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Error bounds for PFASST and related Block Spectral-Deferred-Correction algorithms
时间:2021年08月01日 16:40 点击数:

报告人:Thibaut Lunet

报告地点:腾讯会议ID:425 186 583

报告时间:2021年08月05日星期四22:00-23:00

邀请人:吴树林

报告摘要:

In this talk, we describe all those different elements of PFASST when applied on a simple linear problem (Dahlquist equation), and show the equivalence of Block Gauss-Seidel with the Parareal algorithm used with specific parts of an SDC integrator. Then we derive con- vergence bounds for Block SDC, Block Gauss-Seidel SDC and Block Jacobi SDC, using the generating function technique, already used to determine convergence bounds for Parareal. With those bounds, we show the convergence of Block Gauss-Seidel SDC, that can be used as a direct PinT algorithm through pipe-lining of the sweeps. Also, we highlight the partic- ular convergence order for Block Jacobi SDC that explains why order increase in PFASST appears only after a fixed amount of iterations. Finally, we show how the generating func- tion technique can be extended to a Block Gauss-Seidel update with a FAS correction, and ultimately use it to compute a new convergence bound for PFASST


主讲人简介:

Thibaut Lunet, 现任职于德国汉堡工业大学数学系,主要研究方向为时间依赖微分方程快速算法。近年来在SISC等知名学术期刊上发表多篇高水平论文。

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