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

School of Mathematics and Statistics

Xi'an Jiaotong University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Pages (from-to)	1087-1106
Number of pages	20
Journal	Numerical Algorithms
Volume	79
Issue number	4
DOIs	https://doi.org/10.1007/s11075-018-0475-5
State	Published - 1 Dec 2018

Keywords

Coupled equations
Energy method
Parallelism
Semi-linear
Waveform relaxation

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10.1007/s11075-018-0475-5

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title = "Waveform relaxation of partial differential equations",

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",

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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

M3 - 文章

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JO - Numerical Algorithms

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ER -

Waveform relaxation of partial differential equations

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Keywords

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