Galerkin for Dissipative and Wave Propagation Problems
A/Prof. Yong Liu
Academy of Mathematics and Systems Science, Chinese Academy of Sciences

In this talk, I shall propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special structure of the stiffness matrix which allows us to extend the diagonal Pad\'e approximation to solve the ordinary differential equations with source terms. The unconditional stability, optimal $hp$ error estimates, and $hp$ superconvergence at the nodes of the continuous time Galerkin method are also proved. Numerical examples confirm our theoretical results.

About the Speaker

刘勇,中国科学院数学与系统科学研究院,计算数学所副研究员。分别于2015年,2020年获中国科学技术大学学士和博士学位。2018年至2020年在美国布朗大学应用数学系联合培养。2020年至2022年在中国科学院数学与系统科学研究院,华罗庚数学科学中心做博士后。主要研究领域为高精度数值计算方法,包括间断有限元方法的算法设计及其数值分析、磁流体力学方程的数值模拟及应用等方面。在SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of Computational Physics等杂志发表论文10余篇。

2022-10-31 8:30 AM
Room: Tencent Meeting
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