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Waveform relaxation of partial differential equations

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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.

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Funding

This work was supported by the Natural Science Foundation of China (NSFC) under grant (61663043) and Natural Science Basis Research Plan in Shaanxi Province of China under grant 2016JM5077.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China

    Yao-Lin Jiang & Zhen Miao

Authors
  1. Yao-Lin Jiang
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  2. Zhen Miao
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Correspondence to Yao-Lin Jiang.

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Jiang, YL., Miao, Z. Waveform relaxation of partial differential equations. Numer Algor 79, 1087–1106 (2018). https://doi.org/10.1007/s11075-018-0475-5

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  • DOI: https://doi.org/10.1007/s11075-018-0475-5

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