Waveform relaxation of partial differential equations

Yao Lin Jiang; Zhen Miao

doi:10.1007/s11075-018-0475-5

Waveform relaxation of partial differential equations

Yao Lin Jiang
, Zhen Miao

数学与统计学院

Xi'an Jiaotong University

科研成果: 期刊稿件 › 文章 › 同行评审

5 引用（Scopus）

摘要

This short paper concludes a general waveform relaxation (WR) method at the PDE level for semi-linear reaction-diffusion equations. For the case of multiple coupled PDE(s), new Jacobi WR and Gauss-Seidel WR are provided to accelerate the convergence result of classical WR. The convergence conditions are proved based on energy estimate. Numerical experiments are demonstrated with several WR methods in parallel to verify the effectiveness of the general WR method.

源语言	英语
页（从-至）	1087-1106
页数	20
期刊	Numerical Algorithms
卷	79
期	4
DOI	https://doi.org/10.1007/s11075-018-0475-5
出版状态	已出版 - 1 12月 2018

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10.1007/s11075-018-0475-5

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abstract = "This short paper concludes a general waveform relaxation (WR) method at the PDE level for semi-linear reaction-diffusion equations. For the case of multiple coupled PDE(s), new Jacobi WR and Gauss-Seidel WR are provided to accelerate the convergence result of classical WR. The convergence conditions are proved based on energy estimate. Numerical experiments are demonstrated with several WR methods in parallel to verify the effectiveness of the general WR method.",

keywords = "Coupled equations, Energy method, Parallelism, Semi-linear, Waveform relaxation",

author = "Jiang, \{Yao Lin\} and Zhen Miao",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Miao, Zhen

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N2 - This short paper concludes a general waveform relaxation (WR) method at the PDE level for semi-linear reaction-diffusion equations. For the case of multiple coupled PDE(s), new Jacobi WR and Gauss-Seidel WR are provided to accelerate the convergence result of classical WR. The convergence conditions are proved based on energy estimate. Numerical experiments are demonstrated with several WR methods in parallel to verify the effectiveness of the general WR method.

AB - This short paper concludes a general waveform relaxation (WR) method at the PDE level for semi-linear reaction-diffusion equations. For the case of multiple coupled PDE(s), new Jacobi WR and Gauss-Seidel WR are provided to accelerate the convergence result of classical WR. The convergence conditions are proved based on energy estimate. Numerical experiments are demonstrated with several WR methods in parallel to verify the effectiveness of the general WR method.

KW - Coupled equations

KW - Energy method

KW - Parallelism

KW - Semi-linear

KW - Waveform relaxation

UR - https://www.scopus.com/pages/publications/85040652841

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DO - 10.1007/s11075-018-0475-5

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Waveform relaxation of partial differential equations

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