Fourier Analysis on Schwarz Domain Decomposition Methods for the Biharmonic Equation

SHANG Yue-qiang; HE Yin-nian

doi:10.3879/j.issn.1000-0887.2009.09.012

Volume 30 Issue 9

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SHANG Yue-qiang, HE Yin-nian. Fourier Analysis on Schwarz Domain Decomposition Methods for the Biharmonic Equation[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1100-1106. doi: 10.3879/j.issn.1000-0887.2009.09.012

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Fourier Analysis on Schwarz Domain Decomposition Methods for the Biharmonic Equation

doi: 10.3879/j.issn.1000-0887.2009.09.012

SHANG Yue-qiang^1,2,
HE Yin-nian¹

1.
Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, P. R. China;

Received Date: 2008-12-04
Rev Recd Date: 2009-07-10
Publish Date: 2009-09-15

Abstract

Abstract

Schwarz methods are an important type of domain decomposition methods.Using the Fourier transform tool,the error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation were deduced.It not only concisely proves the convergence of the Schwarz methods from a new point of view,but also provides detailed information about the convergence speeds and their dependence on the overlapping size of subdomains.The obtained results are independent of any unknown constant and discretization method,show that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.
- domain decomposition algorithm,
- Schwarz method,
- Fourier transform,
- biharmonic equation

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References

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